Method and system for constructing double-layer coupled network infectious disease transmission model based on game strategy

Abstract

The invention discloses a method and a system for constructing a double-layer coupled network infectious disease transmission model based on a game strategy. The construction method comprises the following steps: constructing an information dissemination network and a physical contact network; in the information propagation network, modeling is carried out on evolution of individual consciousness by adopting a UAU model according to individual states, and in the physical contact network, modeling is carried out on evolution of individual states by adopting an SIS infectious disease model; introducing a game strategy mechanism of individual consciousness into the information propagation network; constructing a feedback mechanism of individual behaviors in the physical contact network; according to an MMCA method, an information transmission network of a game strategy mechanism and a physical contact network of a feedback mechanism are introduced to construct a double-layer coupled network infectious disease transmission model, and threshold analysis is performed on the double-layer coupled network infectious disease transmission model; according to the method, game strategies and behavior feedback made by individuals after the individuals receive infectious disease information are considered, and the method is used for solving the problem of complex coupling between information transmission and infectious disease transmission in a double-layer coupling network.

Description

Technical Field

[0001] The present invention relates to the field of network science, in particular to the field of complex system modeling and analysis, and more particularly to the coupling dynamics of infectious diseases and information, and specifically to a method and system for constructing a double-layer coupled network infectious disease propagation model based on game strategy. Background Art

[0002] With the acceleration of globalization, the speed and scope of epidemic spread are increasing. For example, influenza, monkeypox, cholera, etc. have always posed a serious threat to public health and safety. Therefore, the study of infectious disease transmission dynamics and control strategies is crucial to protecting public health and maintaining social stability. When infectious diseases spread, individuals receive information related to infectious diseases, and thus make individual behavioral changes (such as wearing masks, isolation, etc.) to "seek benefits and avoid harm". These changes in individual behavior affect the spread of infectious diseases. Therefore, the key to effectively controlling the spread of infectious diseases lies in a deep understanding of the complex interaction between the epidemic dynamics of infectious diseases and human behavior and information dissemination. Especially in today's rapid development of social media and the Internet, the impact of information dissemination on the epidemic cannot be ignored. How to construct an adaptive coupling mechanism between information and infectious disease transmission, propose a modeling method that conforms to the actual contact network of infectious disease transmission, and effectively analyze the coupling effect of information dissemination dynamics on infectious disease transmission dynamics are important for making accurate and efficient public health decisions.

[0003] In the field of infectious disease transmission model research, existing technologies mainly include the construction of various epidemic models, such as SIS (Susceptible-Infected-Susceptible), SIR (Susceptible-Infected-Recovered) model and SEIR (Susceptible-Exposed-Infected-Recovered) model, which are widely used to simulate and predict the transmission path of infectious diseases. However, these traditional models usually only consider contact between individuals as the only way for infectious diseases to spread, ignoring the important role of infectious disease information dissemination in infectious disease prevention and control, and ignoring the impact of individual adaptive game behavior on the coupling of information and transmission. Summary of the invention

[0004] The purpose of the present invention is to provide a method and system for constructing a double-layer coupled network infectious disease propagation model based on game strategy, taking into account the game strategy made by individuals after receiving infectious disease information, so as to solve the impact of individual adaptive behavior on information and propagation dynamics.

[0005] To achieve the above purpose, the present invention provides a method for constructing a double-layer coupled network infectious disease propagation model based on a game strategy, and the technical solution is as follows:

[0006] The double-layer coupled network infectious disease propagation model is applied to the analysis of the evolutionary dynamics of infectious disease propagation. The double-layer coupled network infectious disease propagation model includes: an information propagation network for the evolution of individual consciousness and a physical contact network for the propagation of infectious diseases; the information propagation network layer and the physical contact network include the same nodes; each of the nodes represents an individual; the edge in the information propagation network indicates that there is information propagation behavior between the two nodes connected by the edge; the edge in the physical contact network indicates the physical contact between the two nodes connected by the edge; the construction method includes: constructing the information propagation network and the physical contact network; in the information propagation network, the UAU model is used to model the evolution of individual consciousness according to the individual state, and in the physical contact network, the SIS infectious disease model is used to model the evolution of individual state; the game strategy mechanism of individual consciousness is introduced into the information propagation network; the feedback mechanism of individual behavior is constructed in the physical contact network; the double-layer coupled network infectious disease propagation model is constructed according to the MMCA method, the information propagation network introducing the game strategy mechanism and the physical contact network constructing the feedback mechanism, and the threshold analysis of the double-layer coupled network infectious disease propagation model is performed.

[0007] The MMCA method is a mathematical model method for analyzing the transmission characteristics of infectious diseases that is well known to those skilled in the art and will not be described in detail here.

