CN118116614A - Disease transmission dynamics method based on dynamic isolation - Google Patents
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- 238000002955 isolation Methods 0.000 title claims abstract description 94
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- 238000007781 pre-processing Methods 0.000 claims abstract description 7
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Abstract
The invention belongs to the field of research of complex networks and propagation dynamics, and particularly relates to a disease propagation dynamics method based on dynamic isolation, which comprises the steps of collecting social relationship data of people and preprocessing the social relationship data, and constructing the obtained preprocessed data into a complex network; classifying the nodes in the constructed network and calculating importance indexes of the nodes in the network, and laying a cushion for the construction of a subsequent propagation dynamics model and the calculation of dynamic isolation indexes; comprehensively calculating the calculated node importance indexes to obtain indexes of improved dynamic isolation measures; introducing the dynamic isolation index into the propagation dynamics model to obtain a propagation dynamics model based on dynamic isolation, namely SEIQR model; the propagation dynamics model is propagated on a complex network, compared with the propagation condition without isolation and the condition of removing isolation nodes in different propagation periods, the coverage rate of diseases in the network after the propagation reaches a steady state is observed; the invention is expected to realize more effective prevention and control in a real-world transmission scene, and provides an innovative solution for coping with future infectious disease challenges.
Description
Technical Field
The invention belongs to the field of complex networks and propagation dynamics, and particularly relates to a disease propagation dynamics method based on dynamic isolation.
Background
In recent years, various epidemic diseases are frequently exploded worldwide, so that not only is the safety of human survival threatened, but also the economic and social orders are greatly damaged, and the epidemic diseases have attracted high attention from all human beings.
The human social relationship can be well described in a complex network. As an emerging discipline, complex networks are a research hotspot in the academia due to their wide applicability and develop rapidly. In the real world, creating complex network models helps to study various practical problems in detail. The main steps of studying disease transmission on complex networks include the following: first, the problem of disease transmission in real life is converted into a corresponding mathematical model, which is then converted into a mathematical problem. Secondly, a targeted propagation model is proposed according to a propagation mechanism specific to the disease. The propagation process is then integrated into the model and simulated using a computer. Finally, analyzing the rule of disease transmission according to the simulation experiment result and providing an effective prevention and control strategy.
Current disease transmission control methods rely primarily on fixed isolation measures, such as blocking, isolating areas, etc. These measures are usually implemented based on pre-established protocols and cannot flexibly adapt to the changes of different propagation dynamics and social environments. Thus, there is a need for an isolation strategy that can be dynamically adjusted to optimize based on real-time propagation dynamics information and social feedback. The introduction of dynamic isolation can better balance the relationship between disease spread control and normal operation of society.
Disclosure of Invention
Aiming at the defects existing in the prior art, the invention aims to provide a disease transmission dynamic method based on dynamic isolation, which is used for simulating the disease transmission process in a complex network, and the damage of diseases to nodes in the network is reduced by using corresponding dynamic isolation strategies in networks with different topological structures, so that the safety of the nodes is ensured.
In order to achieve the above purpose, the present invention provides the following technical solutions:
S1: collecting social relation data of people and preprocessing the social relation data, and constructing the preprocessed data into a complex network;
S2: classifying the nodes in the constructed network and calculating importance indexes of the nodes in the network, and laying a cushion for the construction of a subsequent propagation dynamics model and the calculation of dynamic isolation indexes;
S3: comprehensively calculating the calculated node importance indexes to obtain indexes of improved dynamic isolation measures;
s4: introducing the dynamic isolation index into the propagation dynamics model to obtain a propagation dynamics model based on dynamic isolation, namely SEIQR model;
S5: the propagation dynamics model is propagated on a complex network, and compared with the propagation condition without isolation and the condition of node isolation in different propagation periods, the coverage rate of diseases in the network after the propagation reaches a steady state is observed.
Preferentially, the process of preprocessing social relation data of the crowd and constructing a complex network comprises the following steps:
S11: social relationship data of the crowd is collected, individuals in the crowd are regarded as a node on the network, and the relationship between the individuals is expressed as edges in the network, so that the whole crowd forms a social contact network. Abstracting the network into a graph g= { V, E }, where V is a node set and E is an edge set between nodes;
s12: different types of social groups are distinguished, an applicable complex network model is selected, the selection of the model is based on the collected data characteristics so as to better reflect the actual situation of interpersonal relationship, and the selection of a proper topological structure can also better simulate the characteristics of an actual system.
