Epidemic disease transmission analysis method based on complex network

Abstract

The invention discloses an epidemic propagation analysis method based on a complex network, and belongs to the technical field of epidemic propagation control. The method comprises the following steps: according to a complex network theory, constructing an epidemic disease transmission model of a susceptible state S-exposure state E-infection state I-recovery state R coupling dynamic infection and a forward and reverse contact tracking strategy; acquiring basic parameters according to the infection data of a certain epidemic virus, and substituting the basic parameters into the epidemic disease transmission model to obtain a transmission model of the virus; and analyzing the evolutionary process of the epidemic disease by using a transmission model of the virus. According to the method, the real spreading process of spreading the virus from the parent to the offspring is considered, the parent individuals are screened for tracking, the epidemic spreading process under the contact tracking strategy can be more truly described, the effectiveness of the contact tracking strategy is quantitatively evaluated, and theoretical guidance is provided for formulating a reasonable and efficient epidemic intervention strategy.

Description

Technical Field

[0001] The present invention relates to the technical field of epidemic spread control, and in particular to an epidemic spread analysis method based on a complex network. Background Art

[0002] In the real world, epidemic spread can be simplified as a propagation process on a complex network. Epidemic spread has brought serious harm to human society, and implementing intervention strategies during the spread process can effectively reduce losses. Contact tracing has always been an important strategy for controlling the spread of epidemics, interrupting the transmission chain by isolating infected people and tracking contacts at risk of infection. If infected people and contacts with high transmission risks can be identified quickly and accurately, more infections can be effectively prevented, which is crucial to controlling the spread of large-scale epidemics. Therefore, in the field of epidemic spread control technology, epidemic spread modeling based on complex networks combined with the analysis of contact tracing strategies has important practical significance.

[0003] Existing epidemic transmission modeling methods have shortcomings when considering contact tracing strategies. Many models use random tracking strategies, maximum activity strategies, etc. to determine the individuals to be tracked. They regard parent individuals and offspring individuals as equal individuals, ignoring the actual transmission process of the virus from parent to offspring. It is easy for parent individuals to be omitted, resulting in distorted simulation results and difficulty in evolving the real disease control process. Summary of the invention

[0004] In order to solve the above problems, the present invention provides an epidemic transmission analysis method based on complex networks, which takes into account the real transmission process of the virus from parent generation to offspring, screens parent individuals for tracking, and can more realistically characterize the epidemic transmission process under the contact tracing strategy, quantitatively evaluate the effectiveness of the contact tracing strategy, and provide theoretical guidance for formulating reasonable and efficient epidemic intervention strategies.

[0005] In order to achieve the above object, the solution provided by the present invention is as follows: A method for analyzing epidemic spread based on complex networks, comprising the following steps: S1. Based on complex network theory, an epidemic transmission model of susceptible state S-exposed state E-infected state I-recovered state R is constructed with coupled dynamic infection and forward and reverse contact tracing strategies; during the evolution of the epidemic transmission model, the virus spreads from parent individuals to offspring individuals, and the infected state I individuals enter the detected state D after being detected by themselves. The detected state D individuals are isolated and the individuals who have close contact with the detected state D individuals and have not been isolated are tracked, and then the child-parent relationship between the tracked infected individuals and the detected state D individuals is determined. If the tracked infected individual is the parent individual of the detected state D individual, the close contact individuals of the infected individual will continue to be tracked until no infected individuals are tracked or the tracked infected individuals are all offspring individuals; the tracked infected individuals are all isolated; S2. Obtain basic parameters based on the infection data of a certain epidemic virus, and substitute the basic parameters into the epidemic transmission model to obtain a transmission model of the virus; S3. Analyze the evolution of the epidemic using the virus transmission model.