[0008] Furthermore, the game strategy mechanism for introducing individual consciousness into the information dissemination network includes: individuals corresponding to nodes in the information dissemination network play games with individuals corresponding to adjacent nodes, and calculate the strategy imitation probability according to the payoff matrix, so as to influence the state of individuals in the information dissemination network based on the strategy imitation probability; the strategy imitation probability is used to guide the strategy selection of the consciousness state of nodes in the information dissemination network.

[0009] Furthermore, the feedback mechanism for building individual behaviors in the physical contact network includes: in the physical contact network, the nodes of the physical contact network adjust the edges of the nodes in the physical contact network according to the awareness of the nodes in the information dissemination network.

[0010] Furthermore, the double-layer coupled network infectious disease propagation model is constructed according to the MMCA method, the information propagation network introducing the game strategy mechanism, and the physical contact network constructing the feedback mechanism, including: setting the transition probability and benefit matrix between different states of each node in the information propagation network and the physical contact network based on the game strategy mechanism; constructing the double-layer coupled network infectious disease propagation model based on the state of each node in the information propagation network and the physical contact network and the transition probability; the double-layer coupled network infectious disease propagation model describes the dynamic process of the state of all nodes in the information propagation network and the physical contact network changing over time; the threshold analysis of the double-layer coupled network infectious disease propagation model includes: solving the double-layer coupled network infectious disease propagation model, obtaining the state probabilities of nodes in the information propagation network and the physical contact network at different time points, and determining the infectious disease threshold through threshold theory analysis; the infectious disease threshold is used to determine whether an infectious disease breaks out or disappears.

[0011] The present invention also provides a system for constructing a double-layer coupled network infectious disease propagation model based on a game strategy, wherein the double-layer coupled network infectious disease propagation model is applied to the analysis of the evolutionary dynamics of infectious disease propagation, and the double-layer coupled network infectious disease propagation model includes: an information propagation network of individual consciousness evolution and a physical contact network of infectious disease propagation; the information propagation network layer and the physical contact network include the same nodes; each of the nodes represents an individual; an edge in the information propagation network indicates that there is information propagation behavior between the two nodes connected by the edge; an edge in the physical contact network indicates physical contact between the two nodes connected by the edge; the construction system includes: a network construction module for constructing the information propagation network and the physical contact network. A physical contact network; an evolutionary modeling module, used to model the evolution of individual consciousness using the UAU model according to the individual state in the information propagation network, and to model the evolution of individual state in the physical contact network using the SIS infectious disease model; a mechanism introduction module, used to introduce the game strategy mechanism of individual consciousness into the information propagation network; a mechanism construction module, used to construct a feedback mechanism of individual behavior in the physical contact network; a model construction module, used to construct a double-layer coupled network infectious disease propagation model according to the MMCA method, the information propagation network introducing the game strategy mechanism and the physical contact network constructing the feedback mechanism, and to perform threshold analysis on the double-layer coupled network infectious disease propagation model.

[0012] By adopting the above technical solution, the present invention can achieve the following technical effects: This method proposes a double-layer coupled network infectious disease propagation model based on individual game strategy by considering the interaction between infectious disease propagation and information propagation on the double-layer coupled network, which is more in line with the impact of individual behavior on infectious disease propagation in the real infectious disease propagation process, and can provide a certain reference and powerful means for formulating effective infectious disease defense policies. Specifically, the method for constructing a double-layer coupled network infectious disease propagation model based on game strategy described in the present invention has the following beneficial effects:

[0013] (1) Compared with the prior art, the present invention provides a method for constructing a double-layer coupled network infectious disease propagation model based on game strategy, which solves the problem that the existing research has not fully considered the impact of individual game psychology and adaptive behavior on infectious disease propagation, and provides a model that can more comprehensively analyze epidemic spread and control strategies, namely, a double-layer coupled network infectious disease propagation model. This new model can not only simulate the dynamic propagation of infectious diseases in physical contact networks, but also consider the propagation of information and the interaction between physical contact networks and information propagation networks, providing a more comprehensive and accurate model construction method for epidemic spread and control strategy analysis.

[0014] (2) The double-layer coupled network infectious disease propagation model provided by the present invention constructs the propagation process of infectious diseases and information by combining game evolution mechanism, micro-Markov chain method, Monte Carlo random simulation and other methods, uses a variety of theoretical and simulation methods to enhance the reliability of modeling, and analyzes the interaction between the two-layer coupled networks, so that the double-layer coupled network infectious disease propagation model is closer to the complexity of individual behavior and information propagation in the real society, and has higher data reliability and prediction accuracy when conducting infectious disease propagation prediction and analysis, so as to more accurately simulate the epidemic propagation process at different social network levels, and provide more effective and adaptable epidemic prediction and control strategies. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the following briefly introduces the figures required for use in the embodiments or the description of the prior art. Obviously, the figures described below are only some embodiments of the present invention, and for ordinary technicians in this field, other figures can be obtained based on these figures without creative work.

