CN112102960B

CN112102960B - Dynamics-based delay cross information propagation analysis method and system

Info

Publication number: CN112102960B
Application number: CN202011305759.2A
Authority: CN
Inventors: 殷复莲; 吴建宏; 邵雪莹; 夏欣雨; 吕嘉惠; 吴肇良; 王颜颜
Original assignee: Communication University of China
Current assignee: Communication University of China
Priority date: 2020-11-20
Filing date: 2020-11-20
Publication date: 2021-03-05
Anticipated expiration: 2040-11-20
Also published as: CN112102960A

Abstract

The invention provides a delayed cross information propagation analysis method and a system based on dynamics, which comprises the following steps: a network user is an individual, and the individual state is a susceptible state, a forwarding state, an overtime immune state and a direct immune state; monitoring a propagation period of the first piece of information to which the individual is exposed; constructing a first cross information transmission dynamic model of cross transmission of two pieces of information of a first piece of information which issues a second piece of information in a stationary period; constructing a second cross information propagation dynamic model of cross propagation of two pieces of information of a second piece of information issued in the first information outbreak period; and the total number of individuals of each crowd corresponds to the forwarding amount of the two pieces of information, and the change of the total number of individuals of the crowd in the process of transmitting the two pieces of information is predicted by monitoring the accumulated forwarding amount according to the first cross information transmission dynamic model or the second cross information transmission dynamic model. The method and the system accurately analyze the influence of the published information in the long-interval and short-interval delayed cross public sentiment on the new information.

Description

Dynamics-based delay cross information propagation analysis method and system

Technical Field

The invention relates to the technical field of public opinion propagation power system construction, in particular to a dynamics-based delay cross information propagation analysis method and system.

Background

The success of reducing the spread of COVID-19 among the population depends largely on social distance, self-protection, case discovery, quarantine, isolation, and testing effectiveness. The effectiveness of these non-pharmaceutical intervention measures depends on public active participation, which is largely influenced by public opinion. One important challenge in studying effective communication is the cross-propagation of relevant and content inconsistent information at different points in time that is placed on social media. This requires us to adopt certain strategies to optimize the opportunity for publishing key information on social media in the case of a rapid development of the epidemic.

In the field of information dissemination dynamics, rumor dissemination models include a susceptible-infected-exposed-recovered model (SEIR), a susceptible-infected (SI) model, a susceptible-infected-Susceptible (SIs) model, a susceptible-infected-recovered model and the like, and these early studies do not fully solve the important phenomena of delay of release and cross-dissemination of related information in information dissemination in real social media networks.

Two types of double rumor propagation models have been proposed by scholars, the double-sensitive infection recovery (DSIR) model, which assumes that rumors are propagated by direct contact with others through infected nodes; the overall spread of all rumors was studied using a C-DSIR (C-DSIR) ensemble model, with the emphasis on determining how many people did not spread all rumors, how many people were spreading or had spread at least one rumor, and not studying the effect of one rumor propagation delay on the spread of two rumors over the entire time period.

Disclosure of Invention

In view of the above problems, the present invention provides a dynamics-based delay-crossing information propagation analysis method, including:

a network user is taken as an individual, for a first piece of information, the state of the individual is divided into a first susceptible state, a first forwarding state, a timeout immune state and a direct immune state, wherein the first susceptible state is a state that the individual does not contact the first piece of information yet, but has a chance to contact the first piece of information in the future, is easily influenced by the first piece of information and is possible to generate forwarding; the first forwarding state is a state that a first piece of information has been forwarded and is in an active state and can affect other individuals; the overtime immune state is a state that the first piece of information loses the active capability after being forwarded, and the direct immune state is a state that the first piece of information is read and then the forwarding is abandoned to lose the active capability;

monitoring a propagation period of a first piece of information, the propagation period comprising an outbreak period and a plateau period;

constructing a first cross information propagation dynamic model, wherein the first cross information propagation dynamic model is a dynamic model for cross propagation of two pieces of information of a second piece of information issued in a stationary phase of the first piece of information, and comprises the following steps: the status of the individual is divided into a second susceptible status, a third susceptible status, a fourth susceptible status, a second forwarding status and a first immune status, the second susceptible state is a state which is not contacted with the first information and the second information is susceptible to the second information, the third susceptible state is a state which is susceptible to the second information for individuals who are in a timeout immune state for the first information, the fourth susceptible state is a state which is susceptible to the second information for individuals who are in a direct immune state for the first information, the second forwarding state is a state which forwards the second information and can affect other individuals in an active state, the first immune state is a state which forwards the second information and loses the active ability, and the individuals who are in the second susceptible state, the third susceptible state and the fourth susceptible state read the second information and then abandon the forwarding of the second information; dividing different crowds according to the individual state; constructing a first cross information propagation dynamic model, wherein a derivative of the total number of individuals of a crowd relative to time is in a linear relation with the total number of individuals of related crowds according to a transformation direction, and the related crowds are other crowds having transformation relations with the crowd except the crowd in the first immune state;

constructing a second cross information propagation dynamic model, wherein the second cross information propagation dynamic model is a dynamic model for cross propagation of two pieces of information of a second piece of information issued in the outbreak period of the first piece of information, and comprises the following steps: dividing the state of the individual into a third susceptible state, a fourth susceptible state, a fifth susceptible state, a sixth susceptible state, a second forwarding state and a second immune state, wherein the fifth susceptible state is a state which is not contacted with the first information and the second information and is susceptible to the first information or the second information, the sixth susceptible state is a state which is in a first forwarding state of the first information and is susceptible to the second information, the second immune state is a state which is in a state that the second information is already forwarded and loses the active capability, and the individual in the fifth susceptible state, the third susceptible state and the fourth susceptible state abandons forwarding and loses the active capability after reading the second information; dividing different crowds according to the individual state; constructing a second cross information propagation dynamic model, wherein in the second cross information propagation dynamic model, the derivative of the total number of individuals of a crowd relative to time is in a linear relation with the total number of individuals of related crowds according to the transformation direction, and the related crowds are other crowds except crowds in the second immune state and having transformation relations with the crowd;

setting that each individual of one piece of information can only be forwarded once, corresponding the total number of individuals of each crowd with the forwarding amount of the two pieces of information, and predicting the change of the total number of individuals of the crowd in the process of transmitting the two pieces of information according to the first cross information transmission dynamic model or the second cross information transmission dynamic model by monitoring the accumulated forwarding amount.

In one embodiment, the step of constructing the first cross information propagation kinetic model further comprises:

setting model parameters of a first cross information propagation dynamic model, comprising: the second average contact rate is the average rate at which an individual in the third susceptible state can contact the second piece of information; the third average contact rate is the average rate at which an individual in the fourth susceptible state can contact the second piece of information; the fourth average contact rate is the average rate at which an individual in the second susceptible state can contact the second piece of information; the second average forwarding probability is the average probability of forwarding the second piece of information by individuals in the second susceptible state, the third susceptible state and the fourth susceptible state; the second average immune rate is the average rate at which the individual transitions from the second forwarding state to the first immune state; the first strong exposure attraction index is the attraction strength of an individual forwarding the first piece of information to the forwarding of the second piece of information; the weak exposure attraction index is the attraction intensity of an individual who contacts the first piece of information but does not forward the second piece of information; the non-exposure attraction index is the attraction strength of an individual not contacting the first piece of information for forwarding the second piece of information;

a first cross information propagation dynamics model is constructed according to the following formula,

wherein the content of the first and second substances,

、

、

、

and

the total number of individuals in the population of the second, third, fourth, second forwarding and first immune states at time t,

、

and

a fourth average contact rate, a third average contact rate, and a second average contact rate,

in order to be the second average forwarding probability,

in order to obtain a second average immunization rate,

、

and

respectively, a first strong exposure attractiveness index, a weak exposure attractiveness index, and a non-exposure attractiveness index.

Preferably, the step of corresponding the total number of individuals of each crowd to the forwarding amount of the two pieces of information comprises:

estimating the accumulated forwarding amount of the second piece of information according to the following formula through a first cross information propagation dynamic model

Wherein the content of the first and second substances,

is an estimate of the cumulative forwarding of the second piece of information.

Further, preferably, the method further comprises the following steps:

setting an initial value of a model parameter of a first cross information propagation dynamic model;

the method comprises the steps of collecting the accumulated forwarding amount of a second piece of information as an actual value, obtaining the accumulated forwarding amount of the second piece of information as an estimated value through a first cross information propagation dynamic model, obtaining the optimal value of the model parameter of the first cross information propagation dynamic model by adopting a parameter estimation method, carrying out model parameter assignment by adopting the optimal value, and predicting the total number of individuals of different crowds of the two pieces of information changing along with time by adopting the first cross information propagation dynamic model after the model parameter assignment.

In one embodiment, the step of constructing the second cross information propagation kinetic model further comprises:

setting model parameters of a second cross information propagation dynamic model, comprising: the first average contact rate is an average rate at which an individual in a first susceptible state to the first piece of information can contact the first piece of information; the first average forwarding probability is the average probability of forwarding the first piece of information for the individual with the first piece of information in the first susceptible state; the first average immune rate is the average rate of individual transfer of the first information in the first forwarding state to the overtime immune state of the first information; a fifth average exposure rate is an average rate at which individuals in the sixth and third susceptible states can be exposed to the second piece of information; the third average contact rate is the average rate at which an individual in the fourth susceptible state can contact the second piece of information; a sixth average exposure rate is the average rate at which an individual in the fifth susceptible state can be exposed to the second piece of information; the third average forwarding probability is the average probability of forwarding the second piece of information by individuals in a third susceptible state, a fourth susceptible state, a fifth susceptible state and a sixth susceptible state; the third average immune rate is the average rate at which the individual transitions from the second forwarding state to the second immune state; the second strong exposure attraction index is the attraction strength of an individual who is in a fifth susceptible state on the first information or an individual who forwards the first information on the forwarding of the second information; the weak exposure attraction index is the attraction intensity of an individual who contacts the first piece of information but does not forward the second piece of information; the non-exposure attraction index is the attraction strength of an individual not contacting the first piece of information for forwarding the second piece of information;

a second cross information propagation dynamics model is constructed according to the following formula,

wherein the content of the first and second substances,

、

、

、

、

and

the total number of individuals in the population of a fifth susceptible state, a third susceptible state, a fourth susceptible state, a sixth susceptible state, a second forwarding state, and a second immune state, respectively, at time t,

、

and

a sixth average contact rate, a third average contact rate and a fifth average contact rate,

in order to be the third average forwarding probability,

is the third average immune rate and is,

、

and

respectively a second strong exposure attraction index, a weak exposure attraction index and a non-exposure attraction index,

、

and

respectively, a first average contact rate, a first average forwarding probability, and a first average immunization rate.