[0006] As a specific implementation of the present invention, in step S1, constructing the epidemic propagation model includes the following steps: S11. Construct a model network to describe human contact behavior; S12. Constructing an evolution rule for an epidemic transmission model, wherein the evolution rule comprises: The epidemic evolves in the order of susceptible state S-exposed state E-infectious state I-recovered state R, where the susceptible state S is a healthy state that is easily infected, the exposed state E is a state that is contagious after infection and has no symptoms, the infected state I is a state that is contagious after infection and has symptoms, the detected state D is a state where the infected individual is self-detected and isolated after the symptoms appear, and the recovered state R is a healthy state where the infected individual recovers to a non-infectious and not easily infected state; The temporal evolution process of the epidemic transmission model includes the process of increasing and decreasing sources of infection. The process of increasing sources of infection is the process in which unisolated exposed state E and infected state I individuals infect susceptible state S individuals; the process of decreasing sources of infection includes the process in which infected state I individuals are detected and transformed into detected state D, the process in which unisolated infected state I individuals recover to recovered state R, and the process in which exposed state E individuals and infected state I individuals are tracked and identified as infected individuals; recovered state R individuals enter the transmission network, but because they have antibodies, they will not be infected again.

[0007] Furthermore, the evolution process of the epidemic transmission model is carried out in time sequence, and each time step includes the following steps: S121, simulating the process of the exposed state E and infected state I individuals infecting the susceptible state S individuals according to the human contact behavior in the model network, and updating the state of each individual in the model network; the time when the individual enters the exposed state E is the exposure age, and the time when the individual enters the infected state I is the infection age, and the probability of the exposed state E individual and the infected state I individual infecting the susceptible state S individual changes with the exposure age and the infection age respectively; S122. Determine the infected individual detected from the updated infected state I individuals according to the self-detection rate, and convert the infected individual into a detected state D individual. The self-detection rate is the probability that the infected person undergoes self-detection after developing symptoms and is confirmed to be infected. Since self-detection is limited by the self-consciousness of detection, the test kit, and the detection level of the operator, the self-detection rate is often lower than 100%; S123, performing contact tracing on the detected state D individuals added in step S122 one by one in a traversal manner, and the contact tracing of each detected state D individual includes the following steps: S1231, tracking the close contact individuals of the detected state D individual in the network; S1232. Screen out unisolated infected individuals from the close contact individuals, that is, individuals in infection state I or exposure state E but not isolated; S1233. Determine the close contact individuals who have been successfully traced based on the contact tracing success rate and the total number of infected individuals who have not been isolated; S1234. Determine the traced infected individual by combining the tracking detection rate and the total number of close contact individuals that have been successfully traced, and determine whether the traced infected individual is the parent individual of the detected state D individual.

[0008] Taking into account the reasons such as errors in personnel information registration and communication errors, the present invention sets a contact tracing success rate to indicate the probability of successfully tracing a close contact individual. In specific implementation, the product of the contact tracing success rate and the total number of unisolated infected individuals can be used as the number of close contact individuals successfully traced, and then the close contact individuals successfully traced are determined by random selection from the unisolated infected individuals.

[0009] In real life, tracked individuals are generally tested by professional medical institutions, and their self-awareness and accuracy of testing are significantly higher. At this time, the success rate of testing is mainly restricted by the viral load in the infected individual, that is, the success rate varies with the viral load of the infected individual. Therefore, the exposure age or infection age is used to characterize the tracking detection rate of infected individuals who have been successfully detected.

[0010] As a specific implementation of the present invention, in step S1, determining the child-parent relationship between the tracked infected individual and the detected state D individual includes the following steps: S131, using the child-parent relationship calculation formula to determine the child-parent relationship calculation value between the child detected state D individual and the tracked infected individual; ; in, p ij ( f i ; f j ) represents the calculated value of the child-parent relationship; f i Indicates the detected state D individual i How long the symptoms lasted in memory; f j Indicates the detected state D individual i Infected individuals traced j How long the symptoms lasted in memory; f (*) is the probability distribution, where T E Indicates the duration of the exposure period;- T E for T E The opposite of f represents the symptom age of the individual, that is, the length of time since the onset of symptoms in memory; τ represents the infection age of the individual, that is, the length of time since the individual entered the infection state I; S132. Determine the child-parent relationship between the detected state D individual and the tracked infected individual based on the child-parent relationship calculation value and the relationship determination threshold: when the child-parent relationship calculation value is greater than the relationship determination threshold, the detected state D individual is the child individual of the tracked infected individual, otherwise, it is the parent individual.