[0016] Figure 1 Shown is a schematic diagram of the structure of a double-layer coupled network infectious disease propagation model according to an embodiment of the present invention.

[0017] Figure 2 Shown is a flow chart of a method for constructing a double-layer coupled network infectious disease propagation model based on game strategy according to an embodiment of the present invention.

[0018] Figure 3 Shown is a schematic diagram of the AI ​​state node state transition probability tree according to an embodiment of the present invention.

[0019] Figure 4 Shown is a schematic diagram of the AS state node state transition probability tree according to an embodiment of the present invention.

[0020] Figure 5 Shown is a schematic diagram of a US state node state transition probability tree according to an embodiment of the present invention.

[0021] Figure 6a and Figure 6b The MC random simulation and MMCA model based on the double-layer coupling network described in the embodiment of the present invention are respectively shown with respect to the proportion of conscious persons ρ A and the proportion of infected people ρ I A comparative diagram of .

[0022] Figures 7a to 7d It shows a schematic diagram of comparative analysis of using and not using the game evolution mechanism under different infectious disease recovery rates μ and conscious infection coefficients γ as described in an embodiment of the present invention.

[0023] Figures 8a to 8d It shows a schematic diagram of comparative analysis of thresholds with and without the game evolution mechanism in the double-layer coupled network infectious disease propagation model described in an embodiment of the present invention under different infectious disease recovery rates μ and conscious infection coefficients γ.

[0024] Figures 9a to 9d It shows the proportion of infected people ρ under different consciousness adjustment strength coefficients under different infectious disease recovery rates μ and conscious infection coefficients γ according to the embodiment of the present invention. I Schematic diagram of comparative analysis of the relationship between and the transmission rate β.

[0025] Fig.10 The infectious disease recovery rate μ versus the infectious disease threshold β according to the embodiment of the present invention is shown as follows: c Schematic diagram of the impact.

[0026] Fig.11 The display is the consciousness emphasis adjustment coefficient q of the embodiment of the present invention for the infectious disease threshold β c Schematic diagram of the impact.

[0027] Fig.12 The parameter b of the embodiment of the present invention is shown as the ratio of conscious persons ρ A Schematic diagram of the impact.

[0028] Fig.13 The parameter b described in the embodiment of the present invention is shown as the ratio of infected persons ρ I Schematic diagram of the impact.

[0029] Fig.14 Shown is a structural schematic diagram of a modeling system for a double-layer coupled network infectious disease propagation model according to an embodiment of the present invention. DETAILED DESCRIPTION

[0030] The following describes the embodiments of the present invention by specific examples, and those skilled in the art can easily understand other advantages and effects of the present invention from the contents disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed in various ways based on different viewpoints and applications without departing from the spirit of the present invention. It should be noted that the following embodiments and features in the embodiments can be combined with each other without conflict.

[0031] In previous studies on the construction of a two-layer coupled network infectious disease transmission model based on infectious disease transmission, the interaction between epidemic transmission and awareness diffusion has attracted widespread attention. However, most existing models focus on the transmission mechanism of infectious diseases at a single level, failing to fully capture the complexity and multi-layered nature of human social networks, especially ignoring the dynamic interaction between information transmission networks and infectious disease transmission networks.

[0032] In addition, existing studies often ignore the impact of individual behavioral constraints when analyzing the spread of epidemics, especially the interest choices, personal preferences, and behavioral decision-making processes of real individuals when faced with epidemic information. This limitation leads to biased analysis of infectious disease transmission and control strategies. Although some studies have attempted to explore individual interactive behaviors from the perspective of game theory, there is a lack of a method to comprehensively analyze the interaction between information evolution and infectious disease transmission.

[0033] The present invention aims to propose a method for constructing a dual-layer coupled network infectious disease transmission model (UAU-SIS model) to solve the problem of the impact of individual game psychology and self-regulation behavior on infectious disease transmission that has not been fully considered in existing studies, and to provide a model that can more comprehensively analyze epidemic transmission and control strategies. This new model can not only simulate the dynamic transmission of infectious diseases in physical contact networks, but also consider the transmission of information in the information transmission network layer, as well as the interaction between the two layers of networks, providing a more comprehensive and accurate model construction method for epidemic transmission and control strategy analysis. Figures 1 to 14 , the specific implementation of the embodiments of the present invention will be described in detail below in conjunction with the drawings in the embodiments of the present invention.