Further, the process of classifying the nodes in the network and calculating the node importance index includes:
s21: nodes in the network are divided into different categories of susceptibility (S), latency (E), affected person (I), isolation (Q) and rehabilitation person (R);
s22: calculating the degree centrality of nodes in a network, wherein the node degree refers to the number of directly connected nodes with other nodes, and the calculation formula of the degree centrality is as follows:
Where N degree represents the degree of the node and N represents the number of nodes;
S23: the median centrality of a node in the network, i.e. the number of times all shortest paths in the network pass through the node, is calculated. Nodes with high betweenness centrality take important bridge roles in the network; the calculation formula of the median centrality of the node v i is as follows:
Where g ij represents the number of shortest paths from vertex i to vertex j, g ij(vi) represents the number of shortest paths from vertex i to vertex j through vertex v i.
Further, the process of calculating the dynamic isolation measure index comprises the following steps:
S31: for a globally known network, a dynamic isolation measure is adopted, the strategy takes each I-state node as a center, finds out all node sets except isolated or R-state in the range taking omega+1 (omega is a disease latency parameter) as path lengths as candidate isolation objects, and calculates the following three values of first-order neighbors of the nodes: and taking the product of the sum of centrality, the sum of intermediate centrality and the sum of shortest path length from each I-state node as the weight of the node dynamic isolation measure. The calculation formula is as follows:
Where τ (I) is a first-order neighbor node set of node I (excluding nodes that have been isolated or have become R-state), k (j) represents a degree value of a neighbor j of node I, V is a set of all nodes in the network, σ mn (j) represents a shortest path number from node m to node n through node j, σ mn represents a shortest path number between node m and node n, I is a set of all I-state nodes converted from E at a certain time, and d sj represents a shortest path length between I-state nodes s and node j;
s32: for a network which is locally known but globally unknown, adopting a dynamic isolation measure, wherein the isolation strategy takes omega+1 order neighbor node sets of each I-state node as candidate isolation objects, and calculating the number of connecting edges of the nodes and neighbors and the number of adjacent infected nodes. The weight of the node dynamic isolation measure is calculated, and the formula is as follows:
Where k (i) represents the degree value of the neighboring node of node i and p (i) represents the number of neighboring infected nodes of node i.
Further, the process of constructing the propagation dynamics model comprises the following steps:
S41: first, randomly selecting an individual in the propagation network as an infected person who will de-infect S in the neighborhood with a β probability;
s42: each S that comes into contact with the infected person immediately converts to E, shows symptoms after a latency period to I, and is immediately sent to the point hospital for treatment to R once I is reached;
s43: carrying out isolation observation on S, E related to I, converting the isolation to an isolator Q, recovering the uninfected disease to S after the isolation period is finished and recovering the uninfected disease to a transmission network, wherein the infected disease shows that the symptom is changed into I and then sent to a hospital for treatment to be changed into R in the isolation process;
s44: when the R-state node density in the propagation network is no longer changed with time, the system reaches a steady state, and the propagation is ended.
Further, the process of simulating propagation of the propagation dynamics model in the network includes:
S51: two different dynamic isolation measures are adopted on networks with different topological structures to simulate disease transmission, and the coverage rate of the disease in the networks is observed;
S52: in different propagation processes, for example, in the early, middle and later stages of disease propagation, dynamic isolation measures are adopted to observe the coverage rate of the disease in the network, so that the specific node can be isolated more effectively by isolating the specific node in the specific propagation process.
The invention has the beneficial effects that: according to the invention, a complex network is used for simulating the real world, wherein a uniform network and a non-uniform network and truly simulate different groups, so that the disease transmission prediction and control capability can be more accurate; in addition, the isolation strategy can be adjusted in real time, and the flexibility enables the prevention and control measures to be more suitable for different propagation scenes, so that the coping capacity of disease propagation is improved; finally, the invention can furthest lighten the influence of disease prevention and control on society and economy, and the flexible isolation strategy and the social adaptability design lead the control measures to be more in line with the actual demands, thereby being beneficial to keeping the normal order of social operation.