[0011] As a specific implementation of the present invention, step S3 includes setting a threshold for the number of unisolated infected individuals successfully tracked per unit time. When the number of unisolated infected individuals successfully tracked per unit time reaches the threshold, tracking will be stopped, thereby simulating the evolution process of the epidemic under different resource constraints.

[0012] The present invention has the following beneficial effects: The present invention takes into account the actual transmission process of the virus from parent to offspring, and screens parent individuals for tracking. It can more realistically portray the epidemic transmission process under the contact tracing strategy, quantitatively evaluate the effectiveness of the contact tracing strategy, and provide theoretical guidance for formulating reasonable and efficient epidemic intervention strategies.

[0013] Existing technologies are all based on Markov processes, that is, the exposure age and infection age of individuals are not recorded in the model, and it is assumed that the infection probability and tracking probability of epidemic spread are independent of these ages. The present invention records the exposure age and infection age of individuals in the model, takes into account the impact of the dynamic changes of viral load on the entire transmission process, and can improve the authenticity of the transmission description. BRIEF DESCRIPTION OF THE DRAWINGS

[0014] Figure 1 is a flow chart of an embodiment of the present invention; Figure 2 It is a result diagram of simulating the evolution process of an epidemic under different resource restriction conditions in an embodiment of the present invention. DETAILED DESCRIPTION

[0015] The present invention will be further described in detail below in conjunction with embodiments and drawings, but the embodiments of the present invention are not limited thereto.

[0016] Please refer to Figure 1 The epidemic spread analysis method based on complex network in this embodiment includes the following steps: S1. Based on complex network theory, an epidemic transmission model of susceptible state S-exposed state E-infected state I-recovered state R with coupled dynamic infection and forward and reverse contact tracing strategies is constructed, including the following steps; S11. Construct a model network to describe human contact behavior; This embodiment considers the heterogeneity of individual contact patterns and constructs a contact network with large heterogeneity between nodes and edges. This network consists of 5,000 nodes, each node represents an individual, and the edges between nodes represent interpersonal contacts between individuals. The Barabási-Albert model network is used when constructing the network. The specific steps are as follows: S111, initialize a fully connected graph consisting of 5 nodes, each node is directly connected to all other nodes; S112, gradually adding new nodes to the network. Each time a new node is added, two nodes in the existing network are selected for connection. The selection of the connection target node is based on the degree distribution probability of the existing nodes. The connection probability is proportional to the degree value of the target node. S113. Repeat step S112 until the network scale is expanded to 5000 nodes.