[0034] like Figure 1As shown, in one embodiment, the present invention provides a method for constructing a double-layer coupled network infectious disease propagation model based on a game strategy, wherein the double-layer coupled network infectious disease propagation model is applied to infectious disease propagation prediction and analysis, aiming to deeply understand and effectively simulate the influence of individual consciousness and behavior during the epidemic spread; the double-layer coupled network infectious disease propagation model is recorded as a UAU-SIS model, and the double-layer coupled network infectious disease propagation model includes: an information propagation network of information evolution and a physical contact network of infectious disease propagation; the information propagation network and the physical contact network include the same nodes; each of the nodes represents an individual, the nodes in the information propagation network are used to characterize the state of consciousness of infectious diseases, and the nodes in the physical contact network are used to represent the state of individuals during infectious disease propagation; the edges in the information propagation network represent the information propagation between the individuals corresponding to the two nodes connected by the edges; the edges in the physical contact network represent the physical contact between the individuals corresponding to the two nodes connected by the edges (if there is effective contact between individuals, then there is an edge between the corresponding nodes, which is the main way of infectious disease propagation).

[0035] It should be noted that the node degree follows a power law distribution (the degree distribution function follows a power function. Specifically, assuming that the degree of a node in the network is k, then the probability distribution of the node degree P(k) can be expressed as: P(k)∝k -γ . where γ>0 is the power law exponent. )

[0036] It should be noted that the UAU-SIS model integrates the physical contact network of infectious disease transmission and the information propagation network of information evolution. The physical contact network is used to simulate the contact and propagation between individuals in the actual infectious disease transmission process; the information propagation network is used to simulate the propagation process of infectious disease-related information among the population during the transmission of infectious diseases among the population; the two-layer networks have the same nodes but different edges. The edges of the physical contact network represent the contact between individuals; the edges of the information propagation network represent the propagation of information between individuals; this network structure enables the model to clearly simulate the contact and propagation of real infectious diseases and the propagation effect of related infectious disease information between networks and the coupling relationship between the two.

[0037] In the physical contact network, the SIS (Susceptible-Infectious-Susceptible) infectious disease model that conforms to influenza-like infectious diseases is used to describe the transfer and evolution of states between individuals. Node individuals are divided into susceptible state (S) and infectious state (I).

[0038] The susceptible state (S) refers to the state of an individual who has not been infected with a disease but will be infected by contact with an infected person; the infected state (I) refers to the state of an individual who has been infected with a disease and can spread the disease; the transmission mechanism of the classic SIS infectious disease model is as follows: a susceptible individual (S) is infected with a certain probability β after contacting an infected individual (I) and enters the infected state. The infected individual (I) recovers with a probability μ after a period of time, but does not gain immunity after recovery, but returns to the susceptible state (S), so it can be infected again.

[0039] In the information dissemination network, the node individuals are the same as the node individuals in the physical contact network, but the edges represent the paths of information dissemination, reflecting how information is transmitted between individuals. For example, in online social networks, individuals exchange information in any form, and the node individuals are divided into uninformed states (U) and aware states (A); among them, individuals in state A will consciously take protective measures (such as wearing masks, home isolation, disinfection, etc.) to reduce the infection rate of infectious diseases.

[0040] Through the above-mentioned two-layer network coupling structure, not only the transmission path of infectious diseases in the actual contact network is simulated, but also the dynamic evolution of the epidemic prevention awareness of individuals after receiving information related to infectious diseases is simulated.

[0041] In order to simulate the spread of infectious diseases in the population more realistically, based on the above-mentioned UAU-SIS two-layer network model, the main innovative mechanisms and implementation mechanisms of the present invention include the following two points:

[0042] 1. In the information dissemination network, considering the psychological game presented by individuals after being exposed to information about infectious diseases, based on the evolutionary game theory, a mechanism is proposed in which individuals decide whether to imitate other individuals based on the benefits calculated by the payoff matrix. Individuals continuously evolve their consciousness strategies through strategy imitation and payoff adjustment. This evolution not only affects the information dissemination in the information dissemination network, but also affects the contact behavior in the physical contact network. For example, when more and more individuals choose a cooperative strategy (i.e., maintain a conscious state) and continue to take protective measures against infectious diseases, the contact behavior of the entire network will change accordingly, thereby weakening (controlling) the spread of infectious diseases.

[0043] It is assumed that conscious individuals will take the initiative to take epidemic prevention measures and become collaborators in epidemic prevention behavior, while individuals who have not received information will not take epidemic prevention measures and become betrayers.