Preferably, the method further comprises the following steps:

estimating the accumulated forwarding amount of the first piece of information and the accumulated forwarding amount of the second piece of information according to the following formula through a second cross information propagation dynamic model

Wherein the content of the first and second substances,

for an estimate of the cumulative forwarding of the first piece of information,

is an estimate of the cumulative forwarding of the second piece of information.

Further, preferably, the method further comprises the following steps:

setting an initial value of a model parameter of a second cross information propagation dynamic model;

collecting the accumulated forwarding amount of the first piece of information and the second piece of information as actual values, obtaining the accumulated forwarding amount of the first piece of information and the second piece of information through a second cross information propagation dynamic model as estimated values, obtaining the optimal value of the model parameter of the second cross information propagation dynamic model by adopting a parameter estimation method, carrying out model parameter assignment by adopting the optimal value, and predicting the total number of individuals of different crowds of the two pieces of information changing along with time by adopting the second cross information propagation dynamic model after the model parameter assignment.

In one embodiment, the method further comprises the step of performing public opinion monitoring on the first information and the second information through a first cross information propagation dynamic model and a second cross information propagation dynamic model respectively, and comprises the following steps:

obtaining a first information dissemination reproducible number according to a first cross information dissemination dynamics model by the following formula

Wherein the content of the first and second substances,

for the first information to propagate a reproducible number,

、

and

respectively a first strong exposure attraction index, a weak exposure attraction index and a non-exposure attraction index,

in order to be the second average forwarding probability,

in order to obtain a second average immunization rate,

、

and

initial values of the total number of individuals of the first susceptible state, the second susceptible state and the third susceptible state respectively,

the larger the public sentiment outbreak, the faster the public sentiment outbreak speed;

obtaining a second information dissemination reproducible number according to the second cross information dissemination dynamics model by

Wherein the content of the first and second substances,

for the second information to propagate a reproducible number,

in order to be the third average forwarding probability,

is the third average immune rate and is,

、

and

and

respectively the initial values of the total number of individuals in the fifth susceptible state and the sixth susceptible state,

the larger the outbreak, the faster the outbreak.

Preferably, the method further comprises the steps of constructing a delay release information propagation index and analyzing the influence of the model parameters on the propagation of the second piece of information, wherein the delay release information propagation index comprises a first information propagation reproducible number, a second information propagation reproducible number, a propagation peak value, a final scale, a propagation climax time, a propagation outbreak time, a propagation duration, an average outbreak speed and an average decay speed.

According to another aspect of the present invention, there is provided a dynamics-based delay-crossing information propagation analysis system, comprising:

the system comprises a state division module, a network user and a first forwarding module, wherein for a first piece of information, the state of the individual is divided into a first susceptible state, a first forwarding state, an overtime immune state and a direct immune state, and the first susceptible state is a state that the individual does not contact the first piece of information yet, but has a chance to contact the first piece of information in the future, is easily influenced by the first piece of information and is possibly forwarded; the first forwarding state is a state that a first piece of information has been forwarded and is in an active state and can affect other individuals; the overtime immune state is a state that the first piece of information loses the active capability after being forwarded, and the direct immune state is a state that the first piece of information is read and then the forwarding is abandoned to lose the active capability;

the first monitoring module monitors the propagation period of the first piece of information, wherein the propagation period comprises an outbreak period and a stable period;

the first model building module is used for building a first cross information propagation dynamic model, wherein the first cross information propagation dynamic model is a dynamic model for cross propagation of two pieces of information of a second piece of information issued in a stationary period of the first piece of information, and comprises: the status of the individual is divided into a second susceptible status, a third susceptible status, a fourth susceptible status, a second forwarding status and a first immune status, the second susceptible state is a state which is not contacted with the first information and the second information is susceptible to the second information, the third susceptible state is a state which is susceptible to the second information for individuals who are in a timeout immune state for the first information, the fourth susceptible state is a state which is susceptible to the second information for individuals who are in a direct immune state for the first information, the second forwarding state is a state which forwards the second information and can affect other individuals in an active state, the first immune state is a state which forwards the second information and loses the active ability, and the individuals who are in the second susceptible state, the third susceptible state and the fourth susceptible state read the second information and then abandon the forwarding of the second information; dividing different crowds according to the individual state; constructing a first cross information propagation dynamic model, wherein a derivative of the total number of individuals of a crowd relative to time is in a linear relation with the total number of individuals of related crowds according to a transformation direction, and the related crowds are other crowds having transformation relations with the crowd except the crowd in the first immune state;

the second model building module is used for building a second cross information propagation dynamic model, the second cross information propagation dynamic model is a dynamic model for cross propagation of two pieces of information of a second piece of information issued in the outbreak period of the first piece of information, and the second model building module comprises: dividing the state of the individual into a third susceptible state, a fourth susceptible state, a fifth susceptible state, a sixth susceptible state, a second forwarding state and a second immune state, wherein the fifth susceptible state is a state which is not contacted with the first information and the second information and is susceptible to the first information or the second information, the sixth susceptible state is a state which is in a first forwarding state of the first information and is susceptible to the second information, the second immune state is a state which is in a state that the second information is already forwarded and loses the active capability, and the individual in the fifth susceptible state, the third susceptible state and the fourth susceptible state abandons forwarding and loses the active capability after reading the second information; dividing different crowds according to the individual state; constructing a second cross information propagation dynamic model, wherein in the second cross information propagation dynamic model, the derivative of the total number of individuals of a crowd relative to time is in a linear relation with the total number of individuals of related crowds according to the transformation direction, and the related crowds are other crowds except crowds in the second immune state and having transformation relations with the crowd;

and the second monitoring module is used for setting that each individual of one piece of information can only be forwarded once, corresponding the total number of the individuals of each crowd with the forwarding amount of the two pieces of information, and predicting the change of the total number of the individuals of the crowd in the process of transmitting the two pieces of information according to the first cross information transmission dynamic model or the second cross information transmission dynamic model by monitoring the accumulated forwarding amount.

The invention discloses a delay cross information propagation analysis method and a delay cross information propagation analysis system based on dynamics, which consider the interaction of delay release of two pieces of information, provide a propagation dynamics model of delay cross propagation susceptibility-forwarding-immunity (DT-SFI), and divide the model into a long interval delay cross propagation dynamics model (LTI DT-SFI) and a short interval delay cross propagation dynamics model (STI DT-SFI) by distinguishing different time intervals. In the long-interval delay cross-propagation kinetic model, different attractions of new information to immune populations exposed to the first information after the first information tends to be stable are considered; in a short-interval delay cross-propagation kinetic model, different attractions that a forwarding group and an immune group of a first piece of information receive new information when the first piece of information is in an outbreak period are considered, attraction indexes with different contact degrees are provided, and the attraction degrees of the new information to different groups are described. A delay cross propagation index based on forwarding is established, and the interaction between DT-SFI model information is explored on a real data set by using numerical simulation and sensitivity analysis so as to realize the cross propagation of the information.

Drawings

FIG. 1 is a flow chart of a dynamics-based delayed cross-information propagation analysis method of the present invention;

FIG. 2 is a schematic diagram of the delayed information propagation LTI DT-SFI dynamics model of the present invention;

FIG. 3 is a schematic diagram of the delayed information propagation STI DT-SFI dynamics model of the present invention;

FIG. 4 is a schematic illustration of a delayed distribution information propagation index according to the present invention;

FIG. 5 is a schematic diagram of delayed-release cross-propagation of information;

FIG. 6 is a schematic diagram of delayed information propagation LTI DT-SFI dynamical model parameter estimation and numerical fitting;

FIG. 7 is a schematic diagram of delayed information propagation STI DT-SFI dynamical model parameter estimation and numerical fitting;

FIG. 8 shows the LTI DT-SFI under multi-parameter variation

Schematic of PRCCs of (a);

FIG. 9 shows the LTI DT-SFI with multi-parameter variation

And

schematic of PRCCs of (a);

FIG. 10 shows the LTI DT-SFI under multi-parameter variation

、

And

schematic of PRCCs of (a);

FIG. 11 shows the LTI DT-SFI under multi-parameter variation

And

schematic of PRCCs of (a);

FIGS. 12a, 12b and 12c are graphs illustrating the effect of average contact rate on forwarding and forwarding accumulation in LTI DT-SFI;

FIGS. 13a, 13b and 13c are schematic diagrams of the effect of attraction index on forwarding and forwarding cumulant in LTI DT-SFI;

FIG. 14 is a schematic diagram of an information dissemination process where new information is published at different points in time as published information enters a stabilization period;

FIG. 15 shows the multi-parameter variation in STI DT-SFI

Schematic of PRCCs of (a);

FIG. 16 shows the multi-parameter variation in STI DT-SFI

And

schematic of PRCCs of (a);

FIG. 17 shows the multi-parameter variation in STI DT-SFI

、

And

schematic of PRCCs of (a);

FIG. 18 shows the multi-parameter variation in STI DT-SFI

And

schematic of PRCCs of (a);

FIGS. 19a, 19b and 19c are graphs illustrating the effect of average contact rate on forwarding and forwarding accumulation in STI DT-SFI;

FIGS. 20a, 20b and 20c are graphs illustrating the effect of attraction index on forwarding and forward accumulation in STI DT-SFI;

fig. 21 is an information dissemination process where new information is published at different points in time when published information is in a burst period.

Detailed Description

In the following description, for purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of one or more embodiments. It may be evident, however, that such embodiment(s) may be practiced without these specific details. In other instances, well-known structures and devices are shown in block diagram form in order to facilitate describing one or more embodiments.

Various embodiments according to the present invention will be described in detail below with reference to the accompanying drawings.

