CN114999619A - Infectious disease bed dynamic quantification method based on time lag analysis - Google Patents

Infectious disease bed dynamic quantification method based on time lag analysis Download PDF

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CN114999619A
CN114999619A CN202210668571.7A CN202210668571A CN114999619A CN 114999619 A CN114999619 A CN 114999619A CN 202210668571 A CN202210668571 A CN 202210668571A CN 114999619 A CN114999619 A CN 114999619A
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王海华
库俊华
刘衍琼
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Qiongtai Normal University
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Abstract

The invention relates to the technical field of quantification of the number of sickbeds, and discloses a time lag analysis-based method for dynamically quantifying the number of the sickbeds of infectious diseases, which comprises the following steps: constructing a time-lag random infectious disease model under a noise disturbance condition; analyzing the steady-state characteristics of the time-lag stochastic infectious disease model based on the basic regeneration number; collecting information data of an infected group, and determining time-lag random infectious disease model parameters under a complete information condition by using a maximum likelihood estimation method under a continuous observation condition, wherein the time-lag random infectious disease model parameters comprise an infectious disease infection coefficient and a rehabilitation coefficient; and predicting the number of infected persons based on the time-lag random infectious disease model with the determined parameters, and dynamically determining the number of beds according to the predicted number. The time-lag random infectious disease model constructed by the invention can better reflect the state conversion relation of different crowds in the infectious disease transmission process in a real scene, improve the prediction authenticity of the infectious disease development trend, dynamically determine the number of beds according to the number of predicted people, and realize the reasonable quantification of the infectious disease beds.

Description

Infectious disease bed dynamic quantification method based on time lag analysis
Technical Field
The invention relates to the technical field of quantification of the number of sickbeds, in particular to a dynamic quantification method of an infectious disease bed based on time lag analysis.
Background
The infectious diseases have latent stage and infectious stage, and have typical time lag characteristics, such as new coronavirus, monkeypox virus and the like. At present, isolation treatment is mainly used for treating infectious diseases, a large number of independent beds are needed to be used as supports, and the number and the scale of the infectious diseases are difficult to rapidly determine due to the time lag characteristics of the infectious diseases. At present, the bed quantization of infectious diseases is mainly based on expert experience, the rationality is poor, the epidemic situation is easy to leak due to too few settings, the patients are difficult to guarantee, and the treatment time is delayed; and a large amount of public resources are wasted due to excessive arrangement, so that a dynamic quantification method for the infectious disease beds is urgently needed, the infectious disease development trend can be accurately predicted, the construction quantity of the infectious disease beds is guided, and the rational quantification of the infectious disease beds is realized.
Disclosure of Invention
In view of the above, the invention provides an infectious disease bed dynamic quantification method based on time lag analysis, and aims to (1) construct a time lag random infectious disease model under the condition of considering the time lag of the infectious disease latency and random disturbance, wherein the constructed time lag random infectious disease model can better reflect the infectious disease propagation process in a real scene and the state transition relations of susceptible people, latent people, isolated people, infected people and recovery people in different process stages, and is closer to a practical scene, so that the infectious disease development trend prediction authenticity is improved, and the time lag random infectious disease model is reduced along with the reduction of the noise intensity of the random disturbance, and the time lag random infectious disease model is based on the basic regeneration number R 0 When the regeneration number is less than or equal to 1, the regeneration number approaches to a unique disease-free equilibrium point 0 >1, the model approaches to a unique endemic balance point, has stable ambiguity and ensures the validity of a time-lag random infectious disease model; (2) collecting information data of infected persons, determining time-lag random infectious disease model parameters under complete information conditions by using a maximum likelihood estimation method under continuous observation conditions, solving to obtain model parameters, predicting the number of the infected persons based on the time-lag random infectious disease model with the determined parameters, dynamically determining the number of beds according to the predicted number of the persons, avoiding setting too many or too few infectious disease beds, and realizing reasonable quantification of the infectious disease beds.
The invention provides a time lag analysis-based infectious disease bed dynamic quantification method, which comprises the following steps:
s1: constructing a time-lag random infectious disease model under a noise disturbance condition, wherein the time-lag random infectious disease model comprises 5 types of susceptible people, latent people, isolated people, infected people and recovery people, and establishing a state conversion relation of the 5 types of people based on a random differential equation;
s2: analyzing the steady-state characteristics of the time-lag random infectious disease model based on the basic regeneration number, determining the ambiguity resolution of the time-lag random infectious disease model, and ensuring the validity of the time-lag random infectious disease model;
s3: collecting information data of an infected group, and determining time-lag random infectious disease model parameters under a complete information condition by using a maximum likelihood estimation method under a continuous observation condition, wherein the time-lag random infectious disease model parameters comprise an infectious disease infection coefficient and a rehabilitation coefficient;
s4: and predicting the number of infected persons based on the time-lag random infectious disease model with the determined parameters, and dynamically determining the number of beds according to the predicted number.
As a further improvement of the method of the invention:
optionally, the step S1 of constructing a time-lapse stochastic infectious disease model under the noise disturbance condition includes:
constructing a time-lag random infectious disease model under a noise disturbance condition, wherein the noise disturbance is Brownian motion disturbance, the time-lag random infectious disease model comprises 5 types of susceptible population, latent population, isolated population, infected population and recovery population, and the constructed model is as follows:
Figure BDA0003693936920000021
wherein:
(s) (t) represents the number of susceptible population at time t, e (t) represents the number of latent population at time t, i (t) represents the number of infected population at time t, q (t) represents the number of isolated population at time t, r (t) represents the number of recovery population at time t;
α SE indicates the contact rate, alpha, between the susceptible population and the latent population SI Indicating the contact rate of susceptible and infected persons;
epsilon represents the natural mortality rate;
Brow S (t),Brow E (t),Brow I (t),Brow Q (t),Brow R (t) noise disturbances, σ, respectively, suffered by the class 5 population S ,σ E ,σ I ,σ Q ,σ R The intensities of the corresponding noise disturbances are respectively, and in the embodiment of the invention, the noise disturbances suffered by each type of crowd are independent;
∈ E represents the ratio of the latent population to the infected, E I Indicates the cause mortality of the infected population, E Q Indicating disease mortality in the quarantine population;
β E indicates the recovery rate of the latent population, beta I Indicates the recovery rate of the infected population, beta Q Indicating the recovery rate of the isolated population;
μ E represents the ratio of the potential population isolated, μ I Representing the rate at which infected persons are isolated;
τ represents the latency time lag of infectious disease;
the infectious disease infection coefficient and the recovery coefficient are parameters to be solved of a time-lag random infectious disease model, wherein the infectious disease infection coefficient comprises the ratio epsilon of a latent population to an infected person E The recovery factor comprises the recovery rate beta of the infected people I 。
Optionally, the step of S2 of calculating the basic regeneration number of the time-lag stochastic infectious disease model includes:
the calculation formula of the basic regeneration number is as follows:
Figure BDA0003693936920000022
wherein:
a represents the initial number of susceptible population;
R 0 for time-lapse random transmissionThe basic regeneration number of the infection model represents the number of second-generation cases which can be infected when an infection case enters a susceptible population and is not interfered by external force; if R is 0 If the number of the infectious diseases is more than 1, the infectious diseases can spread to the whole crowd; if R is 0 If the ratio is 1 or less, the infectious disease tends to disappear.