[0044] The prisoner's dilemma provides a framework that enables individuals to calculate the strategy imitation probability f(i) (formula (3)) based on the payoff matrix M (formula (1)), where f(i) guides the individual's strategy selection in the information dissemination network, thereby affecting the individual's state in the information dissemination network; specifically, the present invention assumes that the cooperator of the game behavior will accept the epidemic information and take the initiative to take epidemic prevention measures, thereby becoming an A-state individual in the information dissemination network. Similarly, the betrayer of the game behavior will forget the epidemic information and not take protective measures, thereby becoming a U-state individual in the information dissemination network. Game individual i can obtain its own game payoff information Π i (Formula (2)) and the game payoff information Π of the direct neighbor j j (Formula (2)), the probability of state A at the current time step and U state probability In the prisoner's dilemma game, two game participants choose between cooperation and betrayal strategies at the same time. If they cooperate together, each game individual can obtain a benefit R; if they betray together, each game participant can obtain a benefit P; if one person cooperates and the other betrays, the cooperator obtains a benefit S and the betrayer obtains a benefit T. According to previous research, the parameters of the payoff matrix M are set as: R = 1, P = S = 0, T = b. Among them, the parameter b∈(1,2) represents the temptation to betray. The larger the value of b, the more natural selection tends to betray. The payoff matrix M is expressed as:

[0045]

[0046] In each round of the game, each individual plays a prisoner's dilemma game with all direct neighbors to obtain cumulative game benefits. In each round of the game, the individuals corresponding to the nodes in the information dissemination network may be in a conscious state or an unaware state, with probabilities p and p respectively. A =p AI +p AS and p U =p US The game payoff of an individual is the sum of the payoffs obtained from playing with all direct neighbors. Each individual interacts with the direct neighbors defined by the network in pairs. Individual i plays the prisoner's dilemma game with his neighbor j in the information dissemination network layer and obtains payoff Π i is (Formula (2)):

[0047] (2)

[0049] in, and Represent the probabilities that individual i and neighbor j are in a conscious state respectively; and Represent the probabilities that individual i and neighbor j are in an unconscious state respectively.

[0050] In each round of information dissemination game, each individual interacts with all neighbors in the information dissemination network and collects the corresponding cumulative benefits Π i In each round of the game, each individual has an average chance to imitate the strategy of its direct neighbor. That is, each individual randomly selects a direct neighbor and decides whether to adopt the other party's strategy in the next round of the game based on the comparison of the benefits of both parties. The game strategy adjustment dynamics rule adopts the Fermi function. The probability that individual i imitates the strategy of neighbor j is f(i), that is, formula (3)):

[0051] (3)

[0053] Among them, the parameter κ>0 represents the selection intensity (the sensitivity of individuals to income differences); the smaller κ means the more sensitive the individual is to income differences. In this paper, k is set to 0.1.

[0054] 2. Adopt an individual consciousness regulation mechanism in the physical contact network, dynamically adjust social contacts between individuals, reduce contact with infected people, and thus reduce the probability of being infected with infectious diseases. This behavior can not only reduce the infection risk of cooperating individuals, but also influence the behavior of other individuals through the information dissemination network, further inhibit the spread of infectious diseases, and present the dynamic evolution of the physical contact network structure during the spread of infectious diseases. For example, during the spread of infectious diseases, due to the individual's game psychology, individuals will choose to isolate at home or reduce contact with high-risk groups. This behavior is reflected in the physical contact network structure, that is, the consciousness emphasis adjustment coefficient q reflects the effectiveness of conscious nodes in reducing their infection probability. At this time, the probability of a conscious node being infected is β A (1-q), where β A is the basic infection probability of a conscious node without adjustment. When the consciousness emphasis adjustment coefficient q = 0, it means that the consciousness state of the node has no effect on the infection probability in the physical contact layer, and the infection probability remains at β A ; When q=1, it indicates that conscious nodes can completely avoid infection and the infection probability drops to 0.

[0055] The present invention, firstly, formulates a game strategy of individual consciousness in the information dissemination network in combination with the adaptive changes of individual behavior in the context of real infectious diseases; secondly, in order to more realistically simulate the social network dynamics under the epidemic, a network reconstruction mechanism of broken edge reconnection is introduced in the physical contact layer, which characterizes the social behavior adjustment of individuals during the epidemic, such as avoiding high-risk social interactions, reconstructing social networks and other key behavioral characteristics; finally, based on the coupled dynamics of infectious disease propagation and information diffusion, the state transition probability is proposed, and the state space equation of the UAU-SIS model is constructed accordingly; this equation can more effectively and accurately reflect the complex coupling mechanism between information propagation and infectious disease propagation in a double-layer coupled network.