Fig. 1 is a flow chart of a dynamics-based delay-crossing information propagation analysis method according to the present invention, as shown in fig. 1, the delay-crossing information propagation analysis method includes:

step S1, a network user is used as an individual, for a first piece of information, the state of the individual is divided into a first susceptible state, a first forwarding state, a timeout immune state and a direct immune state, the first susceptible state is a state that the individual has not contacted the first piece of information yet, but has an opportunity to contact the first piece of information in the future, is easily influenced by the first piece of information and is possible to generate forwarding; the first forwarding state is a state that a first piece of information has been forwarded and is in an active state and can affect other individuals; the overtime immune state is a state that the first piece of information loses the active capability after being forwarded, and the direct immune state is a state that the first piece of information is read and then the forwarding is abandoned to lose the active capability;

step S2, monitoring the propagation period of the first piece of information, wherein the propagation period comprises an outbreak period and a stable period;

step S3, constructing a first cross information propagation dynamic model, where the first cross information propagation dynamic model is a dynamic model of cross propagation of two pieces of information issuing a second piece of information in a stationary phase of the first piece of information, and includes: the status of the individual is divided into a second susceptible status, a third susceptible status, a fourth susceptible status, a second forwarding status and a first immune status, the second susceptible state is a state which is not contacted with the first information and the second information is susceptible to the second information, the third susceptible state is a state which is susceptible to the second information for individuals who are in a timeout immune state for the first information, the fourth susceptible state is a state which is susceptible to the second information for individuals who are in a direct immune state for the first information, the second forwarding state is a state which forwards the second information and can affect other individuals in an active state, the first immune state is a state which forwards the second information and loses the active ability, and the individuals who are in the second susceptible state, the third susceptible state and the fourth susceptible state read the second information and then abandon the forwarding of the second information; dividing different crowds according to the individual state; constructing a first cross information propagation dynamic model, wherein a derivative of the total number of individuals of a crowd relative to time is in a linear relation with the total number of individuals of related crowds according to a transformation direction, and the related crowds are other crowds having transformation relations with the crowd except the crowd in the first immune state;

step S4, constructing a second cross information propagation dynamic model, where the second cross information propagation dynamic model is a dynamic model of cross propagation of two pieces of information issuing a second piece of information in an outbreak period of the first piece of information, and includes: dividing the state of the individual into a third susceptible state, a fourth susceptible state, a fifth susceptible state, a sixth susceptible state, a second forwarding state and a second immune state, wherein the fifth susceptible state is a state which is not contacted with the first information and the second information and is susceptible to the first information or the second information, the sixth susceptible state is a state which is in a first forwarding state of the first information and is susceptible to the second information, the second immune state is a state which is in a state that the second information is already forwarded and loses the active capability, and the individual in the fifth susceptible state, the third susceptible state and the fourth susceptible state abandons forwarding and loses the active capability after reading the second information; dividing different crowds according to the individual state; constructing a second cross information propagation dynamic model, wherein in the second cross information propagation dynamic model, the derivative of the total number of individuals of a crowd relative to time is in a linear relation with the total number of individuals of related crowds according to the transformation direction, and the related crowds are other crowds except crowds in the second immune state and having transformation relations with the crowd;

and step S5, setting that each individual of one piece of information can only be forwarded once, corresponding the total number of individuals of each crowd with the forwarding amount of the two pieces of information, and predicting the change of the total number of individuals of the crowd in the process of transmitting the two pieces of information according to the first cross information transmission dynamic model or the second cross information transmission dynamic model by monitoring the accumulated forwarding amount.

The focus of the invention is on the effect that one message still has on another message that is issued one after the other after a period of time. Similarly, in the case of partial overlap between the vulnerable groups of two pieces of information, the group exposed to the first piece of information released first will be attracted (more interested or contradicted) by the topic, and when exposed to the second piece of information, a part of the group will generate the forwarding behavior for the second piece of information, and will form a differentiated representation with the group not exposed to the first piece of information. The delay-transmission-reliable-forwarding-equalized model (DT-SFI) constructed by the invention considers two situations: the first method is that a first cross information propagation dynamic model long-time-interval-transmission-reliable-forwarding-immunee (LTI DT-SFI) model is constructed for the situation that the release time of the second piece of information is after the first piece of information is propagated to a stationary phase, as shown in FIG. 2; secondly, when the release time of the second piece of information is in the first information propagation outbreak period, a second cross information propagation dynamic model short-time-interval-transmission-reliable-forwarding-immunee (STI DT-SFI) model is constructed, as shown in FIG. 3.

As shown in fig. 2, the LTI DT-SFI includes a submodel I and a submodel II, the submodel I is a model for propagating a first piece of information before issuing a second piece of information, the submodel II is a model for cross-propagating the second piece of information issued with a delay and the first piece of information, assuming that the information is propagated in a closed and stable environment, focusing on the influence of the first piece of information on the second piece of information, and considering only the information diffusion generated by the forwarding behavior of the individual, the submodel I models the propagation process of the first piece of information issued, and the state that each individual can have is unique and may be in one of the following states:

a first vulnerable state (abbreviated as S1), in which an individual has not yet contacted the first piece of information, but has an opportunity to contact and be Susceptible to the first piece of information in the future, and possibly has a forwarding behavior, and the S1 state only contains a vulnerable group of the first piece of information, because the propagation of the first piece of information and the propagation of the second piece of information do not intersect.

A first Forwarding state (abbreviated F1) in which an individual has forwarded a first piece of information and is still within the exposure period and has the ability to make the individual in the first susceptible state aware of the content of the information and to generate Forwarding behavior, also referred to as the individual in this state being active.

The time-out Immune state (Immune, abbreviated as I11) in which individuals have forwarded the first piece of information and over time exceeded the exposure period and thus no longer have the ability to affect others.

The direct Immune state (Immune, abbreviated as I12) is formed by individuals who are in the state of losing their active ability to give up forwarding due to subjective disinterest in the first information after the individuals who are in the first susceptible state have been exposed to the first information.

Total number of individuals reachable by the first piece of information in an independent propagation phase

The following groups are classified:

at the moment of time

The total number of individuals in the first susceptible state S1

At the moment of time

Total number of individuals in the first forwarding state F1;

at the moment of time

Total number of individuals in the timeout immune state I11;

at the moment of time

Total number of individuals in direct immunization state I12. The total number of individuals of the population in the first susceptible state S1, the first forwarding state F1, the overtime immune state I11 and the direct immune state I12 remains unchanged, i.e. the population is in the first susceptible state S1, the first forwarding state F1, the overtime immune state I11 and the direct immune state I12

。

It is assumed that in the process of forwarding information, for the same information, the same individual can only produce one forwarding action even if the individual contacts the information multiple times. The model parameters involved include:

first average contact rate

And represents the average rate at which an individual in the first susceptible state can be exposed to the first piece of information. An individual in the first forwarding state F1 is exposed to the average in unit time

Individual oneAnd the probability that an individual is a susceptible person is

That is, an individual in the first forwarding state F1 will be able to forward the message in a unit of time

An individual in a first susceptible state is exposed to information, preferably,

。

first average forwarding probability

And represents the average probability that an individual in the first susceptible state will be forwarded after exposure to the first piece of information. Due to the difference of the interest degree of the individual to the information, when the individual is exposed to the information, the individual has the right to decide whether to forward the information.

The average forwarding probability is shown, and, accordingly,

which represents the average probability of not forwarding, preferably,

。

first mean rate of immunization

And represents the average rate at which the individual transitions from the first forwarding state to the overtime immune state. Each piece of information has a certain exposure period after being forwarded,

for averaging the exposure period, i.e. during this averaging time, a forwarding behavior is generatedHas the ability to make the individual in the first vulnerable state aware of the content of the information and to generate forwarding behavior. Preferably, the first and second electrodes are formed of a metal,

。

constructing a submodel I according to the following formula

(1)

(2)

(3)

(4)

Cumulative forwarding of first message

Comprises the following steps:

(5)

in the sub-model I described above,

、

、

、

、

the boundary conditions of (1) include:

initial value: since the burst of the single message starts from one message, the forwarding amount and the accumulated forwarding amount of the single message propagation starting point are both 1, and the number of individuals in the immune state is 0, that is, the number of individuals in the immune state is 0

，

0. Total number of individuals in information dissemination environment (

) Remaining unchanged, the initial number of individuals in the first susceptible state

；

The second information issuing initial value of the submodel II is also the steady state value of the submodel I, and the number of the first forwarding state individuals is increased along with the time

Will eventually go to 0 due to the end of the first information propagation, i.e. it will end up

. Due to the fact that

Number of individuals in first susceptible state

Is a decreasing function and the number of first susceptible state entities

Must be a non-negative number which,

is a finite positive integer. Due to the fact that

Accumulating the forwarding amount

Is an increasing function of the number of bits in the bit stream,

. Accordingly, the final number of individuals in the immune state

And

satisfy the requirement of

The specific value can be obtained by numerical simulation.

In the submodel I, the process of propagating the first piece of information includes:

the first forwarding process, when an individual in the first susceptible state S1 contacts the individual in the first forwarding state F1 and knows the content of the information to be transmitted, will subjectively forward with an average forwarding probability

And forwarding is carried out. That is, the closed stable environment will exist in unit time

Individuals transition from the first susceptible state S1 to a first forwarding state F1.

The direct immunization process, accordingly, in the first transfer process, the closed stable environment will be accompanied by

Individual individuals were transferred from the first susceptible state S1 to the direct immune state I12.

Over time immune process, in unit time, will have

The individual no longer has the ability to make the individual in the first vulnerable state aware of the information content and to generate forwarding behavior due to the exposure period being exceeded, i.e. the transition from the forwarding state F1 to the timeout immune state I11.

The submodel II models a second piece of information that is released later, and the time of release of the second piece of information after the first piece of information has propagated into a plateau, at which stage each individual is uniquely in one of the following states:

a second vulnerable state S2, in which the individual has not yet contacted the second piece of information and the first piece of information, but has a chance to contact the second piece of information in the future and is vulnerable to the second piece of information and possibly having a forwarding action.

A third vulnerable state, I11, is a time-out immune state of the first message, in which individuals who have not yet contacted the second message while they are in the time-out immune state of the first message, but have a chance to contact the second message in the future and are vulnerable to the message and possibly act as a relay.

The fourth vulnerable state is also the first information direct immunization state I12, and the individual in this state has not yet contacted the second information in the direct immunization state of the first information, but has an opportunity to contact the second information in the future and is vulnerable to the information, so that the forwarding action is possible.

A second forwarding state F2, in which the individual has forwarded the second piece of information and is still within the exposure period, and has the ability to make the individual in the vulnerable state (S2, I11, I12) aware of the content of the second piece of information and to generate a forwarding behavior, also called the individual in this state is active.

A first immune state I2, where the individual is composed of several parts: some are individuals who have forwarded a second piece of information and who, over time, have exceeded the exposure period, no longer have the ability to affect others; the other part is composed of individuals who, after being exposed to the second piece of information during the vulnerable state (S2, I11, I12), transform directly into an immune state due to subjective disinterest in the second piece of information.

Total number of individuals reachable by the second piece of information during the propagation phase

The following groups are classified:

at the moment of time

The total number of individuals in the second susceptible state S2.

At the moment of time

The total number of individuals in the third susceptible state and the total number of individuals in the time-out immune state for the first message

Since the individuals in the overtime immune state of the first message are considered to be susceptible to the second message, they are labeled with the same reference numerals.

At the moment of time

The total number of individuals in the fourth susceptible state and the total number of individuals in the state directly immunized against the first message

Direct immune status of the first messageAre considered to be susceptible to a second message, and so are referred to by the same reference numerals.

At the moment of time

The total number of individuals in the second forwarding state F2.