Optionally, the determining the time-lapse stochastic infectious disease model ambiguity in the S2 step includes:
basic regeneration number R of time-lag stochastic infectious disease model 0 When the time lag random infectious disease model is less than or equal to 1, the left formula of the time lag random infectious disease model is 0, and a disease-free balance point n exists in the time lag random infectious disease model 0 (A/ε,0,0,0,0), the disease-free equilibrium point n 0 Due to noise disturbance, fluctuation size and noise intensity sigma S Is in positive correlation;
basic regeneration number R of time-lag stochastic infectious disease model 0 >1 hour, let the left expression of the time-lag stochastic infectious disease model be 0, and solve the time t → ∞ of the time-lag stochastic infectious disease model (S) * ,E * ,I * ,Q * ,R * ) Satisfies the following formula:
Figure BDA0003693936920000023
wherein:
F(k)＝(S(k)-S * ) 2 +(E(k)-E * ) 2 +(I(k)-I * ) 2 +(Q(k)-Q * ) 2 +(R(k)-R * ) 2 ；
Brown＝σ S (S * ) 2 +σ E (E * ) 2 +σ I (I * ) 2 +σ Q (Q * ) 2 +σ R (R * ) 2 ；
sup {. is solving the supremum bound;
time lag stochastic infectious disease model solution (S) at time t → ∞ * ,E * ,I * ,Q * ,R * ) Because the noise disturbance can generate fluctuation, the fluctuation size is in positive correlation with the noise intensity, and the noise intensity is higherSmall, (S) * ,E * ,I * ,Q * ,R * ) The closer to the unique point of endemic balance;
the time-lapse stochastic infectious disease model generates a basic regeneration number R along with the reduction of the noise intensity 0 When the regeneration number is less than or equal to 1, the regeneration number is close to the unique disease-free equilibrium point 0 >1 approaches to a unique endemic balance point, and has stable ambiguity.
Optionally, the collecting information data of the affected people in step S3 includes:
the information data of the affected group is multivariate random observation data, and the time range of the information data of the affected group is [0, T]In the time range [0, T]The state conversion of { S (t), E (t), I (t), Q (t), R (t) } takes place for M times, and the time of the state conversion of the ith time is t i ，Δt i ＝t i+1 -t i ，t i ∈[0,T]And i is 1,2, …, and M, the acquisition result of the information data of the affected people is as follows:
{data i ＝(t i ,S(t i ),E(t i ),I(t i ),Q(t i ),R(t i ))|i＝1,2,…,M,t i ∈[0,T]}
wherein:
S(t i ),E(t i ),I(t i ),Q(t i ),R(t i ) Are each t i The number of susceptible people, the number of latent people, the number of infected people, the number of isolated people and the number of recovery people at the moment.
Optionally, the determining time-lapse stochastic infectious disease model parameters under the complete information condition by using a maximum likelihood estimation method under continuous observation conditions in step S3 includes:
the complete information condition represents the contact rate of known susceptible people and latent people, the contact rate of the susceptible people and infected people, the natural mortality rate, the disease-caused mortality rate of the infected people, the disease-caused mortality rate of isolated people, the isolated rate of the latent people, the isolated rate of the infected people, the recovery rate of the latent people, the recovery rate of the susceptible people and the latent time lag of infectious diseases;
determining time-lag random infectious disease model parameters under a complete information condition by using a maximum likelihood estimation method under a continuous observation condition, wherein the time-lag random infectious disease model parameters comprise an infectious disease infection coefficient and a recovery coefficient, and the maximum likelihood estimation method under the continuous observation condition comprises the following steps:
s31: for any ith state transition, if S (t) i ),E(t i ),I(t i ) Has not switched, the ith state switch is switched in the time interval delta t i The exponential distribution obeyed by the time is:
Figure BDA0003693936920000031
Figure BDA0003693936920000032
Figure BDA0003693936920000033
Figure BDA0003693936920000034
then the probability of this section L 1 (θ) is:
Figure BDA0003693936920000035
theta is a parameter to be solved of the time-lag stochastic infectious disease model;
Ω 1 is S (t) i ),E(t i ),I(t i ) A set of transition times for which the state of (a) has not been transitioned;
s32: for any ith state transition, if I (t) i ) The state of (b) is changed, the ith state change is carried out in the time interval delta t i The probability obeyed is:
p{I(t i ) Increase } - [ alpha ] SI S(t i )I(t i )Δt i
p{I(t i ) Decreasing ∈ E E E(t i -τ)-(ε+∈ I +β I +μ I )I(t i )Δt i
Then the probability of this section L 2 (θ) is:
Figure BDA0003693936920000036
Ω 2 is I (t) i ) Increased set of state transition times, Ω 3 Is I (t) i ) A reduced set of state transition times;
s33: constructing a likelihood function L (θ):
Figure BDA0003693936920000041
Figure BDA0003693936920000042
Figure BDA0003693936920000043
Figure BDA0003693936920000044
Figure BDA0003693936920000045
wherein:
∈ E the ratio of conversion of the latent population to the infected, beta I The recovery rate for the infected population;
s34: taking logarithm to likelihood function L (theta) to obtain J (theta), and setting parameter to epsilon E ,β I The partial derivatives are calculated to obtain the following equation:
Figure BDA0003693936920000046
Figure BDA0003693936920000047
let equation left be 0, obtain parameter solution result:
Figure BDA0003693936920000048
optionally, the predicting the number of patients based on the time-lag stochastic infectious disease model with determined parameters in step S4, and dynamically determining the number of beds according to the predicted number of patients includes:
substituting the numbers of susceptible people, latent people, isolated people, infected people and recovery people at the initial moment into a time-lag random infectious disease model with determined parameters, and outputting the result by the model
Figure BDA0003693936920000049
The method comprises the steps of obtaining the state conversion results of different crowds at the current moment, simultaneously representing the crowds of different crowds at the next moment, obtaining the infected crowd number and the isolated crowd number at the predicted moment, determining the bed number of the infectious disease infected crowd and the bed number of the isolated crowd in advance according to the infected crowd number and the isolated crowd number at the predicted moment, and achieving dynamic quantification of the infectious disease bed.