[0056] like Figure 2 As shown, in one embodiment, the construction method includes:

[0057] Step S1: construct the information dissemination network and the physical contact network.

[0058] In one embodiment, the information dissemination network and the physical contact network are both BA networks.

[0059] Specifically, a heterogeneous two-layer network structure and mechanism that conforms to the actual contact network is constructed based on complex network theory-the construction of network carriers: one layer is the information dissemination network, and the other layer is the physical contact network. Both layers are BA networks; in these two layers, the total number of nodes N = 1000; specifically, the number of original nodes connected to each new node in the information dissemination network is 4, while the m value in the physical contact network is 3. The degree distribution of the network presents a power-law distribution, showing the heterogeneity between individual contacts, and provides an effective model framework for studying the complex coupling relationship between information dissemination and infectious disease transmission.

[0060] It should be noted that the BA network, namely the Barabási-Albert network model, is a mathematical model that describes the network topology. The model is based on two basic principles: growth and preferential connectivity. Growth refers to the fact that new nodes will continue to join the network during its development; preferential connectivity means that newly added nodes are more inclined to establish connections with existing nodes with higher degrees. These characteristics together lead to the "scale-free nature" of the network, that is, there are a few nodes with extremely high degrees in the network, while the degrees of most nodes are relatively low. The displayed contact networks, social networks, transportation networks, etc. all show certain scale-free characteristics.

[0061] In one embodiment, the BA network construction method is as follows:

[0062] 1) Initial network: Start with a small fully connected initial network, usually containing m0 initial nodes, where m0 ≥ 2.

[0063] 2) Node growth: Each time a new node is added, recorded as node n, and it is connected to m nodes (m≤m0) in the existing network. The connection of the new node is based on the principle of priority connection.

[0064] 3) Priority connection: The probability ∏(k) that a new node n is connected to an existing node i ) and the degree k of the existing node i Proportional to: Among them, k i is the degree of an existing node i (i.e., the number of edges connected to it), and ∑ j k j is the sum of the degrees of all existing nodes.

[0065] 4) Repeat steps: As new nodes are continuously added, repeat steps 2) and 3) to gradually increase the number of nodes and edges until the network reaches the desired scale, forming a scale-free network in which the degree distribution of nodes follows a power-law distribution, i.e., most nodes have low degrees, and a few nodes have a large number of connections, reflecting the characteristic of "the rich get richer".

[0066] Step S2: In the information dissemination network, the UAU model is used to model the evolution of individual consciousness according to the individual state, and in the physical contact network, the SIS infectious disease model is used to model the evolution of individual state.

[0067] Specifically, in the information dissemination network, the UAU (Uninformed-Aware-Uninformed) model is used to model the individual consciousness state, and individuals are divided into two states: conscious state (i.e., state A) and unconscious state (i.e., state U); in the physical contact network, the SIS (Susceptible-Infectious-Susceptible) infectious disease model that conforms to influenza-like diseases is used to describe the transfer and evolution of states between individuals, and node individuals are divided into susceptible state (S) and infected state (I).

[0068] It should be noted that at the information dissemination network layer, if a person is aware of an infectious disease and has a tendency to change behavior, his / her state is recorded as conscious (A), while the uninformed node (U) is unaware of the risk of infection and does not take any preventive measures; the A-state node in the information dissemination network can choose whether to imitate the state of the U-state neighbor node based on the benefits by playing games with its neighbors. Similarly, the A-state node can also choose to lose perception and return to the U state based on the benefits.

[0069] Step S3: Introduce the game strategy mechanism of individual consciousness into the information dissemination network.

[0070] In one embodiment, the game strategy mechanism for introducing individual consciousness into the information dissemination network includes: individuals corresponding to nodes in the information dissemination network play games with individuals corresponding to adjacent nodes, and calculate the strategy imitation probability according to the payoff matrix to influence the state of individuals in the information dissemination network based on the strategy imitation probability; the strategy imitation probability is used to guide the strategy selection of the consciousness state of nodes in the information dissemination network.

[0071] In one embodiment, it is assumed that conscious individuals will take the initiative to take epidemic prevention measures and become collaborators in epidemic prevention behavior, while individuals who have not received information will not take epidemic prevention measures and become betrayers.