At the moment of time

Total number of individuals in the first immune state I2.

The total population in the vulnerable states S2, I11 and I12, the second forwarding state F2 and the first immune state I2 for the second piece of information remains unchanged, i.e. the total population is in the vulnerable states S2, I11 and I12

。

Parameters related to the submodel II include:

fourth average contact rate

An average rate at which individuals in the time-out immune state I11 for the first message can be exposed to the second message,

。

third average contact Rate

An average rate at which an individual in susceptible state I12 immunized directly against the first piece of information can be exposed to the second piece of information,

。

second average contact velocity

An average rate at which the individual in the second susceptible state S2 can be exposed to the second piece of information,

。

second average forwarding probability

And represents the average probability of forwarding the information after the individual in the susceptible state (S2, I11, I12) contacts the second piece of information. Due to the difference of the interest degree of the individual to the information, when the individual contacts the information, the individual has the right to decide whether to forward the information,

the average forwarding probability is shown. The average forwarding probability has a value range of

；

Second mean immunization Rate

The average rate at which individuals transition from the second forwarding state F2 to the first immune state I2 is indicated. Each piece of information has a certain exposure period after being forwarded,

to average the exposure period, i.e. the average time during which the individual who generated the forwarding behavior has the ability to make the individual in a vulnerable state aware of the content of the information and generate the forwarding behavior, it is preferred that,

；

first strong exposure attraction index

Which is a measure of the strength of the attraction of an individual forwarding a first piece of information to forwarding a second piece of information due to an interest in the content, preferably,

；

weak exposure attraction index

An individual who has contacted the first piece of information but has not forwarded it will, due to knowledge of the content, be a measure of the strength of the attraction to forward the second piece of information, preferably,

；

index of non-exposure attraction

The measure of the strength of the attraction of an individual not touching the first piece of information to forward the second piece of information is, preferably,

。

sub-model II was constructed according to the following formula:

(6)

(7)

(8)

(9)

(10)

accumulated forwarding amount of post-release second message

The information can be acquired from a network propagation platform,

(11)

some initial values in the submodel II are determined by steady-state values of the submodel I, and the remaining initial values and steady-state values can be obtained from equations (6) to (11), specifically:

initial value: since the single message burst starts from one message, the forwarding amount and the accumulated forwarding amount of the single message propagation starting point are both 1, and the number of individuals in the first immune state is 0, that is, the number of individuals in the first immune state is 0

，

0. Initial value of a group affected by a first piece of information in a state susceptible to a second piece of information

And

steady state values propagated for the first piece of information

And

then the initial number of individuals in a susceptible state

；

Steady state value: forwarding state individual number over time

Will eventually go to 0 due to the end of the information propagation, i.e. it will go to

. Equations (4.7) - (4.9) because

，

，

It can be seen that the number of susceptible state individuals

、

And

are all decreasing functions, and the number of susceptible state individuals must be a non-negative number, so there will be

，

，

Are all finite positive integers. In equation (11), because

The accumulated forwarding amount can be obtained

Is an increasing function, and then obtains

. Accordingly, the final number of individuals in the immune state tends to

。

In the submodel II, the step of affecting the propagation process of the second piece of information by the first piece of information includes:

the strong exposure forwarding process is that when an individual I11 in the overtime immune state for the first information contacts an individual in the second forwarding state F2 and knows the content of the second information to be transmitted, the individual subjectively and averagely forwards the information with the average forwarding probability under the action of the strong exposure attractiveness index

The individual transitions from the third vulnerable state to a second forwarding state F2.

In the weak exposure forwarding process, when an individual I11 in a direct immune state for a first piece of information contacts an individual in a second forwarding state F2 and knows the content of a second piece of information to be transmitted, the average forwarding probability is subjectively obtained under the action of the weak exposure attractiveness index

And forwarding is carried out. That isIs that the closed stable environment will have

The individual transitions from the fourth vulnerable state to a second forwarding state F2.

The non-exposure forwarding process is that when an individual not contacting the first message and in the second message second susceptible state S2 contacts the individual in the second forwarding state F2 and knows the content of the second message to be transmitted, the individual subjectively and averagely forwards the second message with the average forwarding probability under the action of the non-exposure attractiveness index

It is decided whether to forward. That is, the closed stable environment will exist in unit time

The individuals are transitioned from the second vulnerable state S2 to a second forwarding state F2.

The direct immunization process is accompanied by the closed and stable environment in the three forwarding processes

，

And

individual were transferred from the susceptible state (I11, I12 and S2) to the first immune state I2.

Over time immune process, in unit time, will have

The individual no longer has the ability to make the individual in the vulnerable state aware of the information content and to generate forwarding behavior due to the exposure period being exceeded, i.e. the transition from the second forwarding state F2 to the first immune state I2.

As shown in fig. 3, the STI DT-SFI includes a submodel I 'and a submodel III, the submodel I' is a model of the propagation of the first piece of information, the submodel III models the second piece of information that is released later, and the release time of the second piece of information is during the burst period of the propagation of the first piece of information, during which stage each individual is uniquely in one of the following states:

a fifth vulnerable state S'1, in which the individual has not yet contacted the first piece of information and the second piece of information, but has an opportunity to contact the first piece of information or the second piece of information in the future and is vulnerable to the first piece of information or the second piece of information, and may have a forwarding behavior, which includes the whole of the first piece of information and the second piece of information that may be forwarded.

The sixth susceptible state F'1 is in the first forwarding state of the first piece of information, and the individual in this state is in the exposure period after the first piece of information is forwarded, and has not yet contacted the second piece of information, but has an opportunity to contact the second piece of information in the future, is susceptible to the information, and may have a forwarding behavior.

The second forwarding state is F2, and individuals in the vulnerable state (S '1, I11, I12, F' 1) know the content of this information and produce forwarding behavior, also called individuals in this state are active.

A second immune state I3, in which the individual is composed of several parts, one of which is an individual who has forwarded a second message and who, over time, has exceeded the exposure period and no longer has the ability to affect others; the other part is the composition of individuals who are in a susceptible state (S '1, I11, I12, F' 1) and who, after exposure to a second message, transform directly into an immune state due to subjective disinterest in the message.

Total number of individuals reachable by the stage of propagating two pieces of information simultaneously

The method comprises the following steps:

a total number of individuals in a fifth susceptible state at time t; at time t, the total number of individuals in the immunity state I11 overtime on the first message

(ii) a At time t, the total number of individuals in the direct immunization state I12 for the first message

；

The total number of individuals in the sixth susceptible state F'1 at time t;

the total number of individuals in the second forwarding state F2 at time t;

at time t, the total number of individuals in the second immune state I3.

The total number of people in the vulnerable state (S '1, I11, I12, F' 1), the second forwarding state F2 and the second immune state I3 remains unchanged, i.e. the

。

The model parameters involved include:

sixth average contact rate

Indicating the average rate at which individuals in the forward state F1 and the timeout immune state I11 can access the second piece of information, preferably,

；

third average contact Rate

Indicating the average rate at which individuals in susceptible state I12 who are directly immunized against the first piece of information can be exposed to the second piece of information, preferably,

。

fifth average contact rate

Indicating the average rate at which individuals in the fifth susceptible state S'1 can be exposed to the second piece of information, preferably,

。

third average forwarding probability

Indicating the average probability of forwarding the information after exposure to the second piece of information by an individual in a vulnerable state (S '1, I11, I12, F' 1), preferably,

；

third mean immune Rate

The average rate at which individuals transition from the second forwarding state F2 to the second immune state I3 is indicated. Each piece of information has a certain exposure period after being forwarded,

；

second strong exposure attraction index

Which is a measure of the strength of the attraction of an individual who is in the forwarding exposure period or has forwarded a first piece of information, to forward a second piece of information due to an interest in the content, preferably,

。

weak exposure attraction index

An individual who has contacted the first piece of information but has not forwarded it is a measure of the strength of the attraction of the two pieces of information to forward it due to knowledge of the content, preferably,

。

index of non-exposure attraction

Which is a measure of the strength of the attraction of an individual not touching the first piece of information to forward the second piece of information, preferably,

。

sub-model III can be represented as:

(12)

(13)

(14)

(15)

(16)

(17)

accumulated forwarding amount of first information and second information issued later

And

respectively as follows:

(18)

(19)

part of initial values in the delay information propagation STI DT-SFI submodel III are selected from submodel I

The remaining initial values and steady-state values may be analytically derived from the associated differential equations (12) - (19), specifically:

initial value: i.e. the initial value of information dissemination. Since the burst of the single message starts from one message, the forwarding amount and the accumulated forwarding amount of the single message propagation starting point are both 1, and the number of individuals in the immune state is 0, that is, the number of individuals in the immune state is 0

，

And

steady state values propagated for the first piece of information

And

then the initial number of individuals in a susceptible state

；

Steady state value: forwarding state individual number over time

And

，

. Equations (14) - (19) because

It can be seen that the number of susceptible state individuals

For a decreasing function, the number of individual states that are susceptible must be a non-negative number, so there will be

Is a finite positive integer. Over time, information propagation eventually becomes stable, i.e., stable

Then, then

. In equations (18) and (19), since

And

the accumulated forwarding amount can be obtained

And

are all increasing functions, and then obtain

And

. Accordingly, the final number of individuals in the immune state tends to

。

The above state transitions include several important processes:

a strong exposure forwarding process, when one is in a first information forwarding state and exceeds the exposure period after forwarding the first information and is in a second information susceptible state F

1 and I11 will subjectively forward with an average probability under the strong exposure attractiveness index after contacting the individuals in the second forwarding state F2 and knowing the content of the second piece of information to be transmitted

And

individual susceptible state of freedom F

1 and I11 transition to the second forwarding state F2.

The weak exposure forwarding process is that when an individual who contacts the first piece of information but is not forwarded and is in the second information susceptible state I12 contacts an individual who is in the second forwarding state F2 and knows the content of the second piece of information to be transmitted, the weak exposure forwarding process subjectively forwards the second piece of information with an average forwarding probability under the action of the weak exposure attractiveness index

The individual is transferred from the susceptible state I12 to a second forwarding state F2.

Non-exposure forwarding process, a vulnerable state S when a piece of information is not contacted with the first and second pieces of information

After the individual 1 contacts the individual in the second forwarding state F2 and knows the content of the second piece of information to be transmitted, the individual subjectively forwards the information with the average forwarding probability under the action of the unexposed attraction index

Individual susceptible state S

1 transitions to the second forwarding state F2.

The direct immunization process, correspondingly, in the three forwarding processes, will be accompanied by the closed and stable environment

，

，

And

individual susceptible state (F)

1, I11, I12 and S

1) Transfer to the second immune state I3.