[0017] S12. Constructing an evolution rule for an epidemic transmission model, wherein the evolution rule comprises: The epidemic evolves in the order of susceptible state S-exposed state E-infectious state I-recovered state R, where the susceptible state S is a healthy state that is easily infected, the exposed state E is a state that is contagious after infection and has no symptoms, the infected state I is a state that is contagious after infection and has symptoms, the detected state D is a state where the infected individual is self-detected and isolated after the symptoms appear, and the recovered state R is a healthy state where the infected individual recovers to a non-infectious and not easily infected state; the length of time that an individual enters the exposed state E is the exposure age, and the length of time that an individual enters the infected state I is the infection age; The virus spreads from parent individuals to offspring individuals. After being detected by themselves, the infected state I individuals enter the detected state D. The detected state D individuals are isolated, and individuals who have been in close contact with the detected state D individuals and have not been isolated are tracked. Then, the child-parent relationship between the tracked infected individuals and the detected state D individuals is determined. If the tracked infected individual is the parent individual of the detected state D individual, the close contact individuals of the infected individual continue to be tracked until no infected individuals are tracked or the tracked infected individuals are all offspring individuals; the tracked infected individuals are all isolated; The temporal evolution process of the epidemic transmission model includes the process of increasing the source of infection and the process of decreasing the source of infection. The process of increasing the source of infection is the process in which the exposed state E and infected state I individuals who have not been isolated infect the susceptible state S individuals; the process of decreasing the source of infection includes the process in which the infected state I individuals are detected and transformed into the detected state D, the process in which the infected state I individuals who have not been isolated recover to the recovered state R, and the process in which the exposed state E individuals and the infected state I individuals are tracked and identified as infected individuals and thus isolated. Among them, the isolated individuals, including the infected individuals tracked and identified from the exposed state E individuals and the infected state I individuals, and the detected state D individuals, no longer participate in the spread of the virus and contact with people, and the recovered state R individuals enter the transmission network, but because they have antibodies, they will not be infected again, so they no longer participate in the spread of the virus, but will participate in contact with people; The evolution process of the epidemic transmission model is carried out in time sequence, and each time step includes the following steps: S121. According to the human contact behavior in the model network, the process of the exposed state E and infected state I individuals infecting the susceptible state S individuals is simulated, and the state of each individual in the model network is updated; considering that the infectivity is related to the viral load, therefore, in this embodiment, the probability of the exposed state E individual infecting the susceptible state S individual varies with the exposure age, and the probability of the infected state I individual infecting the susceptible state S individual varies with the infection age; S122. Determine the infected individual detected from the updated infected state I individuals according to the self-detection rate, convert the infected individual into a detected state D individual and isolate the individual. The self-detection rate is the probability that the infected person will be confirmed infected after self-detection after developing symptoms. Since self-detection is limited by the self-consciousness of detection, the test kit and the detection level of the operator, the self-detection rate is often lower than 100%; S123, performing contact tracing on the detected state D individuals added in step S122 one by one in a traversal manner, and the contact tracing of each detected state D individual includes the following steps: S1231, tracking the close contact individuals of the detected state D individual in the network; S1232. Screen out unisolated infected individuals from the close contact individuals, that is, individuals in infection state I or exposure state E but not isolated; S1233. Determine the close contact individuals who have been successfully traced based on the contact tracing success rate and the total number of infected individuals who have not been isolated; S1234. Determine the traced infected individual by combining the tracking detection rate and the total number of close contact individuals that have been successfully traced, and determine whether the traced infected individual is the parent individual of the detected state D individual.

[0018] In this embodiment, the contact tracing success rate is used to represent the probability of successfully tracing a close contact individual, and the product of the contact tracing success rate and the total number of unisolated infected individuals is taken as the number of close contact individuals successfully traced. The close contact individuals who are successfully traced are then determined by random selection from the unisolated infected individuals.

[0019] In this embodiment, the exposure age and infection age are used to characterize the tracking detection rate of successfully detected infected individuals, that is, the tracking detection rate varies with the exposure age or the infection age, and infected individuals with different exposure ages or infection ages are selected and detected with their corresponding tracking detection rates, and then isolated.

[0020] Determining the child-parent relationship between the traced infected individual and the detected state D individual includes the following steps: S131, using the child-parent relationship calculation formula to determine the child-parent relationship calculation value between the child detected state D individual and the tracked infected individual; ; in, p ij ( f i ; f j ) represents the calculated value of the child-parent relationship; f i Indicates the detected state D individuali How long the symptoms lasted in memory; f j Indicates the detected state D individual i Infected individuals traced j How long the symptoms lasted in memory; f (*) is the probability distribution, where T E Indicates the duration of the exposure period;- T E for T E The opposite of f represents the symptom age of the individual, that is, the length of time since the onset of symptoms in memory; τ represents the infection age of the individual, that is, the length of time since the individual entered the infection state I; S132. Determine the child-parent relationship between the detected state D individual and the tracked infected individual based on the calculated value of the child-parent relationship and the relationship threshold: if the calculated value of the child-parent relationship is greater than the relationship threshold, the detected state D individual is the child individual of the tracked infected individual; otherwise, it is the parent individual.