Drawings
The invention will be described in further detail with reference to the drawings and the detailed description.
FIG. 1 is a flow chart of a dynamic isolation-based disease propagation kinetics method in accordance with the present invention;
FIG. 2 is a schematic representation of a model of propagation dynamics SEIQR of the present invention;
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
FIG. 1 is a flow chart of a dynamic isolation-based disease propagation dynamics method according to the present invention, the method comprising: collecting social relation data of people and preprocessing a data set; constructing a complex network by using the data set, and constructing networks with different topological structures according to the characteristics of the network; calculating an importance index of the network node; calculating indexes of dynamic isolation measures according to the calculated factors such as node importance and the like; constructing a propagation dynamics model, and introducing an isolation state; finally, in different topological structures, adopting different isolation indexes and different time isolation measures to observe the coverage rate of viruses in a network; FIG. 2 is a schematic representation of a model of the propagation dynamics SEIQR of the present invention, the basic idea of which is to divide the total population (N) into susceptible population (S), exposed population (E), infected population (I), isolated population (Q) and recovered population (R),
The specific process of the disease transmission dynamics method based on dynamic isolation comprises the following steps:
S1: collecting social relation data of people and preprocessing the social relation data, and constructing the preprocessed data into a complex network;
In the embodiment of the present invention, the step S1 specifically includes:
S11: social relationship data of the crowd is collected, individuals in the crowd are regarded as a node on the network, and the relationship between the individuals is expressed as edges in the network, so that the whole crowd forms a social contact network. Abstracting the network into a graph g= { V, E }, where V is a node set and E is an edge set between nodes;
S12: distinguishing different types of social groups, selecting an applicable complex network model, wherein the complex network can be divided into a uniform network and a heterogeneous network, the uniform network has random connection, equal probability connection and small world characteristics, the connection between all nodes has the same probability, and the network characteristics are suitable for class groups; while heterogeneous networks have no scalability, few nodes have extremely high degrees, and most nodes are relatively low, the network characteristics are adapted to community groups; constructing two networks with different topological structures to simulate the reality;
S2: classifying the nodes in the constructed network and calculating importance indexes of the nodes in the network, and laying a cushion for the construction of a subsequent propagation dynamics model and the calculation of dynamic isolation indexes;
in the embodiment of the present invention, the step S2 specifically includes:
s21: nodes in the network are divided into different categories of susceptibility (S), latency (E), affected person (I), isolation (Q) and rehabilitation person (R);
s22: calculating the degree centrality of nodes in a network, wherein the node degree refers to the number of directly connected nodes with other nodes, and the calculation formula of the degree centrality is as follows:
Where N degree represents the degree of the node and N represents the number of nodes;
S23: the median centrality of a node in the network, i.e. the number of times all shortest paths in the network pass through the node, is calculated. Nodes with high betweenness centrality take important bridge roles in the network; the calculation formula of the median centrality of the node v i is as follows:
Where g ij represents the number of shortest paths from vertex i to vertex j, g ij(vi) represents the number of shortest paths from vertex i to vertex j through vertex v i.
S3: comprehensively calculating the calculated node importance indexes to obtain indexes of improved dynamic isolation measures;
In the embodiment of the present invention, the step S3 specifically includes:
S31: for a globally known network, a dynamic isolation measure is adopted, the strategy takes each I-state node as a center, finds out all node sets except isolated or R-state in the range taking omega+1 (omega is a disease latency parameter) as path lengths as candidate isolation objects, and calculates the following three values of first-order neighbors of the nodes: and taking the product of the sum of centrality, the sum of intermediate centrality and the sum of shortest path length from each I-state node as the weight of the node dynamic isolation measure. The calculation formula is as follows:
Where τ (I) is a first-order neighbor node set of node I (excluding nodes that have been isolated or have become R-state), k (j) represents a degree value of a neighbor j of node I, V is a set of all nodes in the network, σ mn (j) represents a shortest path number from node m to node n through node j, σ mn represents a shortest path number between node m and node n, I is a set of all I-state nodes converted from E at a certain time, and d sj represents a shortest path length between I-state nodes s and node j;
s32: for a network which is locally known but globally unknown, adopting a dynamic isolation measure, wherein the isolation strategy takes omega+1 order neighbor node sets of each I-state node as candidate isolation objects, and calculating the number of connecting edges of the nodes and neighbors and the number of adjacent infected nodes. The weight of the node dynamic isolation measure is calculated, and the formula is as follows:
Where k (i) represents the degree value of the neighboring node of node i and p (i) represents the number of neighboring infected nodes of node i.