Over time immune process, in unit time, will have

The individual no longer has the ability to make the individual in the vulnerable state aware of the second piece of information content and to generate a forwarding behavior due to the exposure period being exceeded, i.e. the transition from the second forwarding state F2 to the second immune state I3.

In the delay cross information propagation submodel I provided by the invention, a parameter to be estimated and an initial value vector which are firstly issued with a first piece of information are set as

To obtain the LS error function

(26)

Wherein

Indicating that the first piece of information is released first in the parameter

Under the condition of

The numerical result of (1) corresponds to formula (5);

representing the real accumulated forwarding amount of the first piece of information issued first;

，

is the sampling time.

In the delay information propagation LTI DT-SFI submodel II, the parameter to be estimated and the initial value vector of the second piece of information which is issued later are set as

To obtain the LS error function

(27)

Wherein

Second piece of information released after presentation in parameter

Under the condition of

The numerical result of (a) corresponds to formula (11);

the real accumulated forwarding amount of the second piece of information is issued after the representation;

，

is the sampling time.

In the delayed information propagation STI DT-SFI, the sub-model I' and the sub-model I have the same parameter estimation, and in the sub-model III, the parameters to be estimated and the initial value vectors of two pieces of successively issued information are set as

To obtain the LS error function

(28)

Wherein the content of the first and second substances,

and

respectively representing two pieces of cross information in parameters

Under the condition of

And

the numerical result of (a), corresponding to equations (18) and (19);

and

respectively representing the real accumulated forwarding amounts of two delayed cross information propagations;

，

is the sampling time.

At the beginning of information distribution, if the forwarding amount of the second information which is distributed in a delayed way is decreased, the public opinion is not exploded, namely in the formula (9),

，

，

when it is satisfied

The theory shows a tendency of attenuation, i.e.

(20)

Due to forwarding of the population

Is a non-negative number, equation (20) can be converted to

(21)

Delay information propagation LTI DT-SFI kinetic model information propagation reproducible number of

(22)

Wherein the content of the first and second substances,

the reproducible number of the first information dissemination shows that at the beginning of public opinion outbreak, the number of other forwarding individuals can be influenced by the active time of one forwarding individual,

、

and

respectively a first strong exposure attraction index, a weak exposure attraction index and a non-exposure attraction indexThe index of the attractive force is,

in order to be the second average forwarding probability,

in order to obtain a second average immunization rate,

、

and

the larger the size, the faster the public sentiment erupts, when

In time, the total number of the delayed outburst information forwarding groups at the beginning of information release shows a descending trend, and public opinion cannot outburst; when in

In time, at the beginning of delayed outbreak information release, the total number of forwarding groups shows an ascending trend, public opinion is bound to outbreak, and

the larger the burst, the faster the burst rate.

At the beginning of information distribution, if the forwarding amount of the second information which is distributed in a delayed way per unit time is decreased, the public opinion is not exploded, namely in the formula (16),

，

，

，

when it is satisfied

The theory shows a tendency of attenuation, i.e.

(23)

Due to forwarding of the population

Is a non-negative number, and formula (23) can be converted to

(24)

Delay information propagation STI DT-SFI kinetic model information propagation reproducible number is

(25)

For the second information to propagate a reproducible number,

in order to be the third average forwarding probability,

is the third average immune rate and is,

、

and

and

the larger the size, the faster the public sentiment erupts, when

the larger the burst, the faster the burst rate.

In an embodiment of the invention, the invention takes delay information issued by the same opinion leader (media with influence on microblog) in a period of time as an example to perform numerical fitting of a delay cross information propagation (DT-SFI) dynamics model so as to verify the effectiveness of the model. Considering that the same opinion leader has the same concerned individuals and the connection relation of the multi-level concerned individuals, different information issued by the same opinion leader has higher possibility of generating cross propagation, and the model provided by the invention can be more fully verified by performing numerical fitting based on the message data issued by the same opinion leader. Of course, cross propagation may occur even if the two are not the same opinion leader. The model of the present invention is not limited by data.

The case data used for numerical fitting of the invention is that only ordinary 20200202# is thought by information # released at 2.2nd.2nd.8: 41 in 2020, the social donation bulletin # accepted by # Wuhan jin Yin Tan Hospital released at 2.2nd.2nd.10: 41 in 2020 and 3 community transmission cases # appeared for the first time in # Shenzhen released at 2.2nd.12nd.51 in 2020. Of these three pieces of information, there are 742 individuals (6.04%) in total 12283 that forwarded the first piece of information, which accounts for 10.36% of the total 7161 that forwarded the second piece of information; 1158 individuals (16.17%) of the total amount of the second message forwarded the third message accounted for 10.26% of the total amount of the third message forwarded 11289. The above conclusions are sufficient to illustrate the generality of the delayed cross information propagation phenomenon.

Tables 1-3 show the cumulative forwarding amounts of the three pieces of information at each time when the information is up to the next day 10:51, and the sampling frequency is 10 minutes/time. Accordingly, fig. 5 shows a variation trend chart of the accumulated forwarding amount. As shown in fig. 5, it can be seen that when the first message is in the period of the outbreak state, the second message is issued, the outbreak period of the second message is relatively short, and the overall development trend is relatively gentle; and the third message is issued after the second message enters the stationary phase, the burst duration of the third message has a longer period than that of the second message, and the accumulated forwarding amount is relatively higher.

TABLE 1

Time	0	10min	20min	30min	40min	50min	60min	70min
									Information I	47	597	940	1208	1458	1691	1937	2182
Time	80min	90min	100min	110min	2h	3h	4h	5h
									Information I	2477	2952	3461	3917	4390	6366	7501	8281
Time	6h	7h	8h	9h	10h	11h	12h	13h
									Information I	8846	9293	9638	9954	10199	10435	10795	11138
Time	14h	15h	16h	17h	18h	19h	20h	21h
									Information I	11459	11812	12013	12088	12109	12119	12128	12136
Time	22h	23h	24h	25h	26h
									Information I	12140	12146	12157	12171	12184

TABLE 2

Time	2h	3h	4h	5h	6h	7h	8h
								Information II	15	1281	2615	4013	4817	5322	5685
Time	9h	10h	11h	12h	13h	14h	15h
								Information II	5932	6052	6152	6264	6317	6380	6401
Time	9h	17h	18h	19h	20h	21h	22h
								Information II	6423	6434	6447	6454	6455	6456	6458
Time	23h	24h	25h	26h
								Information II	6460	6461	6465	6471

TABLE 3

Time	d 9h	10h	11h	12h	13h	14h	15h
								Information III
	20	1180	4244	6235	7595	8572	9103
								Time	16h	17h	18h	19h	20h	21h	22h
Information III	9381	9569	9642	9680	9700	9736	9764
								Time	23h	24h	25h	26h
Information III	9800	9864	9943	10006

Fig. 6 shows the fitting result of two cross information values with long release time intervals in tables 2-3, that is, the information III is propagated after the information II is propagated into the stable period. In the figure, the asterisk and the circle are respectively the real accumulated forwarding amount values of the information II and the information III, and the straight line and the dotted line are respectively the delay information propagation STI DT-SFI accumulated forwarding amount estimated values drawn by the information II and the information III according to the parameter estimation result. Fig. 7 shows the results of the numerical fitting of two pieces of cross information in tables 1-2, which are spaced apart by a short time interval, i.e., the information II is propagated just before the information I is propagated and has not yet entered the stationary phase. In the figure, the asterisk and the circle are the actual accumulated forwarding amount numerical values of the information I and the information II, the dotted line and the straight line are the delay information propagation LTI DT-SFI accumulated forwarding amount estimated values drawn by the information I in different time periods according to the parameter estimation result, and the dotted line is the accumulated forwarding amount estimated value of the information II. As can be seen from the parameter estimation fitting curves of fig. 7 to 8, for the cross asynchronous propagation information under various release strategies, the delayed cross information propagation DT-SFI dynamical model provided by the invention can achieve a good numerical fitting effect, and the feasibility of the model is verified.

According to the long delay cross information propagation cases of tables 2-3, the parameter estimation results of the delay information propagation submodel I and submodel II are respectively given in tables 4-5. As can be seen from Table 5, the average contact velocity during the propagation of the information III after the information II has entered the propagation plateau

The maximum value of (A) indicates that an individual immunized against the published message II will be more likely to be exposed to the post-published message III, while the average exposure rate

A small value of (a) indicates that a vulnerable group of post-release information III will be exposed to new information at a relatively low rate. Comparing three attractiveness indices

、

And

in which weak exposure attraction index

Maximum, meaning that message III is most attractive to direct immunisation of individuals to whom message II has been distributed, a strong exposure attraction index

Minimum, meaning that message III is least attractive to overtime immunized individuals for which message II was published.

TABLE 4

Name (R)	Description of the invention description of the description, description of the description of C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\626737dest _ path _ image275.jpg	Description of the invention description of the description, description of the description of C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\936757dest _ path _ image276.jpg	Description of the invention description of the C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\698040dest _ path _ image277.jpg	Description of the invention description of the description, description of the description of C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\883034dest _ path _ image278.jpg
					Numerical value	5.6458 Description of the invention description of the description, description of the description of C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\905216dest _ path _ image279.jpg	1.5757	1.7901 Description of the invention description of the description, description of the description of C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\25619dest _ path _ image280.jpg	0.0020

TABLE 5

Name (R)

Description of the invention description of the description, description of the description of C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\398832dest _ path _ image281.jpg

Description of the invention description of the C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\262882dest _ path _ image282.jpg

Description of the invention description of the C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\638107dest _ path _ image283.jpg

Description of the invention description of the description, description of the description of C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\319624dest _ path _ image284.jpg

Description of the invention description of the C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\789919dest _ path _ image285.jpg

Description of the invention description of the C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\723240dest _ path _ image286.jpg

Description of the invention description of the description, description of the description of C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\985594dest _ path _ image287.jpg

Description of the invention description of the C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\572434dest _ path _ image288.jpg

Description of the invention description of the description, description of the description of C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\264446dest _ path _ image289.jpg

Numerical value

0.8994

0.0023

1.0871 Description of the invention description of the C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\361977dest _ path _ image280.jpg

0.2468

1.9895

0.5559

2.9516 Description of the invention description of the C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\213259dest _ path _ image280.jpg

0.9858

7.4439 Description of the invention description of the description, description of the description of C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\846365dest _ path _ image279.jpg

According to the short delay cross information propagation cases of tables 1-2, tables 6-7 show the submodel I of the delay information propagation STI DT-SFI, respectively

And the parameter estimation result of the submodel III. As can be seen from Table 7, the average contact rate is the cross-propagation phase resulting from the distribution of message II while message I is still in the burst period

、

Compared with

、

Is much larger, showing that a population that has been exposed to message I will be exposed to post-release message II at a greater rate than a new, vulnerable population. Further, non-exposure attractiveness index

The greatest of the three attractiveness indices indicates that the release of information II is more attractive to the new vulnerable group due to the smaller time interval between the two releases of information.