[0021] S2. Obtain basic parameters based on the infection data of a certain epidemic virus, and substitute the basic parameters into the epidemic transmission model to obtain a transmission model of the virus; The proportion of infected individuals who self-test and isolate among symptomatic infected persons among publicly confirmed cases is counted as the self-detection rate; the probability of infection of exposed individuals E of different exposure ages for susceptible individuals S in contact with them per unit time, and the probability of infection of infected individuals I of different infection ages for susceptible individuals S in contact with them per unit time are obtained from existing infectious research data; the contact tracing success rate is the ratio of the number of close contacts actually traced to the number of close contacts determined, which is obtained through existing contact tracing survey data; the probability distribution of the exposure period duration is obtained from existing research data on the incubation period of the epidemic; from the existing case data, the symptom onset time recorded for each case individual is first obtained, and then the actual symptom onset time of each case individual is inferred by combining the viral load data of the case individual and the existing research data on the correlation between viral load and symptom onset time. The individual memory deviation duration is obtained by calculating the difference between the symptom onset time recorded for each case individual and the actual symptom onset time, and finally this duration is counted for multiple case individuals to obtain f (τ- f); By calculating the actual symptom onset time of each case individual, we can further calculate the exposure age or infection age of the case individual when it is successfully traced and detected, and statistically analyze the distribution of the exposure age and infection age of all case individuals. The proportion of the number of case individuals with the same exposure age or infection age to the total number of case individuals detected by tracement is used as the tracement detection rate corresponding to the exposure age or infection age.

[0022] S3. Use the virus transmission model to simulate the virus evolution process and evaluate the effectiveness of the contact tracing strategy; This step includes setting a threshold for the number of infected individuals that are successfully traced and not isolated per unit time step. When the number of infected individuals that are successfully traced and not isolated per unit time reaches this threshold, the trace will be stopped, thereby simulating the evolution of the virus under different resource constraints. In addition, the relationship threshold can also be adjusted to simulate the evolution of the epidemic under different contact tracing strategies. The total number of infected people in the statistical simulation results is used as the outbreak scale, and the effectiveness of the contact tracing strategy is evaluated by the size of the outbreak.

[0023] This example uses the novel coronavirus as an example to simulate the results. Figure 2 As shown in the figure, when the threshold of the number of unisolated infected individuals successfully traced per unit time is 200, the contact tracing strategy with a relationship threshold of 0.9 has a relatively lower outbreak scale, indicating that the contact tracing strategy has a relatively better epidemic control effect under this resource constraint; when the threshold of the number of unisolated infected individuals successfully traced per unit time exceeds 500, the contact tracing strategy with a relationship threshold θ of 0.1 has a relatively lower outbreak scale, indicating that the contact tracing strategy has a relatively better epidemic control effect under this resource constraint.

[0024] The above are only preferred specific implementations of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by any technician familiar with the technical field within the technical scope disclosed in the embodiments of the present invention should be covered within the protection scope of the present invention.

Claims

1. A method for analyzing epidemic spread based on complex networks, characterized in that: The steps include: S1. Based on complex network theory, an epidemic transmission model of susceptible state S-exposed state E-infected state I-recovered state R is constructed with coupled dynamic infection and forward and reverse contact tracing strategies; during the evolution of the epidemic transmission model, the virus spreads from parent individuals to offspring individuals, and the infected state I individuals enter the detected state D after being detected by themselves. The detected state D individuals are isolated and the individuals who have close contact with the detected state D individuals and have not been isolated are tracked, and then the child-parent relationship between the tracked infected individuals and the detected state D individuals is determined. If the tracked infected individual is the parent individual of the detected state D individual, the close contact individuals of the infected individual will continue to be tracked until no infected individuals are tracked or the tracked infected individuals are all offspring individuals; the tracked infected individuals are all isolated; S2. Obtain basic parameters based on the infection data of a certain epidemic virus, and substitute the basic parameters into the epidemic transmission model to obtain a transmission model of the virus; S3. Analyze the evolution of the epidemic using the virus transmission model.