In order to solve the above problems, the present invention also provides a device for dynamically quantifying an infectious disease bed based on time lag analysis, the device comprising:
the infectious disease model construction device is used for constructing a time-lag random infectious disease model under a noise disturbance condition, analyzing the steady-state characteristics of the time-lag random infectious disease model based on a basic regeneration number, and determining time-lag random infectious disease model parameters under a complete information condition by using a maximum likelihood estimation method under a continuous observation condition, wherein the time-lag random infectious disease model parameters comprise an infectious disease infection coefficient and a rehabilitation coefficient;
the information data acquisition device is used for acquiring information data of the infected people;
the infectious disease bed dynamic quantification device is used for predicting the number of infected persons based on the time-lag random infectious disease model with the determined parameters and dynamically determining the number of beds according to the predicted number.
In order to solve the above problem, the present invention also provides an electronic device, including:
a memory storing at least one instruction; and
and the processor executes the instructions stored in the memory to realize the infectious disease bed dynamic quantification method based on time lag analysis.
In order to solve the above problem, the present invention further provides a computer-readable storage medium, which stores at least one instruction executed by a processor in an electronic device to implement the above-mentioned method for dynamic quantification of infectious disease bed based on time lag analysis.
Compared with the prior art, the invention provides a time-lag analysis-based infectious disease bed dynamic quantification method, which has the following advantages:
firstly, the scheme provides a time-lag random infectious disease model under a noise disturbance condition, wherein the noise disturbance is brownian motion disturbance, the time-lag random infectious disease model comprises 5 types of susceptible people, latent people, isolated people, infected people and recovery people, and the constructed model is as follows:
Figure BDA0003693936920000051
wherein: s (t) represents the number of susceptible people at the time t, E (t) represents the number of latent people at the time t, I (t) represents the number of infected people at the time t, Q (t) represents the number of isolated people at the time t, and R (t) represents the number of recovery people at the time t; alpha is alpha SE Indicates the contact rate, alpha, between the susceptible population and the latent population SI Representing susceptible and infected personsThe contact rate; epsilon represents the natural mortality rate; brow S (t),Brow E (t),Brow I (t),Brow Q (t),Brow R (t) noise disturbances, σ, respectively, suffered by the class 5 population S ,σ E ,σ I ,σ Q ,σ R The intensities of the corresponding noise disturbances are respectively, and in the embodiment of the invention, the noise disturbances suffered by each type of crowd are independent; e is the same as E Represents the ratio of the latent population to the infected, E I Indicates the cause mortality of the infected population, E Q Indicating disease mortality in the quarantine population; beta is a E Indicates the recovery rate of the latent population, beta I Indicates the recovery rate of the infected population, beta Q Indicating the recovery rate of the isolated population; mu.s E Represents the ratio of the potential population isolated, μ I Representing the rate at which infected persons are isolated; τ represents the latency time lag of infectious disease; the infectious disease infection coefficient and the recovery coefficient are parameters to be solved of a time-lag random infectious disease model, wherein the infectious disease infection coefficient comprises the ratio epsilon of a latent population to an infected person E The recovery factor comprises the recovery rate beta of the infected people I . Calculating the basic regeneration number of the time-lag stochastic infectious disease model, wherein the calculation formula of the basic regeneration number is as follows:
Figure BDA0003693936920000052
wherein: a represents the initial number of susceptible population; r 0 The basic regeneration number of a time-lag random infectious disease model represents the number of second-generation cases which can be infected when one infectious case enters a susceptible population and is not interfered by an external force; if R is 0 If the number of the infectious diseases is more than 1, the infectious diseases can be spread to the whole population; if R is 0 If the ratio is 1 or less, the infectious disease tends to disappear. Basic regeneration number R of time-lag stochastic infectious disease model 0 When the time lag random infectious disease model is less than or equal to 1, the left formula of the time lag random infectious disease model is 0, and a disease-free balance point n exists in the time lag random infectious disease model 0 (A/ε,0,0,0,0), the disease-free equilibrium point n 0 Due to noise disturbance, fluctuation size and noise intensity sigma S Is in positive correlation; basic regeneration number R of time-lag stochastic infectious disease model 0 >1 hour, let the left expression of the time-lag stochastic infectious disease model be 0, and solve the time t → ∞ of the time-lag stochastic infectious disease model (S) * ,E * ,I * ,Q * ,R * ) Satisfies the following formula:
Figure BDA0003693936920000053
wherein: f (k) ═ S (k) — S * ) 2 +(E(k)-E * ) 2 +(I(k)-I * ) 2 +(Q(k)-Q * ) 2 +(R(k)-R * ) 2 ；Brown＝σ S (S * ) 2 +σ E (E * ) 2 +σ I (I * ) 2 +σ Q (Q * ) 2 +σ R (R * ) 2 (ii) a sup {. is solving the supremum bound; time lag stochastic infectious disease model solution (S) at time t → ∞ * ,E * ,I * ,Q * ,R * ) Because the noise disturbance can generate fluctuation, the fluctuation size is in positive correlation with the noise intensity, and the smaller the noise intensity is, (S) * ,E * ,I * ,Q * ,R * ) The closer to the unique point of endemic balance; compared with the traditional scheme, the time-lag random infectious disease model is constructed under the condition that the time lag of the infectious disease latency and random disturbance are considered, the constructed time-lag random infectious disease model can reflect the infectious disease transmission process in the real scene, and the state conversion relations of susceptible people, latent people, isolated people, infected people and recovery people in different process stages are closer to the real scene, so that the prediction reality of the infectious disease development trend is improved, and the constructed model reduces the noise intensity along with the random disturbance, and the time-lag random infectious disease model is based on the basic regeneration number R 0 When the regeneration number is less than or equal to 1, the regeneration number approaches to a unique disease-free equilibrium point 0 >1 hour approaches to a unique endemic balance point, has stable ambiguity and ensures the validity of a time-lag random infectious disease model.