S4: introducing the dynamic isolation index into the propagation dynamics model to obtain a propagation dynamics model based on dynamic isolation, namely SEIQR model;
In the embodiment of the present invention, the step S4 specifically includes:
S41: first, randomly selecting an individual in the propagation network as an infected person who will de-infect S in the neighborhood with a β probability;
s42: each S that comes into contact with the infected person immediately converts to E, shows symptoms after a latency period to I, and is immediately sent to the point hospital for treatment to R once I is reached;
s43: carrying out isolation observation on S, E related to I, converting the isolation to an isolator Q, recovering the uninfected disease to S after the isolation period is finished and recovering the uninfected disease to a transmission network, wherein the infected disease shows that the symptom is changed into I and then sent to a hospital for treatment to be changed into R in the isolation process;
s44: when the R-state node density in the propagation network is no longer changed with time, the system reaches a steady state, and the propagation is ended.
The basic idea of the SEIQR model is to divide the total population (N) into susceptible population (S), exposed population (E), infected population (I), isolated population (Q) and recovered population (R), i.e. the following relationship exists at time t:
N＝S(t)+E(t)+I(t)+Q(t)+R(t)
The basic assumption of this model is: the total population N is unchanged and only the infectivity of the infected population I is considered, not the infectivity of the exposed population E and the isolated population Q. Thus, this model can be described by the following set of differential equations:
wherein, beta is the infection rate; sigma is the incidence of disease; p is the detection rate; gamma is the recovery rate.
S5: the propagation dynamics model is propagated on a complex network, and compared with the propagation condition without isolation and the condition of node isolation in different propagation periods, the coverage rate of diseases in the network after the propagation reaches a steady state is observed.
In the embodiment of the present invention, the step S5 specifically includes:
S51: two different dynamic isolation measures are adopted on networks with different topological structures to simulate disease transmission, and the coverage rate of the disease in the networks is observed;
S52: in different propagation processes, for example, in the early, middle and later stages of disease propagation, dynamic isolation measures are adopted to observe the coverage rate of the disease in the network, so that the specific node can be isolated more effectively by isolating the specific node in the specific propagation process.
While the foregoing is directed to embodiments, aspects and advantages of the present invention, other and further details of the invention may be had by the foregoing description, it will be understood that the foregoing embodiments are merely exemplary of the invention, and that any changes, substitutions, alterations, etc. which may be made herein without departing from the spirit and principles of the invention.
Claims (6)
1. A disease transmission dynamics method based on dynamic isolation is characterized by collecting social relation data of people and preprocessing the social relation data, constructing the preprocessed data into a complex network, calculating importance indexes of nodes in the network, synthesizing the importance indexes of the nodes to obtain dynamic isolation measures, introducing the dynamic isolation measures into transmission dynamics, and performing simulation on the networks with different topological structures to obtain the coverage rate of diseases in the final network.
The disease transmission dynamics method based on dynamic isolation specifically comprises the following steps:
S1: collecting social relation data of people and preprocessing the social relation data, and constructing the preprocessed data into a complex network;
S2: classifying the nodes in the constructed network and calculating importance indexes of the nodes in the network, and laying a cushion for the construction of a subsequent propagation dynamics model and the calculation of dynamic isolation indexes;
S3: comprehensively calculating the calculated node importance indexes to obtain indexes of improved dynamic isolation measures;
S4: introducing the dynamic isolation index into a propagation dynamics model to obtain a propagation dynamics model based on dynamic isolation, namely a SEIQR (Susceptible-Exposed-Infected-Quarantined-Recovered) model;
S5: the propagation dynamics model is propagated on a complex network, and compared with the propagation condition without isolation and the condition of node isolation in different propagation periods, the coverage rate of diseases in the network after the propagation reaches a steady state is observed.