[0072] Specifically, the prisoner's dilemma provides a framework that enables individuals to calculate the strategy imitation probability f(i) (formula (3)) based on the payoff matrix M (formula (1)), where f(i) guides the individual's strategy selection in the information dissemination network, thereby affecting the individual's state in the information dissemination network; specifically, the present invention assumes that the cooperator of the game behavior will accept the epidemic information and take the initiative to take epidemic prevention measures, thereby becoming an A-state individual in the information dissemination network. Similarly, the betrayer of the game behavior will forget the epidemic information and not take protective measures, thereby becoming a U-state individual in the information dissemination network. Game individual i can obtain its own game payoff information Π i (Formula (2)) and the game payoff information Π of the direct neighbor j j (Formula (2)), the probability of state A at the current time step and U state probability In the prisoner's dilemma game, two game participants choose between cooperation and betrayal strategies at the same time. If they cooperate together, each game individual can obtain a benefit R; if they betray together, each game participant can obtain a benefit P; if one person cooperates and the other betrays, the cooperator obtains a benefit S and the betrayer obtains a benefit T. According to previous research, the parameters of the payoff matrix M are set as: R = 1, P = S = 0, T = b. Among them, the parameter b∈(1,2) represents the temptation to betray. The larger the value of b, the more natural selection tends to betray. The payoff matrix M is expressed as:

[0073]

[0074] In each round of the game, each individual plays a prisoner's dilemma game with all direct neighbors to obtain cumulative game benefits. In each round of the game, the individuals corresponding to the nodes in the information dissemination network may be in a conscious state or an unaware state, with probabilities p and p respectively. A =p AI +p AS and p U =p USThe game payoff of an individual is the sum of the payoffs obtained from playing with all direct neighbors. Each individual interacts with the direct neighbors defined by the network in pairs. Individual i plays the prisoner's dilemma game with his neighbor j in the information dissemination network layer and obtains payoff Π i is (Formula (2)):

[0075]

[0076] in, and Represent the probabilities that individual i and neighbor j are in a conscious state respectively; and Represent the probabilities that individual i and neighbor j are in an unconscious state respectively.

[0077] In each round of information dissemination game, each individual interacts with all neighbors in the information dissemination network and collects the corresponding cumulative benefits Π i In each round of the game, each individual has an average chance to imitate the strategy of its direct neighbor. That is, each individual randomly selects a direct neighbor and decides whether to adopt the other party's strategy in the next round of the game based on the comparison of the benefits of both parties. The game strategy adjustment dynamics rule adopts the Fermi function. The probability that individual i imitates the strategy of neighbor j is f(i), that is, formula (3)):

[0078]

[0079] Among them, the parameter k>0 represents the selection intensity (the sensitivity of individuals to income differences); the smaller κ means the more sensitive the individual is to income differences, and κ is set to 0.1 in this paper.

[0080] Specifically, a prisoner's dilemma model is introduced into the information dissemination network, and a game evolution mechanism of individual consciousness is constructed to characterize the individual's strategy selection process between information dissemination and epidemic prevention behavior. This aims to simulate people in real life deciding whether to accept information and make behavioral changes through games with their neighbors.

[0081] It should be noted that by introducing a game strategy mechanism into the information dissemination network, cross-layer interaction between the information dissemination network and the physical contact network is facilitated. Nodes in the physical contact network (i.e., actual individuals or entities) will implement adaptive social behavior adjustments based on changes in the consciousness state of the corresponding individuals in the information dissemination network. This process involves re-evaluating neighbor connections (i.e., social connections), which is specifically manifested in deciding whether to maintain existing contact relationships or disconnect connections based on the results of individual consciousness adjustment in order to optimize the protection strategy of individuals or groups.

[0082] Step S4: constructing a feedback mechanism for individual behavior in the physical contact network.

[0083] Specifically, an individual behavior feedback mechanism is introduced into the physical contact network to adjust the probability of conscious individuals being infected in order to analyze the coupled impact of information and infectious disease transmission.

[0084] In one embodiment, the feedback mechanism for building individual behaviors in the physical contact network includes: in the physical contact network, the nodes of the physical contact network adjust the edges of the nodes in the physical contact network according to the awareness of the nodes in the information dissemination network.

[0085] In one embodiment, the adjustment is achieved by a consciousness emphasis adjustment coefficient q.

[0086] Specifically, q reflects the effectiveness of conscious nodes in reducing their infection probability. At this time, the probability of conscious nodes being infected is β A (1-q), where β A is the basic infection probability of a conscious node without adjustment. When the consciousness emphasis adjustment coefficient q = 0, it means that the consciousness state of the node has no effect on the infection probability in the physical contact layer, and the infection probability remains at β A ; When q=1, it indicates that conscious nodes can completely avoid infection and the infection probability drops to 0.

[0087] Step S5: construct a double-layer coupled network infectious disease propagation model according to the MMCA method, the information propagation network introducing the game strategy mechanism, and the physical contact network constructing the feedback mechanism, and perform threshold analysis on the double-layer coupled network infectious disease propagation model.