Meanwhile, the scheme determines time-lag random infectious disease model parameters under the complete information condition by using a maximum likelihood estimation method under the continuous observation condition, and realizes the dynamic quantification of the infectious disease bed under the consideration of the infectious disease latency time-lag condition, wherein the time-lag random infectious disease model parameters comprise an infectious disease infection coefficient and a recovery coefficient, and the maximum likelihood estimation method under the continuous observation condition has the following flow: for any ith state transition, if S (t) i ),E(t i ),I(t i ) Has not switched, the ith state switch is switched in the time interval delta t i The exponential distribution obeyed when:
Figure BDA0003693936920000061
Figure BDA0003693936920000062
Figure BDA0003693936920000063
Figure BDA0003693936920000064
then the probability of this section L 1 (θ) is:
Figure BDA0003693936920000065
theta is a parameter to be solved of the time-lag stochastic infectious disease model; omega 1 Is S (t) i ),E(t i ),I(t i ) A set of transition times for which the state of (a) has not been transitioned; for any ith state transition, if I (t) i ) The state of (b) is changed, the ith state change is carried out in the time interval delta t i The probability obeyed is:
p{I(t i ) Increase } - [ alpha ] SI S(t i )I(t i )Δt i
p{I(t i ) Decrement ∈ E E(t i -τ)-(ε+∈ I +β I +μ I )I(t i )Δt i
Then the probability of this section L 2 (θ) is:
Figure BDA0003693936920000066
Ω 2 is I (t) i ) Increased set of state transition times, Ω 3 Is I (t) i ) A reduced set of state transitions;
constructing a likelihood function L (θ):
Figure BDA0003693936920000067
Figure BDA0003693936920000068
Figure BDA0003693936920000069
Figure BDA00036939369200000610
Figure BDA00036939369200000611
∈ E the ratio of conversion of the latent population to the infected, beta I The recovery rate for the infected population; taking logarithm to likelihood function L (theta) to obtain J (theta), and setting parameter to epsilon E ,β I The partial derivatives are calculated to obtain the following equation:
Figure BDA00036939369200000612
Figure BDA00036939369200000613
let equation left be 0, obtain parameter solution result:
Figure BDA00036939369200000614
substituting the numbers of susceptible people, latent people, isolated people, infected people and recovery people at the initial moment into a time-lag random infectious disease model with determined parameters, and outputting the result by the model
Figure BDA00036939369200000615
The method comprises the steps of obtaining the state conversion results of different crowds at the current moment, simultaneously representing the number of the crowds of the different crowds at the next moment, obtaining the number of infected crowds and the number of isolated crowds at the predicted moment, determining the number of beds of the infectious disease infected crowds and the number of beds of the isolated crowds in advance according to the number of the infected crowds and the number of the isolated crowds at the predicted moment, avoiding setting too many or too few infectious disease beds, and achieving reasonable quantification of the infectious disease beds.
Drawings
Fig. 1 is a schematic flowchart of a method for quantifying the dynamic status of an infectious disease bed based on time lag analysis according to an embodiment of the present invention;
FIG. 2 is a functional block diagram of an apparatus for quantifying the dynamic status of a contagious disease bed based on time lag analysis according to an embodiment of the present invention;
fig. 3 is a schematic structural diagram of an electronic device for implementing a time lag analysis-based infectious disease bed dynamic quantification method according to an embodiment of the present invention.
The implementation, functional features and advantages of the objects of the present invention will be further explained with reference to the accompanying drawings.
Detailed Description
It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
The embodiment of the application provides a time-lag analysis-based infectious disease bed dynamic quantification method. The main execution body of the infectious disease bed dynamic quantification method based on time lag analysis includes, but is not limited to, at least one of electronic devices such as a server and a terminal, which can be configured to execute the method provided by the embodiments of the present application. In other words, the method for dynamically quantifying the infectious disease bed based on time lag analysis may be performed by software or hardware installed in a terminal device or a server device, and the software may be a block chain platform. The server includes but is not limited to: a single server, a server cluster, a cloud server or a cloud server cluster, and the like.
Example 1:
s1: constructing a time-lag random infectious disease model under a noise disturbance condition, wherein the time-lag random infectious disease model comprises 5 types of susceptible people, latent people, isolated people, infected people and recovery people, and establishing a state conversion relation of the 5 types of people based on a random differential equation.
In the step S1, constructing a time-lag stochastic infectious disease model under the noise disturbance condition, including:
constructing a time-lag random infectious disease model under a noise disturbance condition, wherein the noise disturbance is Brownian motion disturbance, the time-lag random infectious disease model comprises 5 types of susceptible population, latent population, isolated population, infected population and recovery population, and the constructed model is as follows:
Figure BDA0003693936920000071
wherein:
(s) (t) represents the number of susceptible population at time t, e (t) represents the number of latent population at time t, i (t) represents the number of infected population at time t, q (t) represents the number of isolated population at time t, r (t) represents the number of recovery population at time t;
α SE indicates the contact rate, alpha, between the susceptible population and the latent population SI Indicating the contact rate of susceptible and infected persons;
epsilon represents the natural mortality rate;
Brow S (t),Brow E (t),Brow I (t),Brow Q (t),Brow R (t) noise disturbances, σ, respectively, suffered by the class 5 population S ,σ E ,σ I ,σ Q ,σ R The intensities of the corresponding noise disturbances are respectively, and in the embodiment of the invention, the noise disturbances suffered by each type of crowd are independent;
∈ E represents the ratio of the latent population to the infected, E I Indicates the cause mortality of the infected population, E Q Indicating disease mortality of the sequestered population;
β E indicates the recovery rate of the latent population, beta I Indicates the recovery rate, beta, of the infected population Q Indicating the recovery rate of the isolated population;
μ E represents the ratio of the potential population isolated, μ I Representing the rate at which infected persons are isolated;
τ represents the latency time lag of infectious disease;
the infectious disease infection coefficient and the recovery coefficient are parameters to be solved of a time-lag random infectious disease model, wherein the infectious disease infection coefficient comprises the ratio epsilon of a latent population to an infected person E The recovery factor comprises the recovery rate beta of the infected people I 。
S2: and analyzing the steady-state characteristic of the time-lag random infectious disease model based on the basic regeneration number, determining the ambiguity resolution of the time-lag random infectious disease model, and ensuring the validity of the time-lag random infectious disease model.