2. The method for analyzing epidemic spread based on complex networks according to claim 1, characterized in that: In step S1, constructing the epidemic spread model includes the following steps: S11. Construct a model network to describe human contact behavior; S12. Constructing an evolution rule for an epidemic transmission model, wherein the evolution rule comprises: The epidemic evolves in the order of susceptible state S-exposed state E-infectious state I-recovered state R, where the susceptible state S is a healthy state that is easily infected, the exposed state E is a state that is contagious after infection and has no symptoms, the infected state I is a state that is contagious after infection and has symptoms, the detected state D is a state where the infected individual is self-detected and isolated after the symptoms appear, and the recovered state R is a healthy state where the infected individual recovers to a non-infectious and not easily infected state; The temporal evolution process of the epidemic transmission model includes the process of increasing and decreasing sources of infection. The process of increasing sources of infection is the process in which unisolated exposed state E and infected state I individuals infect susceptible state S individuals; the process of decreasing sources of infection includes the process in which infected state I individuals are detected and transformed into detected state D, the process in which unisolated infected state I individuals recover to recovered state R, and the process in which exposed state E individuals and infected state I individuals are tracked and identified as infected individuals; recovered state R individuals enter the transmission network.

3. The method for analyzing epidemic spread based on complex networks according to claim 2, characterized in that: The evolution process of the epidemic transmission model is carried out in time sequence, and each time step includes the following steps: S121, simulating the process of the exposed state E and infected state I individuals infecting the susceptible state S individuals according to the human contact behavior in the model network, and updating the state of each individual in the model network; the time when the individual enters the exposed state E is the exposure age, and the time when the individual enters the infected state I is the infection age, and the probability of the exposed state E individual and the infected state I individual infecting the susceptible state S individual changes with the exposure age and the infection age respectively; S122. Determine the infected individual detected from the updated infected state I individuals according to the self-detection rate, and convert the infected individual into a detected state D individual. The self-detection rate is the probability that the infected person will be confirmed to be infected after self-detection after developing symptoms. S123, performing contact tracing on the detected state D individuals added in step S122 one by one in a traversal manner, and the contact tracing of each detected state D individual includes the following steps: S1231, tracking the close contact individuals of the detected state D individual in the network; S1232. Screen out unisolated infected individuals from the close contact individuals, that is, individuals in infection state I or exposure state E but not isolated; S1233. Determine the close contact individuals who have been successfully traced based on the contact tracing success rate and the total number of infected individuals who have not been isolated; S1234. Determine the traced infected individual by combining the tracking detection rate and the total number of close contact individuals that have been successfully traced, and determine whether the traced infected individual is the parent individual of the detected state D individual.

4. The method for analyzing epidemic spread based on complex networks according to claim 1, characterized in that: Determining the child-parent relationship between the traced infected individual and the detected state D individual includes the following steps: S131, using the child-parent relationship calculation formula to determine the child-parent relationship calculation value between the child detected state D individual and the tracked infected individual; ； in, p ij ( φ i ; φ j ) represents the calculated value of the child-parent relationship; φ i Indicates the detected state D individual i How long the symptoms lasted in memory; φ j Indicates the detected state D individual i Infected individuals traced j How long the symptoms lasted in memory; f (*) is the probability distribution, where T E Indicates the duration of the exposure period;- T E for T E The opposite of φ represents the individual's symptom age, i.e., how long symptoms have been present in memory; τ represents the infection age of the individual, that is, the length of time it takes for the individual to enter infection state I; S132. Determine the child-parent relationship between the detected state D individual and the tracked infected individual based on the calculated value of the child-parent relationship and the relationship threshold: if the calculated value of the child-parent relationship is greater than the relationship threshold, the detected state D individual is the child individual of the tracked infected individual; otherwise, it is the parent individual.

5. The method for analyzing epidemic spread based on complex networks according to claim 1, characterized in that: Step S3 includes setting a threshold for the number of infected individuals that are not isolated and successfully traced per unit time. When the number of infected individuals that are not isolated and successfully traced per unit time reaches the threshold, the tracking will be stopped, thereby simulating the evolution of the epidemic under different resource constraints.

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