2. The dynamic isolation-based disease propagation kinetics method according to claim 1, wherein the step S1 specifically comprises:
S11: social relationship data of the crowd is collected, individuals in the crowd are regarded as a node on the network, and the relationship between the individuals is expressed as edges in the network, so that the whole crowd forms a social contact network. Abstracting the network into a graph g= { V, E }, where V is a node set and E is an edge set between nodes;
s12: different types of social groups are distinguished, an applicable complex network model is selected, the selection of the model is based on the collected data characteristics so as to better reflect the actual situation of interpersonal relationship, and the selection of a proper topological structure can also better simulate the characteristics of an actual system.
3. The dynamic isolation-based disease propagation kinetics method according to claim 1, wherein the step S2 specifically comprises:
s21: nodes in the network are divided into different categories of susceptibility (S), latency (E), affected person (I), isolation (Q) and rehabilitation person (R);
s22: calculating the degree centrality of nodes in a network, wherein the node degree refers to the number of directly connected nodes with other nodes, and the calculation formula of the degree centrality is as follows:
Where N degree represents the degree of the node and N represents the number of nodes;
S23: the median centrality of a node in the network, i.e. the number of times all shortest paths in the network pass through the node, is calculated. Nodes with high betweenness centrality take important bridge roles in the network; the calculation formula of the median centrality of the node v i is as follows:
Where g ij represents the number of shortest paths from vertex i to vertex j, g ij(vi) represents the number of shortest paths from vertex i to vertex j through vertex v i.
4. The dynamic isolation-based disease propagation kinetics method according to claim 1, wherein the step S3 specifically comprises:
S31: for a globally known network, a dynamic isolation measure is adopted, the strategy takes each I-state node as a center, finds out all node sets except isolated or R-state in the range taking omega+1 (omega is a disease latency parameter) as path lengths as candidate isolation objects, and calculates the following three values of first-order neighbors of the nodes: and taking the product of the sum of centrality, the sum of intermediate centrality and the sum of shortest path length from each I-state node as the weight of the node dynamic isolation measure. The calculation formula is as follows:
Where τ (I) is a first-order neighbor node set of node I (excluding nodes that have been isolated or have become R-state), k (j) represents a degree value of a neighbor j of node I, V is a set of all nodes in the network, σ mn (j) represents a shortest path number from node m to node n through node j, σ mn represents a shortest path number between node m and node n, I is a set of all I-state nodes converted from E at a certain time, and d sj represents a shortest path length between I-state nodes s and node j;
s32: for a network which is locally known but globally unknown, adopting a dynamic isolation measure, wherein the isolation strategy takes omega+1 order neighbor node sets of each I-state node as candidate isolation objects, and calculating the number of connecting edges of the nodes and neighbors and the number of adjacent infected nodes. The weight of the node dynamic isolation measure is calculated, and the formula is as follows:
Where k (i) represents the degree value of the neighboring node of node i and p (i) represents the number of neighboring infected nodes of node i.
5. The dynamic isolation-based disease propagation kinetics method according to claim 1, wherein the step S4 specifically comprises:
S41: first, randomly selecting an individual in the propagation network as an infected person who will de-infect S in the neighborhood with a β probability;
s42: each S that comes into contact with the infected person immediately converts to E, shows symptoms after a latency period to I, and is immediately sent to the point hospital for treatment to R once I is reached;
S43: carrying out isolation observation on S, E related to I, converting the isolation into Q, recovering the uninfected disease into S after the isolation period is finished and recovering the uninfected disease into a transmission network, wherein the infected disease shows that the symptom is changed into I and then sent to a hospital for treatment to be changed into R in the isolation process;
s44: when the R-state node density in the propagation network is no longer changed with time, the system reaches a steady state, and the propagation is ended.
6. The dynamic isolation-based disease propagation kinetics method according to claim 1, wherein the step S5 specifically comprises:
S51: two different dynamic isolation measures are adopted on networks with different topological structures to simulate disease transmission, and the coverage rate of the disease in the networks is observed;
S52: in different propagation processes, for example, in the early, middle and later stages of disease propagation, dynamic isolation measures are adopted to observe the coverage rate of the disease in the network, so that the specific node can be isolated more effectively by isolating the specific node in the specific propagation process.
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