The step S2 of calculating the basic regeneration number of the time-lag stochastic infectious disease model includes:
the calculation formula of the basic regeneration number is as follows:
Figure BDA0003693936920000081
wherein:
a represents the initial number of susceptible population;
R 0 the basic regeneration number of a time-lag random infectious disease model represents the number of second-generation cases which can be infected when one infectious case enters a susceptible population and is not interfered by an external force; if R is 0 If the number of the infectious diseases is more than 1, the infectious diseases can be spread to the whole population; if R is 0 If the ratio is 1 or less, the infectious disease tends to disappear.
Determining the ambiguity of the time-lapse stochastic infectious disease model in the step S2 comprises the following steps:
basic regeneration number R of time-lag stochastic infectious disease model 0 When the time lag random infectious disease model is less than or equal to 1, the left formula of the time lag random infectious disease model is 0, and a disease-free balance point n exists in the time lag random infectious disease model 0 (A/ε,0,0,0,0), the disease-free equilibrium point n 0 Due to noise disturbance, fluctuations are generated, the size of the fluctuations and the noise intensity sigma S Is in positive correlation;
basic regeneration number R of random infectious disease model when time lag 0 >1 hour, let the left expression of the time-lag stochastic infectious disease model be 0, and solve the time t → ∞ of the time-lag stochastic infectious disease model (S) * ,E * ,I * ,Q * ,R * ) Satisfies the following formula:
Figure BDA0003693936920000082
wherein:
F(k)＝(S(k)-S * ) 2 +(E(k)-E * ) 2 +(I(k)-I * ) 2 +(Q(k)-Q * ) 2 +(R(k)-R * ) 2 ；
Brown＝σ S (S * ) 2 +σ E (E * ) 2 +σ I (I * ) 2 +σ Q (Q * ) 2 +σ R (R * ) 2 ；
sup {. is solving the supremum bound;
time lag stochastic infectious disease model solution (S) at time t → ∞ * ,E * ,I * ,Q * ,R * ) Because the noise disturbance can generate fluctuation, the fluctuation size is in positive correlation with the noise intensity, and the noise is generatedThe smaller the sound intensity, (S) * ,E * ,I * ,Q * ,R * ) The closer to the unique point of endemic balance;
the time-lapse stochastic infectious disease model generates a basic regeneration number R along with the reduction of the noise intensity 0 When the regeneration number is less than or equal to 1, the regeneration number approaches to a unique disease-free equilibrium point 0 >1 approaches to a unique endemic balance point, and has stable ambiguity.
S3: collecting information data of an infected person, and determining time-lag random infectious disease model parameters under a complete information condition by using a maximum likelihood estimation method under a continuous observation condition, wherein the time-lag random infectious disease model parameters comprise an infectious disease infection coefficient and a rehabilitation coefficient.
In the step S3, determining time-lag stochastic infectious disease model parameters under the complete information condition by using a maximum likelihood estimation method under the continuous observation condition, the method includes:
the complete information condition represents the contact rate of known susceptible people and latent people, the contact rate of the susceptible people and infected people, the natural mortality rate, the caused disease mortality rate of the infected people, the caused disease mortality rate of isolated people, the isolated rate of the latent people, the isolated rate of the infected people, the recovery rate of the latent people, the recovery rate of the susceptible people and the latent time lag of infectious diseases;
determining time-lag stochastic infectious disease model parameters under a complete information condition by using a maximum likelihood estimation method under a continuous observation condition, wherein the time-lag stochastic infectious disease model parameters comprise an infectious disease infection coefficient and a recovery coefficient, and the maximum likelihood estimation method under the continuous observation condition comprises the following steps:
s31: for any ith state transition, if S (t) i ),E(t i ),I(t i ) Has not switched, the ith state switch is switched in the time interval delta t i The exponential distribution obeyed by the time is:
Figure BDA0003693936920000091
Figure BDA0003693936920000092
Figure BDA0003693936920000093
Figure BDA0003693936920000094
then the probability of this section L 1 (θ) is:
Figure BDA0003693936920000095
theta is a parameter to be solved of the time-lag stochastic infectious disease model;
Ω 1 is S (t) i ),E(t i ),I(t i ) A set of transition times for which the state of (a) has not transitioned;
s32: for any ith state transition, if I (t) i ) The state of (b) is changed, the ith state change is carried out in the time interval delta t i The probability obeyed is:
p{I(t i ) Increase } - [ alpha ] SI S(t i )I(t i )Δt i
p{I(t i ) Decrement ∈ E E(t i -τ)-(ε+∈ I +β I +μ I )I(t i )Δt i
Then the probability of this section L 2 (θ) is:
Figure BDA0003693936920000096
Ω 2 is I (t) i ) Increased set of state transition times, Ω 3 Is I (t) i ) A reduced set of state transition times;
s33: constructing a likelihood function L (θ):
Figure BDA0003693936920000097
Figure BDA0003693936920000098
Figure BDA0003693936920000099
Figure BDA00036939369200000910
Figure BDA00036939369200000911
wherein:
∈ E the ratio of conversion of the latent population to the infected, beta I The recovery rate for the infected population;
s34: taking logarithm to likelihood function L (theta) to obtain J (theta), and setting parameter to epsilon E ,β I And (3) solving the partial derivative to obtain the following equation:
Figure BDA00036939369200000912
Figure BDA00036939369200000913
let equation left be 0, obtain parameter solution result:
Figure BDA00036939369200000914
s4: and predicting the number of infected persons based on the time-lag random infectious disease model with the determined parameters, and dynamically determining the number of beds according to the predicted number.