TABLE 6

Name (R)	Description of the invention description of the description, description of the description of C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245638 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\260182dest _ path _ image278.jpg	Description of the invention description of the C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\969512dest _ path _ image277.jpg	Description of the invention description of the description, description of the description of C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\779205dest _ path _ image276.jpg	Description of the invention description of the C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\491071dest _ path _ image291.jpg
					Numerical value	0.9823	8.2700 Description of the invention description of the description, description of the description of C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\312397dest _ path _ image292.jpg	3.9986	5.1682 Description of the invention description of the C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\317262dest _ path _ image293.jpg

TABLE 7

Name (R)

Description of the invention description of the description, description of the description of C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\83093dest _ path _ image278.jpg

Description of the invention description of the C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\238130dest _ path _ image277.jpg

Description of the invention description of the description, description of the description of C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\773017dest _ path _ image276.jpg

Description of the invention description of the C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\355308dest _ path _ image294.jpg

Description of the invention description of the description, description of the description of C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\106970dest _ path _ image295.jpg

Description of the invention description of the C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\924753dest _ path _ image282.jpg

Description of the invention description of the description, description of the description of C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\455092dest _ path _ image296.jpg

Description of the invention description of the description, description of the description of C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\332918dest _ path _ image297.jpg

Description of the invention description of the C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\807761dest _ path _ image285.jpg

Description of the invention description of the C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\39023dest _ path _ image286.jpg

Description of C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\315545dest _ path _ image298.jpg

Description of the invention description of the description, description of the description of C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\98694dest _ path _ image289.jpg

Numerical value

0.009 1

3.6601 Description of the invention description of the C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\467358dest _ path _ image280.jpg

3.4777

0.0788

0.0037

0.8184

6.8834 Description of the invention description of the description, description of the description of C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\361365dest _ path _ image292.jpg

0.0406

0.0109

0.1868

1.9159

7.4439 Description of the invention description of the description, description of the description of C: \ Program Files (x86) \ gwssi \ CPC client \ cases \ inventions \ 245648 ef7-a8ca-4a3C-afc5-19fa5ac49f1f \ new \100002\866296dest _ path _ image279.jpg

The delay cross information propagation is the key research content of the invention, and the invention focuses on the influence of each parameter on the second information propagation condition. The parameter sensitivity analysis of the invention is to analyze the sensitivity of multi-parameter to delay release information propagation index, each parameterThe influence of the number on the propagation condition of the delay information and the influence of the delay time on the propagation condition of the delay information are carried out. As shown in fig. 4, the method for analyzing the propagation of the delayed cross information further includes constructing a propagation index of the delayed release information, and analyzing the influence of the model parameter on the propagation of the second piece of information, where the propagation index of the delayed release information includes a first information propagation reproducible number, a second information propagation reproducible number, and a propagation peak of the second piece of information

Final scale of

Propagation of climax time

Time of propagation of

Propagation duration

Average burst velocity

And average rate of decay

Specifically:

obtaining information dissemination reproducible numbers (a first information dissemination reproducible number or/and a second information dissemination reproducible number) through the initial total number of individuals of the susceptible population, wherein the information dissemination reproducible numbers represent the severity of public sentiment event outbreaks;

judging whether the information transmission reproducible number is more than 1, less than 1 or equal to 1;

if the information transmission reproducible number is less than 1, the number of the individuals in the forwarding state is reduced, and the information cannot be exploded; if the information propagation reproducible number is more than 1, indicating the individual in the forwarding stateThe number will grow exponentially; if it is not

Indicating that the number of individuals in the forwarding state has not changed;

predicting public opinion transmission peak value by adopting numerical simulation method through curve of total number of individuals of crowd in forwarding state changing along with time

The public sentiment propagation peak represents the propagation peak of the public sentiment hot spot event, as shown in fig. 8, which represents the time-varying curve of the total number of individuals in the forwarding state for the second message

Maximum value of (d);

the moment when the number of the individuals in the forwarding state is increased to the first set proportion of the public sentiment propagation peak value is taken as the public sentiment outbreak starting moment

Predicting the public opinion outbreak starting moment;

the moment when the number of the individuals in the forwarding state is increased to the public sentiment propagation peak value is taken as the public sentiment outbreak peak value moment

Predicting the public opinion outbreak peak time;

the moment when the number of the individuals in the forwarding state is reduced to a second set proportion of the public sentiment propagation peak value is taken as the public sentiment outbreak ending moment

Predicting the finish time of public sentiment outbreak,

in the case of the outbreak period,

；

the number of individuals in a forwarding state in unit time from the starting moment of public sentiment outbreak to the peak moment of the public sentiment outbreak is taken as the public sentiment outbreak rate

The public opinion outbreak rate is predicted;

using the number of individuals in a forwarding state in unit time from the peak moment of public sentiment outbreak to the end moment of the public sentiment outbreak as the rate of public sentiment decline

For example, the first set proportion and the second set proportion are equal, and the threshold value is set in advance

，

When is coming into contact with

When it is known

The public sentiment outbreak rate and decline rate can be defined as

And

mean rate from start to peak and mean rate from peak to end of a public opinion hotspot event outbreak;

the method comprises the steps of taking the number of individuals in a forwarding state in unit time from the starting moment of public sentiment outbreak to the ending moment of the public sentiment outbreak as an average rate, and realizing prediction of the public sentiment average rate;

by means of numerical simulation byCumulative amount of total number of individuals of population of forwarding states

Time-varying curve prediction of cumulative forwarding over an event burst period

。

The information transmission period comprises an outbreak period and a stable period, wherein the outbreak period is from the starting time of the public sentiment outbreak to the ending time of the public sentiment outbreak, namely, the information transmission starts until the information transmission tends to be stable, and the stable period is after the ending time of the public sentiment outbreak, namely, the information transmission is gradually stable, and the information transmission does not continue to be spread.

In LTI DT-SFI, as shown in FIGS. 8 and 9, at the parameters

、

、

、

、

、

、

、

And initial value

Under the change of conditionsPropagation index for delayed release information

PRCCs results of (a). In order to more clearly analyze the influence of the published information on new information, the initial value of the number of individuals in each state is set by combining case data

、

、

、

、

、

、

And fixing the first stage parameters

、

、

. The parameter boundary range of the selected sample is specified at the same time:

has a parameter boundary range of

，

Has a parameter boundary range of

，

Has a parameter boundary range of

；

Has a parameter boundary range of

；

Has a parameter boundary range of

、

、

Has a parameter boundary range of

(ii) a Initial value of total amount of susceptible population

Has a boundary range of

。

FIG. 8 shows model parameters

、

Reproducible number of long delay cross information propagation based on forwarding

The influence of (c). Wherein the average contact rate

Weak exposure attraction index

Non-exposure attraction index

Forward probability

And second stage susceptible population initial value

Index to information propagation reproducibility

With a decisive positive influence, while the parameters

And

the positive correlation effect of (A) is relatively weak while the average immunization rate is

Has strong negative influence on the material. In general, if the parameters can be adjusted by some control measures

、

、

、

And an initial value

Increase or parameter

The mutual correlation degree between the information is strengthened by reducing the information, so that the initial propagation capacity of the post-release information can be strengthened; on the contrary, the parameters are influenced by external force

、

、

、

And an initial value

Reduction or parameter

And if the size is increased, the initial propagation capacity of post-release information can be reduced.

FIG. 9 is a graph of long delay crossover information propagation peaks based on forwarding

And final scale

The effect of (a) was analyzed. From the PRCCs results, the parameter delays the information propagation peak

And final scale

The influence of (2) is similar. Wherein the non-exposure attraction index

Forward probability

And susceptible population initialization

For delay information propagation peak

And final scale

With a decisive positive influence. The strong attraction force parameter and the weak attraction force parameter of the immune group expressing the published information have weak influence. The reason is that since post-published information enters in the stable state of published information, the interval between the post-published information and the post-published information is long, most individuals who contact the published information enter the immune state, and in addition, the individuals have the possibility of forgetting or leaving the social network platform, so most individuals can not browse related contents any more. In addition, mean immunization Rate

For peak value

Has strong negative effect. The aboveThe conclusion shows that after the published information enters the stable stage and is separated from the post-published information for a long time, the contact individuals of the post-published information have no obvious effect on the post-published information, and therefore, the information dissemination can be promoted by influencing the number of new susceptible groups.

FIG. 10 illustrates climax propagation times for forwarding-based long-delay cross information

Time of propagation of

And propagation duration

Has been analyzed to grasp

And

the influence of (2) can be used to determine the propagation end time

And (6) performing calculation. As shown in the figure, the parameters

、

And

for climax time

Time of propagation of

And propagation duration

With similar negative correlation effects, in which several parameters contribute to burst length

Has a minimum influence, especially the parameters

It has little effect thereon. Parameter(s)

Has weak negative correlation influence on each time correlation index, and parameters

Then it is the control duration

And plays a strong negative correlation role.

FIG. 11 shows the average burst rate of forwarding-based long-delay cross information propagation under multi-model parameter variation

And average rate of decay

PRCCs results of (a). From the significance test results, the non-exposure attractiveness index

And forwarding probability

Has main positive correlation influence on the speed, and is easy to be influenced by the initial value of the population

Plays a relatively strong positive role, and the parameters

For average burst rate

Plays a strong negative role. In addition, the other parameters do not have a significant effect on the rate. That is, when the parameter is

、

And an initial value

At increased time, burst rate

And rate of decay

Will be increased therewith; while following the parameter

Rate of decrease of

And also improved. From the whole view, parameters

The impact on the rate is relatively greater.

Fig. 12a, 12b, 12c and fig. 13a, 13b, 13c show the forwarding amount of each key parameter pair

And accumulating the forwarding amounts

Of their effect, they are at any timeThe variance between them also determines various forwarding-based long delay cross information propagation indices. Default values of the parameters are given

，

，

，

，

，

，

，

，

0.9858，

，

，

，

. Where FIG. 12a is in range

Internal variation parameter

FIG. 12b is in the range

Internal variation parameter

FIG. 12c is in the range

Internal variation parameter

FIG. 13a is in the range

Internal variation strong exposure attraction index

FIG. 13b is in the range

Internal variation weak exposure attraction index

FIG. 13c is in the range

Internal variation non-exposure attractiveness index

The other parameters and initial values are set as default values.