In the step S4, predicting the number of patients based on the time-lag stochastic infectious disease model with the determined parameters, and dynamically determining the number of beds according to the predicted number, including:
substituting the numbers of susceptible people, latent people, isolated people, infected people and recovery people at the initial moment into a time-lag random infectious disease model with determined parameters, and outputting the result by the model
Figure BDA00036939369200000915
The method comprises the steps of obtaining the state conversion results of different crowds at the current moment, simultaneously representing the crowds of different crowds at the next moment, obtaining the infected crowd number and the isolated crowd number at the predicted moment, determining the bed number of the infectious disease infected crowd and the bed number of the isolated crowd in advance according to the infected crowd number and the isolated crowd number at the predicted moment, and achieving dynamic quantification of the infectious disease bed.
Example 2:
as shown in fig. 2, the functional block diagram of the apparatus for quantifying the dynamic state of an infectious disease bed based on time lag analysis according to an embodiment of the present invention is provided, which can implement the method for quantifying the dynamic state of an infectious disease bed based on time lag analysis in embodiment 1.
The infectious disease bed dynamic quantification device 100 based on time lag analysis can be installed in electronic equipment. According to the realized function, the infectious disease bed dynamic quantification device based on time lag analysis can comprise an infectious disease model construction device 101, an information data acquisition device 102 and an infectious disease bed dynamic quantification device 103. The module of the present invention, which may also be referred to as a unit, refers to a series of computer program segments that can be executed by a processor of an electronic device and that can perform a fixed function, and that are stored in a memory of the electronic device.
The infectious disease model construction device 101 is used for constructing a time-lag random infectious disease model under a noise disturbance condition, analyzing the steady-state characteristics of the time-lag random infectious disease model based on a basic regeneration number, and determining time-lag random infectious disease model parameters under a complete information condition by using a maximum likelihood estimation method under a continuous observation condition, wherein the time-lag random infectious disease model parameters comprise an infectious disease infection coefficient and a rehabilitation coefficient;
the information data acquisition device 102 is used for acquiring information data of the affected people;
and the infectious disease bed dynamic quantification device 103 is used for predicting the number of infected persons based on the time-lag random infectious disease model with the determined parameters and dynamically determining the number of beds according to the predicted number of persons.
In detail, in the embodiment of the present invention, when the modules in the apparatus 100 for quantifying the bed status of an infectious disease based on time-lag analysis are used, the same technical means as the method for quantifying the bed status of an infectious disease based on time-lag analysis described in fig. 1 are used, and the same technical effects can be produced, which is not described herein again.
Example 3:
fig. 3 is a schematic structural diagram of an electronic device for implementing a time lag analysis-based infectious disease bed dynamic quantification method according to an embodiment of the present invention.
The electronic device 1 may comprise a processor 10, a memory 11 and a bus, and may further comprise a computer program, such as a bed dynamics quantification program 12 based on time lag analysis, stored in the memory 11 and executable on the processor 10.
The memory 11 includes at least one type of readable storage medium, which includes flash memory, removable hard disk, multimedia card, card-type memory (e.g., SD or DX memory, etc.), magnetic memory, magnetic disk, optical disk, etc. The memory 11 may in some embodiments be an internal storage unit of the electronic device 1, e.g. a removable hard disk of the electronic device 1. The memory 11 may also be an external storage device of the electronic device 1 in other embodiments, such as a plug-in mobile hard disk, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash memory Card (Flash Card), and the like, provided on the electronic device 1. Further, the memory 11 may also include both an internal storage unit and an external storage device of the electronic device 1. The memory 11 may be used not only to store application software installed in the electronic device 1 and various types of data, such as codes of the time lag analysis-based epidemic bed dynamic quantification program 12, but also to temporarily store data that has been output or will be output.
The processor 10 may be formed of an integrated circuit in some embodiments, for example, a single packaged integrated circuit, or may be formed of a plurality of integrated circuits packaged with the same function or different functions, including one or more Central Processing Units (CPUs), microprocessors, digital Processing chips, graphics processors, and combinations of various control chips. The processor 10 is a Control Unit (Control Unit) of the electronic device, connects various components of the electronic device by using various interfaces and lines, and executes various functions and processing data of the electronic device 1 by running or executing programs or modules (an infectious disease bed dynamic quantification program based on time lag analysis, and the like) stored in the memory 11 and calling data stored in the memory 11.
The bus may be a Peripheral Component Interconnect (PCI) bus, an Extended Industry Standard Architecture (EISA) bus, or the like. The bus may be divided into an address bus, a data bus, a control bus, etc. The bus is arranged to enable connection communication between the memory 11 and at least one processor 10 or the like.
Fig. 3 only shows an electronic device with components, and it will be understood by a person skilled in the art that the structure shown in fig. 3 does not constitute a limitation of the electronic device 1, and may comprise fewer or more components than shown, or a combination of certain components, or a different arrangement of components.
For example, although not shown, the electronic device 1 may further include a power supply (such as a battery) for supplying power to each component, and preferably, the power supply may be logically connected to the at least one processor 10 through a power management device, so as to implement functions of charge management, discharge management, power consumption management, and the like through the power management device. The power supply may also include any component of one or more dc or ac power sources, recharging devices, power failure detection circuitry, power converters or inverters, power status indicators, and the like. The electronic device 1 may further include various sensors, a bluetooth module, a Wi-Fi module, and the like, which are not described herein again.
Further, the electronic device 1 may further include a network interface, and optionally, the network interface may include a wired interface and/or a wireless interface (such as a WI-FI interface, a bluetooth interface, etc.), which are generally used for establishing a communication connection between the electronic device 1 and other electronic devices.
Optionally, the electronic device 1 may further comprise a user interface, which may be a Display (Display), an input unit (such as a Keyboard), and optionally a standard wired interface, a wireless interface. Alternatively, in some embodiments, the display may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, an OLED (Organic Light-Emitting Diode) touch device, or the like. The display, which may also be referred to as a display screen or display unit, is suitable for displaying information processed in the electronic device 1 and for displaying a visualized user interface, among other things.
It is to be understood that the described embodiments are for purposes of illustration only and that the scope of the appended claims is not limited to such structures.
The time lag analysis based epidemic bed dynamics quantification program 12 stored in the memory 11 of the electronic device 1 is a combination of a plurality of instructions, which when executed in the processor 10, can realize:
constructing a time-lag random infectious disease model under a noise disturbance condition;
analyzing the steady-state characteristic of the time-lag random infectious disease model based on the basic regeneration number, and determining the ambiguity of the time-lag random infectious disease model;
acquiring information data of an infected crowd, and determining time-lag random infectious disease model parameters under a complete information condition by using a maximum likelihood estimation method under a continuous observation condition;
predicting the number of infected persons based on the time-lag random infectious disease model with the determined parameters, and dynamically determining the number of beds according to the predicted number.
Specifically, the specific implementation method of the processor 10 for the instruction may refer to the description of the relevant steps in the embodiments corresponding to fig. 1 to fig. 3, which is not repeated herein.
It should be noted that the above-mentioned numbers of the embodiments of the present invention are merely for description, and do not represent the merits of the embodiments. And the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, apparatus, article, or method that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, apparatus, article, or method. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other like elements in a process, apparatus, article, or method that includes the element.
Through the above description of the embodiments, those skilled in the art will clearly understand that the method of the above embodiments can be implemented by software plus a necessary general hardware platform, and certainly can also be implemented by hardware, but in many cases, the former is a better implementation manner. Based on such understanding, the technical solution of the present invention may be embodied in the form of a software product, which is stored in a storage medium (e.g., ROM/RAM, magnetic disk, optical disk) as described above and includes instructions for enabling a terminal device (e.g., a mobile phone, a computer, a server, or a network device) to execute the method according to the embodiments of the present invention.
The above description is only a preferred embodiment of the present invention, and not intended to limit the scope of the present invention, and all modifications of equivalent structures and equivalent processes, which are made by using the contents of the present specification and the accompanying drawings, or directly or indirectly applied to other related technical fields, are included in the scope of the present invention.

Claims (7)

1. A method for dynamically quantifying an infectious disease bed based on time lag analysis is characterized by comprising the following steps:
s1: constructing a time-lag random infectious disease model under a noise disturbance condition, wherein the time-lag random infectious disease model comprises 5 types of susceptible people, latent people, isolated people, infected people and recovery people, and establishing a state conversion relation of the 5 types of people based on a random differential equation;
s2: analyzing the steady-state characteristics of the time-lag random infectious disease model based on the basic regeneration number, determining the ambiguity resolution of the time-lag random infectious disease model, and ensuring the validity of the time-lag random infectious disease model;
s3: collecting information data of an infected crowd, and determining time-lag random infectious disease model parameters under a complete information condition by using a maximum likelihood estimation method under a continuous observation condition, wherein the maximum likelihood estimation method under the continuous observation condition comprises the following steps:
determining time-lag random infectious disease model parameters under a complete information condition by using a maximum likelihood estimation method under a continuous observation condition, wherein the time-lag random infectious disease model parameters comprise an infectious disease infection coefficient and a recovery coefficient, and the maximum likelihood estimation method under the continuous observation condition comprises the following steps:
s31: for any ith state transition, if S (t) i )，E(t i )，I(t i ) Has not switched, the ith state switch is switched in the time interval delta t i The exponential distribution obeyed when:
Figure FDA0003693936910000011
Figure FDA0003693936910000012
Figure FDA0003693936910000013
Figure FDA0003693936910000014
then the probability of this section, L 1 (θ) is:
Figure FDA0003693936910000015
theta is a parameter to be solved of the time-lag stochastic infectious disease model;
Ω 1 is S (t) i )，E(t i )，I(t i ) A set of transition times for which the state of (a) has not been transitioned;
s32: for any ith state transition, if I (t) i ) The state of (b) is changed, the ith state change is carried out at time interval delta t i The probability obeyed is:
p{I(t i ) Increase } - [ alpha ] SI S(t i )I(t i )Δt i
p{I(t i ) Decreasing ∈ E E E(t i -τ)-(ε+∈ I +β I +μ I )I(t i )Δt i
Then the probability of this section L 2 (θ) is:
Figure FDA0003693936910000016
Ω 2 is I (t) i ) Increased set of state transition times, Ω 3 Is I (t) i ) A reduced set of state transition times;
s33: constructing a likelihood function L (θ):
Figure FDA0003693936910000017
Figure FDA0003693936910000018
Figure FDA0003693936910000019
Figure FDA00036939369100000110
Figure FDA00036939369100000111
wherein:
∈ E the ratio of conversion of the latent population to the infected, beta I The recovery rate for the infected population;
s34: taking logarithm to likelihood function L (theta) to obtain J (theta), and setting parameter to epsilon E ，β I And (3) solving the partial derivative to obtain the following equation:
Figure FDA0003693936910000021
Figure FDA0003693936910000022
let equation left be 0, obtain parameter solution result:
Figure FDA0003693936910000023
s4: and predicting the number of infected persons based on the time-lag random infectious disease model with the determined parameters, and dynamically determining the number of beds according to the predicted number.