Comparing and analyzing the influence of the single index change of the average contact rate and the attraction index of the graphs 12a, 12b and 12c and the graphs 13a, 13b and 13c on the forwarding amount and the accumulated forwarding amount of the post-release information in unit time, wherein the average contact rate

And non-exposure attractiveness index

The overall trend of the influence on the forwarding amount and the accumulated forwarding amount is the same: dependent on the parameter

And

the increase of the forwarding amount and the cumulative forwarding amount in the unit time increases the burst speed, the peak value which can be reached by the total number of the individuals in the forwarding state in the unit time is higher, and the final scale is larger. In addition, the average contact rate

Has weak influence on explosion time and explosion speed, and weak exposure attraction index

The final scale of the accumulated forwarding amount is slightly influenced, and the accumulated forwarding amount is increased in a steady state along with the increase of the parameters. Average contact rate

And strong exposure attraction index

There is no significant impact on forwarding-based long-delay cross information propagation. The above key parameters have no significant impact on the forwarding-based long-delay cross-message propagation burst time, climax time, and duration, which is also consistent with PRCCs results.

Fig. 14 simulates the tendency of new information III shown in table 3 to be released and propagated at different points in time after information II in table 2 enters the stabilization phase. It can be seen that the time of new information release mainly affects the spreading process of public opinion, and has little influence on the spreading scale of public opinion. If new information is released in a period of stable public opinion propagation of released information, the interaction effect among the information is higher at the earlier time point of the information release, the diffusion range reaching at the same time point is larger, the final propagation scale is relatively wider, but the overall influence on the scale is relatively little.

FIGS. 15-17 show model parameters of the STI DT-SFI dynamics model for delay information propagation

、

For information propagation index

PRCCs sensitivity results of (g). In combination with the case, we set the initial value of the number of individuals in each state to be

，

，

，

，

，

，

And estimating parameters using the first stage

、

、

、

When post-calculation release information comes in

、

、

The value of (2) is matched with the parameter estimation result when new information is released

、

、

、

. Setting the parameter boundary range of the selected sample:

has a parameter boundary range of

，

Has a parameter boundary range of

，

Has a parameter boundary range of

；

Has a parameter boundary range of

；

Has a parameter boundary range of

，

Has a parameter boundary range of

Has a parameter boundary range of

、

Has a parameter boundary range of

、

Has a parameter boundary range of

(ii) a Initial value of total amount of susceptible population

Has a boundary range of

。

FIG. 15 shows model parameters in a forwarding-based short-delay cross-information propagation model

、

And initial value of overall susceptible population

Reproducible number of short delay cross information propagation based on forwarding

The influence of (c). Wherein the average contact rate

Non-exposure attraction index

Forward probability

And initial value of susceptible population

Index to information propagation reproducibility

With a decisive positive influence, the mean immunization rate

Has strong negative influence, and the parameter

、

、

And

the positive correlation effect of (a) is relatively weak. In general, if the parameters can be adjusted by some control measures

、

、

And an initial value

Increase or parameter

If the number of the messages is reduced, the initial propagation capacity of the post-release information can be increased; conversely, the parameters can be changed by changing the parameters

、

、

And an initial value

Reduction or parameter

Increased to reduce the initial propagation capacity of post-release information。

FIG. 16 is a graph of short delay cross information propagation peaks based on forwarding

And final scale

Was analyzed for sensitivity factors. From the PRCCs results, each parameter pair information propagation peak

And final scale

The influence of (2) is similar. Wherein the average contact rate

And

probability of forwarding

Weak exposure attraction index

Non-exposure attraction index

And susceptible population initialization

For forwarding-based short delay cross information propagation peak

And final scale

Has strong positive effect.Wherein the initial value of the susceptible population

Plays a main role in influence; average exposure rate of directly immunized group of published information to post-published information

And strong exposure attraction index of post-release information to forwarding crowd and overtime immune crowd of the released information

The resulting effect is weak. The above results show that the strong exposure attraction index of the individual who is in the forwarding exposure period or forwards the first piece of information forwards the second piece of information due to the interest in the content

In contrast, individuals who have contacted the first piece of information but have not forwarded the second piece of new information are more sensitive to the weak exposure attractiveness index due to knowledge of the content. In addition, mean immunization Rate

For peak value

Has strong negative effect.

FIG. 17 illustrates climax propagation times for forwarding-based short-delay cross information

Time of propagation of

And propagation duration

Analysis is carried out, and in the same way, mastered

And

the influence of (2) can be used to determine the propagation end time

And (6) carrying out analysis. As shown, each parameter is for climax time

And propagation burst time

All are not obvious, only the parameters

、

And initial value

For the duration

Has certain negative influence on the parameters

A weaker positive influence is produced. This means that the average contact rate at which an individual in a vulnerable state can contact the second piece of information is such as to affect the duration of the propagation of the delayed information

The smaller the average contact rate is, the longer the new information propagation time is within a certain range, thereby slowing down the information propagation process.

FIG. 18 shows the variation of multiple parametersShort delay cross information propagation average burst rate based on forwarding

And average rate of decay

PRCCs results of (a). From the significance test results, the average contact rate

、

Probability of forwarding

Weak exposure attraction index

Non-exposure attraction index

And susceptible population initialization

Average burst rate for information propagation

And average rate of decay

Has strong positive correlation influence. Average rate at which an individual in a susceptible state directly immunized against a first message can be exposed to a second message

And strong exposure attraction of an individual who is in a forwarding exposure period or has forwarded the first piece of information to forward the second piece of information due to the interest in the contentIndex of refraction

The effect on the rate is not significant. That is, with the parameter

、

、

、

、

And an initial value

Can increase the burst rate

And rate of decay

(ii) a Conversely, a decrease in the parameter slows the propagation rate.

FIGS. 19a, 19b, 19c and FIGS. 20a, 20b, 20c show key parameters versus forwarding amounts

And accumulating the forwarding amounts

The influence of (c). Default values of the parameters are given

，

，

，

，

，

，

，

，

1.9159，

，

，

，

. Wherein FIG. 19a is in range

Internal variation parameter

FIG. 19b is in the range

Internal variation parameter

FIG. 19c is in the range

Internal variation parameter

(ii) a FIG. 20a is in range

Internal variation strong exposure attraction index

FIG. 20b is in the range

Internal variation weak exposure attraction index

FIG. 20c is in the range

Internal variation non-exposure attractiveness index

The other parameters and initial values are set as default values.

The influence of the single index change of the average contact rate and the attraction index in fig. 19a, 19b and 19c and fig. 20a, 20b and 20c on the forwarding amount and the accumulated forwarding amount of the post-release information in unit time is comparatively analyzed. Wherein the larger each of the average contact rate and the attraction index, the larger the forwarding amount per unit time and the accumulated forwarding amount, and the final scale of information propagation is affected. Average contact rate

、

And weak exposure attraction index

Non-exposure attraction index

The method is a main influence factor for the change of the short delay cross information propagation trend based on forwarding, and can play a more significant role in the final scale of information propagation within a certain range, so that a certain guiding strategy can be adopted to control the change trend of the parameters. In addition, strong exposure attraction index

Only a small range of influence is produced,

the influence of the parameters is weaker, and the influence of the parameters on the explosion time and the explosion speed is also very weak, which is consistent with the PRCCs result.

Fig. 21 simulates the propagation trend of new information II as shown in table 2 being released at different points in time when information I in table 1 is in the outbreak phase. It can be seen that the time of release of new information significantly affects the process and ultimate scale of public opinion dissemination. The earlier the information is released, the greater the interaction between the information, the faster the information propagation speed, and the larger the final scale.

Preferably, the delay cross information propagation analysis method of the present invention further includes: different model parameters are adjusted by combining the parameter sensitivity analysis result of each model parameter related to the delay cross information propagation index based on forwarding, so as to realize scientific guidance on the release strategy and the delay cross information propagation, and specifically:

for two pieces of information with longer release time interval, the average exposure rate of the parameters is influenced

And non-exposure attractiveness index

The value of (2) can intuitively influence the role of a large number of new susceptible groups participating in information dissemination. Therefore, if it is desired to expand the spread of new information, it is possible to increase the information spread by convincing some opinion leaders having a large number of individuals of interest to participate in the information spread

And

thereby enhancing the attention of the new susceptible group to the new release related information; conversely, if it is desired to reduce the level of interest in the new information, it may be desirable to delay the release of the new information in an effort to reduce the inter-information correlation parameter

、

、

And

effectively reducing the inter-relation between the information.

For two pieces of information with short release time interval, aiming at average contact rate

And

non-exposure attraction index

Weak exposure attraction index

These parameters, which characterize an individual's exposure to new information and the attractiveness of two related pieces of information, require the formulation of strategies that can increase or decrease the interplay between the pieces of information to achieve effective control of the information dissemination index. If it is desired to extend the dissemination of new information, the average exposure rate can be made rich by publishing the content

And weak exposure attraction index

The relevance and the attraction of related new release information to the release information contact individual are increased as much as possible, so that the diffusion of new information is promoted; second, the impression of the vulnerable group on new release information can be enhanced by convincing some opinion leaders during the release of the release information in combination with their respective insights, thereby augmenting

And

to enlarge the propagation size. Accordingly, if it is desired to reduce the appeal of new information to other individuals, the attention of the individual may be reduced by avoiding the release of new information during the outbreak of released information.