2. The method for quantification of infectious disease bed dynamics based on time lag analysis according to claim 1, wherein the step of S1 is to construct a time-lag stochastic infectious disease model under noise disturbance conditions, comprising:
constructing a time-lag random infectious disease model under a noise disturbance condition, wherein the noise disturbance is Brownian motion disturbance, the time-lag random infectious disease model comprises 5 types of susceptible population, latent population, isolated population, infected population and recovery population, and the constructed model is as follows:
Figure FDA0003693936910000024
wherein:
(s) (t) represents the number of susceptible population at time t, e (t) represents the number of latent population at time t, i (t) represents the number of infected population at time t, q (t) represents the number of isolated population at time t, r (t) represents the number of recovery population at time t;
α SE indicates the contact rate, alpha, between the susceptible population and the latent population SI Indicating the contact rate of susceptible and infected persons;
epsilon represents the natural mortality rate;
Brow S (t)，Brow E (t)，Brow I (t)，Brow Q (t)，Brow R (t) noise disturbances, σ, respectively, suffered by the class 5 population S ，σ E ，σ I ，σ Q ，σ R Respectively the intensity of the corresponding noise disturbance;
∈ E represents the ratio of the latent population to the infected, E I Indicates the cause mortality of the infected population, E Q Indicating disease mortality in the quarantine population;
β E indicates the recovery rate of the latent population, beta I Indicates the recovery rate of the infected population, beta Q Indicating the recovery rate of the isolated population;
μ E represents the ratio of the potential population isolated, μ I Representing the rate at which infected persons are isolated;
τ represents the latency time lag of infectious disease;
infection coefficient of the infectious disease and rehabilitationThe coefficient is a parameter to be solved of a time-lag random infectious disease model, wherein the infectious disease infection coefficient comprises the ratio epsilon of a latent population to an infected person E The recovery factor comprises the recovery rate beta of the infected people I 。
3. The method of claim 2, wherein the step of S2 of calculating the basic regeneration number of the time-lapse stochastic infectious disease model comprises:
the calculation formula of the basic regeneration number is as follows:
Figure FDA0003693936910000025
wherein:
a represents the initial number of susceptible population;
R 0 the basic regeneration number of a time-lag random infectious disease model represents the number of second-generation cases which can be infected when one infectious case enters a susceptible population and is not interfered by an external force; if R is 0 If the number of the infectious diseases is more than 1, the infectious diseases can spread to the whole crowd;
if R is 0 If the ratio is 1 or less, the infectious disease tends to disappear.
4. The method for quantification of infectious disease bed dynamics based on time lag analysis according to claims 2-3, wherein the step of S2 for determining ambiguity of time lag stochastic infectious disease model comprises:
basic regeneration number R of random infectious disease model when time lag 0 When the time lag random infectious disease model is less than or equal to 1, the left formula of the time lag random infectious disease model is 0, and a disease-free balance point n exists in the time lag random infectious disease model 0 (A/ε,0,0,0,0), the disease-free equilibrium point n 0 Due to noise disturbance, fluctuation size and noise intensity sigma S Is in positive correlation;
basic regeneration number R of time-lag stochastic infectious disease model 0 When the time is more than 1, the left formula of the time-lag random infectious disease model is 0, and the time-lag random infectious disease modelSolution (S) of model at time t → ∞ * ，E * ，I * ，Q * ，R * ) Satisfies the following formula:
Figure FDA0003693936910000031
wherein:
F(k)＝(S(k)-S * ) 2 +(E(k)-E * ) 2 +(I(k)-I * ) 2 +(Q(k)-Q * ) 2 +(R(k)-R * ) 2 ；
Brown＝σ S (S * ) 2 +σ E (E * ) 2 +σ I (I * ) 2 +σ Q (Q * ) 2 +σ R (R * ) 2 ；
sup {. is solving the supremum bound;
time lag stochastic infectious disease model solution (S) at time t → ∞ * ，E * ，I * ，Q * ，R * ) Because the noise disturbance can generate fluctuation, the fluctuation size is in positive correlation with the noise intensity, and the smaller the noise intensity is, (S) * ，E * ，I * ，Q * ，R * ) The closer to the unique point of endemic balance;
the time-lapse stochastic infectious disease model generates a basic regeneration number R along with the reduction of the noise intensity 0 When the regeneration number is less than or equal to 1, the regeneration number approaches to a unique disease-free equilibrium point 0 The point > 1 approaches a unique point of local disease balance.
5. The method of claim 1, wherein the step of collecting information data of the affected person in step S3 comprises:
the information data of the affected group is multivariate random observation data, and the time range of the information data of the affected group is [0, T]In the time range [0, T]The state conversion of { S (t), E (t), I (t), Q (t), R (t) } takes place for M times, and the time of the state conversion of the ith time ist i ，Δt i ＝t i+1 -t i ，t i ∈[0，t]1, 2.. M, the acquisition result of the information data of the affected group is as follows:
{data i ＝(t i ，S(t i )，E(t i )，I(t i )，Q(t i )，R(t i ))|i＝1，2，...，M，t i ∈[0，T]}
wherein:
S(t i )，E(t i )，I(t i )，Q(t i )，R(t i ) Are each t i The number of susceptible people, the number of latent people, the number of infected people, the number of isolated people and the number of recovery people at the moment.
6. The method of claim 1, wherein the step of S4, based on the parameter-determining time-lapse stochastic infectious disease model, predicts the number of patients, and dynamically determines the number of beds according to the predicted number, comprising:
substituting the numbers of susceptible people, latent people, isolated people, infected people and recovery people at the initial moment into a time-lag random infectious disease model with determined parameters, and outputting the result by the model
Figure FDA0003693936910000032
The method is characterized in that the method is a state conversion result of different crowds at the current moment, meanwhile, the number of the crowds of the different crowds at the next moment is represented, the number of infected crowds and the number of isolated crowds at the predicted moment are obtained, and the number of beds of the infected crowds and the number of isolated crowds at the predicted moment are determined in advance according to the number of the infected crowds and the number of the isolated crowds at the predicted moment.
7. An infectious disease bed dynamic quantification device based on time lag analysis, characterized in that the device comprises:
the infectious disease model construction device is used for constructing a time-lag random infectious disease model under a noise disturbance condition, analyzing the steady-state characteristics of the time-lag random infectious disease model based on a basic regeneration number, and determining time-lag random infectious disease model parameters under a complete information condition by using a maximum likelihood estimation method under a continuous observation condition, wherein the time-lag random infectious disease model parameters comprise an infectious disease infection coefficient and a rehabilitation coefficient;
the information data acquisition device is used for acquiring information data of the infected people;
the device for dynamically quantifying the infectious disease bed is used for predicting the number of infected persons based on a time-lag random infectious disease model with determined parameters and dynamically determining the number of beds according to the predicted number of persons so as to realize the method for dynamically quantifying the infectious disease bed based on time-lag analysis as claimed in any one of claims 1 to 6.
CN202210668571.7A 2022-06-14 2022-06-14 Infectious disease bed dynamic quantification method based on time lag analysis Withdrawn CN114999619A (en)

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Publication number Priority date Publication date Assignee Title
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN115331796A (en) * 2022-10-17 2022-11-11 中科厚立信息技术(成都)有限公司 Intensive learning-based sickbed resource allocation optimization method, system and terminal

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