The invention discloses a delay cross information propagation analysis system based on dynamics, which comprises:

the system comprises a state division module, a network user and a first information processing module, wherein the state of the first information processing module is divided into an easily influenced state, a forwarding state, an overtime immune state and a direct immune state, the easily influenced state is a state that the first information processing module is not contacted with the first information, but the first information processing module is likely to be contacted with the first information and is easily influenced by the first information, and the first information processing module is likely to generate the forwarding state; the forwarding state is a state in which information has been forwarded and is in an active state, which can have an influence on other individuals; the overtime immune state is a state that the information is forwarded and then the active capability is lost, and the direct immune state is a state that the information is read and then the forwarding is abandoned and the active capability is lost;

the first model building module is used for building a first cross information propagation dynamic model, wherein the first cross information propagation dynamic model is a dynamic model for cross propagation of two pieces of information of a second piece of information issued in a stationary period of the first piece of information, and comprises: the status of the individual is divided into a first susceptible status, a second susceptible status, a third susceptible status, a forwarding status and a first immune status, the first susceptible state is a state which is not contacted with the first information and the second information is susceptible to the second information, the second susceptible state is a state which is susceptible to the second information for individuals who are in a timeout immune state for the first information, the third susceptible state is a state which is susceptible to the second information for individuals who are in a direct immune state for the first information, the forwarding state is a state which forwards the second information and can affect other individuals in an active state, the first immune state is a state which forwards the second information and loses the active ability, and individuals who are in the first susceptible state, the second susceptible state and the third susceptible state give up forwarding the second information and lose the active ability after reading the second information; dividing different crowds according to the individual state; constructing a first cross information propagation dynamic model in which the derivative of the total number of individuals of a crowd with respect to time and the total number of individuals of related crowds are in a linear relation according to a transformation direction, wherein the related crowds are other crowds having a transformation relation with the crowd except the crowd in an immune state;

the second model building module is used for building a second cross information propagation dynamic model, the second cross information propagation dynamic model is a dynamic model for cross propagation of two pieces of information of a second piece of information issued in the outbreak period of the first piece of information, and the second model building module comprises: dividing the state of the individual into a second susceptible state, a third susceptible state, a fourth susceptible state, a fifth susceptible state, a forwarding state and a second immune state, wherein the fourth susceptible state is a state which is not contacted with the first information and the second information and is susceptible to the first information or the second information, the fifth susceptible state is a state which is in the forwarding state of the first information and is susceptible to the second information, the second immune state is a state which is in the forwarding state of the first information and loses the active capability by forwarding the second information, and the individual in the fourth susceptible state, the second susceptible state and the third susceptible state abandons the state of losing the active capability by forwarding the second information; dividing different crowds according to the individual state; constructing a second cross information propagation dynamic model in which the derivative of the total number of individuals of a crowd with respect to time and the total number of individuals of related crowds are in a linear relationship according to a transformation direction, wherein the related crowds are other crowds having a transformation relationship with the crowd except the crowd in the immune state;

The inventor realizes that the release of relevant information is delayed properly, so that the interest of users can be attracted in the process of propagating public hot spot events, and the information propagation efficiency is improved. The main purpose of the invention is to know the cross propagation dynamics of the information in the emergent public health event to make an optimal strategy, to distribute the relevant information at a proper time point, to ensure the maximum interaction between the information, and to realize effective cooperative propagation.

The dynamics-based delay cross information propagation analysis method and system provided by the invention are used for researching an information delay cross propagation mechanism, analyzing a general mode of the delay cross information propagation mechanism, researching the influence of published information in long-interval and short-interval delay cross public sentiments on new information by establishing a model, mastering the popular trend of the internet in advance and detecting the propagation of microblog information, and designing a publishing strategy of related information to realize effective communication public opinions by analyzing the influence of attraction index related information propagation and analyzing important factors of delayed publishing related information propagation. And accurately analyzing the influence of the published information in the long-interval and short-interval delayed cross public sentiment on new information, and predicting the public sentiment. The method can judge and predict the current development situation and future changes of information transmission in time, and has great significance for maintaining social stability and constructing a harmonious society. In addition, the ordinary differential equation is used for constructing power systems under different types of time intervals, public sentiment indexes are constructed, and finally, a public sentiment control strategy is recommended according to public sentiment sensitivity analysis.

The specific implementation of the delay cross information propagation analysis system of the present invention is substantially the same as the specific implementation of the delay cross information propagation analysis method, and will not be described herein again.

Although the present invention has been described in detail with reference to the preferred embodiments, it will be understood by those skilled in the art that various changes may be made and equivalents may be substituted for elements thereof without departing from the spirit and scope of the present invention.

Claims

1. A dynamics-based delay-crossing information propagation analysis method is characterized by comprising the following steps:

setting that each individual of one piece of information can only be forwarded once, corresponding the total number of individuals of each crowd with the forwarding amount of the two pieces of information, and predicting the change of the total number of individuals of the crowd in the process of transmitting the two pieces of information according to a first cross information transmission dynamic model or a second cross information transmission dynamic model by monitoring the accumulated forwarding amount;

wherein the step of constructing a first cross information propagation dynamics model further comprises:

setting model parameters of a first cross information propagation dynamic model, comprising: the second average contact rate is the average rate at which an individual in the second susceptible state can contact the second piece of information; the third average contact rate is the average rate at which an individual in the fourth susceptible state can contact the second piece of information; the fourth average contact rate is the average rate at which an individual in the third susceptible state can contact the second piece of information; the second average forwarding probability is the average probability of forwarding the second piece of information by individuals in the second susceptible state, the third susceptible state and the fourth susceptible state; the second average immune rate is the average rate at which the individual transitions from the second forwarding state to the first immune state; the first strong exposure attraction index is the attraction strength of an individual forwarding the first piece of information to the forwarding of the second piece of information; the weak exposure attraction index is the attraction intensity of an individual who contacts the first piece of information but does not forward the second piece of information; the non-exposure attraction index is the attraction strength of an individual not contacting the first piece of information for forwarding the second piece of information;

wherein the content of the first and second substances,

、

、

、

and

、

and

in order to be the second average forwarding probability,

in order to obtain a second average immunization rate,

、

and

respectively a first strong exposure attraction index, a weak exposure attraction index and a non-exposure attraction index;

wherein the step of constructing a second cross information propagation dynamics model further comprises:

wherein the content of the first and second substances,

、

、

、

、

and

、

and

in order to be the third average forwarding probability,

is the third average immune rate and is,

、

and

、

and

a first average contact rate, a first average forwarding probability, and a first average immunization rate, respectively;

wherein, still include:

combining the parameter sensitivity analysis result of each model parameter related to the delay cross information propagation index based on forwarding, adjusting different model parameters to realize scientific guidance of the release strategy and the delay cross information propagation, comprising the following steps:

for the issue of the second information in the stationary period of the first information, the two issue time intervals are comparedLong information, influence on the parameter average exposure

And non-exposure attractiveness index

If it is desired to enlarge the propagation range of the second piece of information, the value of (2) is increased

And

(ii) a If the attention degree of the second piece of information is desired to be reduced, the correlation parameter between the pieces of information is reduced

、

、

And

the value of (2) to effectively reduce the interrelationship between the information;

issuing a second message during the burst of the first message, the two messages having a shorter time interval between the two messages, with respect to the average contact rate

And

non-exposure attraction index

Weak exposure attraction index

These parameters, which characterize the exposure of an individual to new information and the attraction between two related pieces of information, require the formulation of strategies that increase or decrease the interplay between the pieces of information to achieve control over the index of information propagation and, if it is desired to expand the propagation of the second piece of information, the average exposure rate

And weak exposure attraction index

Increase, increase

And

to increase the size of the dissemination and to reduce the attention of the individual by avoiding the release of the second message during the outbreak period in which the first message was released if it is desired to reduce the attractiveness of the second message to other individuals.

2. The delay-crossing information propagation analysis method according to claim 1, wherein the step of correlating the total number of individuals of each population with the forwarding amounts of two pieces of information comprises:

Wherein the content of the first and second substances,

as a second messageAn estimate of the cumulative forwarding amount of (a).

3. The delay-interleaved information-propagation analysis method according to claim 2, further comprising:

4. The delay-interleaved information-propagation analysis method as claimed in claim 1, further comprising:

5. The method for analyzing delayed cross information propagation according to claim 1, further comprising the step of performing public opinion monitoring on the first information and the second information through the first cross information propagation dynamics model and the second cross information propagation dynamics model, respectively, comprising:

Wherein the content of the first and second substances,

for the first information to propagate a reproducible number,

、

and

respectively being a first strong exposure attraction index, a weak exposure attraction index and a non-exposure attraction index, the first strong exposure attraction index being the attraction strength of an individual who forwards a first piece of information to the forwarding of a second piece of information, the weak exposure attraction index being the attraction strength of an individual who contacts the first piece of information but does not forward the second piece of information, the non-exposure attraction index being the attraction strength of an individual who does not contact the first piece of information to the forwarding of the second piece of information,

a second average forwarding probability, the second average forwarding probability being an average probability that an individual in the second vulnerable state, the third vulnerable state, and the fourth vulnerable state forwards the second piece of information,

a second average immunization rate, the second average immunization rate being an average rate at which the individual transitions from the second forwarding state to the first immunization state,

、

and

initial values of the total number of individuals of the second susceptible state, the third susceptible state and the fourth susceptible state respectively,

、

and

a fourth average contact rate, a third average contact rate, and a second average contact rate, respectively, the second average contact rate being an average rate at which an individual in the second susceptible state can contact the second piece of information, the third average contact rate being an average rate at which an individual in the fourth susceptible state can contact the second piece of information, the fourth average contact rate being an average rate at which an individual in the third susceptible state can contact the second piece of information,

Wherein the content of the first and second substances,

is a secondThe information can be propagated by a reproducible number,

the third average forwarding probability is an average probability that an individual in the third vulnerable state, the fourth vulnerable state, the fifth vulnerable state and the sixth vulnerable state will forward the second piece of information,

a third average immunization rate, which is an average rate at which the individual transitions from the second forwarding state to the second immunization state,

、

and

respectively are a second strong exposure attraction index, a weak exposure attraction index and a non-exposure attraction index, the second strong exposure attraction index is the attraction strength of an individual who is in a fifth susceptible state to the first information or an individual who forwards the first information to the second information,

and

、

and

a sixth average contact rate, a third average contact rate, and a fifth average contact rate, respectively, the fifth average contact rate being the average rate at which an individual in the sixth susceptible state and the third susceptible state can contact the second piece of information, the sixth average contact rate being the average rate at which an individual in the fifth susceptible state can contact the second piece of information,

the larger the outbreak, the faster the outbreak.

6. The method of claim 5, further comprising constructing a delay spread information propagation index, analyzing the influence of model parameters on the propagation of the second piece of information, wherein the delay spread information propagation index comprises a first information propagation reproducible number, a second information propagation reproducible number, a propagation peak value, a final size, a propagation climax time, a propagation burst time, a propagation duration, an average burst speed, and an average decay speed of the second piece of information.

7. A dynamics-based delayed cross information propagation analysis system, comprising:

the second monitoring module is used for setting that each individual of one piece of information can only be forwarded once, corresponding the total number of individuals of each crowd with the forwarding amount of the two pieces of information, and predicting the change of the total number of individuals of the crowd in the process of transmitting the two pieces of information according to the first cross information transmission dynamic model or the second cross information transmission dynamic model by monitoring the accumulated forwarding amount;

the step of constructing the first cross information propagation dynamics model by the first model construction module further comprises:

wherein the content of the first and second substances,

、

、

、

and

、

and

in order to be the second average forwarding probability,

in order to obtain a second average immunization rate,

、

and

the step of constructing the second cross information propagation dynamics model by the second model construction module further includes:

wherein the content of the first and second substances,

、

、

、

、

and

、

and

in order to be the third average forwarding probability,

is the third average immune rate and is,

、

and

、

and

wherein, still include:

for the second piece of information issued in the stationary period of the first piece of information, the two pieces of information with longer issuing time intervals influence the average exposure rate of the parameters

And non-exposure attractiveness index

And

、

、

And

And

non-exposure attraction index

Weak exposure attraction index

And weak exposure attraction index

Increase, increase

And