[0088] Specifically, according to the MMCA (Microscopic Markov Chain Approach) algorithm, a microscopic Markov chain equation based on UAU-SIS (i.e., a two-layer coupled network infectious disease propagation model, corresponding to formula (5)) is constructed and solved to study the transition probability of each node between different states in the two-layer network and the coupling behavior of disease propagation dynamics and information propagation.

[0089] In one embodiment, the double-layer coupled network infectious disease propagation model is constructed according to the MMCA method, the information propagation network introducing the game strategy mechanism, and the physical contact network constructing the feedback mechanism, including: setting the transition probability and benefit matrix between different states of each node in the information propagation network and the physical contact network based on the game strategy mechanism; constructing the double-layer coupled network infectious disease propagation model based on the state of each node in the information propagation network and the physical contact network and the transition probability; the double-layer coupled network infectious disease propagation model describes the dynamic process of the state of all nodes in the information propagation network and the physical contact network changing over time.

[0090] It should be noted that the transfer probability is affected by the individual's state of consciousness, the characteristics of infectious disease transmission and the social interaction pattern; the payoff matrix is ​​used to quantify the expected benefits of an individual under different strategy choices. For example, maintaining contact may increase the risk of infection but may also gain social benefits, while disconnecting the connection may reduce the risk but may sacrifice social capital.

[0091] The present invention considers the interaction between the information dissemination network and the physical contact network in the double-layer coupled network infectious disease propagation model. The interaction between these two dynamics is described as follows:

[0092] Once an individual is in state I, he / she will immediately move to state A, where the probability of an unconscious individual becoming conscious is σ = 100%. Nodes that are aware of infectious diseases at the UAU layer will take measures to prevent infection. Therefore, parameter β regulates the probability of a node being infected. In the framework of the SIS model, the infectiousness parameter depends on the state of the nodes in the information dissemination network; specifically, β U It is used to adjust the probability of infection in an uninformed state, and β A =γβ U It is used to adjust the probability of infection in the informed state. Therefore, the parameter γ ranges from 0 (indicating complete vaccination) to 1 (indicating that information awareness has no effect on the epidemic). Individuals play the consciousness evolution game under the prisoner game framework and adjust the relationship between strategy selection and physical contact network by calculating the payoff matrix.

[0093] Therefore, individuals in the two-layer coupled network infectious disease transmission model with evolutionary game can be in three different states: uninformed and susceptible (US), aware and susceptible (AS), or aware and infected (AI); among them, the uninformed and infected (UI) state is false because according to the definition of the dynamic process, it will immediately become aware and infected (AI).

[0094] The UAU-SIS model that introduces the game strategy mechanism and the feedback mechanism of individual behavior is further explained below through specific embodiments.

[0095] The transitions and probabilities between nodes in the model are as follows Figures 3 to 5 As shown in the probability tree, probability trees are usually used to describe the occurrence process of random events, which can more clearly understand the state transition and probability in the Markov chain process. The probability tree consists of nodes (representing states) and branches (representing the transitions between states and their probabilities).

[0096] 1. Construct MMCA model: According to the MMCA algorithm, construct and solve the microscopic Markov chain equation based on UAU-SIS to study the transition probability of each node between different states in the two-layer network and the coupling behavior of disease transmission dynamics and information propagation.

[0097] Define the transition probabilities between different states, which are affected by the individual's state of consciousness, the characteristics of disease transmission, and the social interaction pattern. In the information dissemination network, the probability that an uninformed person does not choose to accept the information after the game and remains an uninformed person is expressed as r i (t), the probability that a conscious person does not choose to forget information after the game and is still conscious is expressed as θ i (t); In a physical contact network, the probability that node i is informed and not infected by any neighbor is If node i is unaware and not infected by any neighbor, the probability is Then the state transition probability based on the game strategy and behavior feedback co-evolution model is:

[0098]

[0099] Among them, it is allowed that A=(a ij ) N×N and B=(b ij ) N×N They represent the adjacency matrices corresponding to the information dissemination network and the physical contact network, respectively. Here, the network is an undirected network. If there is an edge between node i and node j, then a ij =a ji =1, b ij =b ji =1, otherwise a ij =a ji =0, b ij =b ji =0;β A represents the infection probability of conscious nodes; β U Represents the infection probability of an unconscious node.

[0100] It should be noted that i and j represent only general characters.

[0101] According to the individual's information awareness state and infectious disease infection state, each node i has three states at time t: an infected person who is aware of infectious diseases (AI), an infected person who is aware of infectious diseases (AS), and an infected person who is not aware of infectious diseases (US). The probabilities of the three states at time t are expressed as Here, the cooperative individual is defined as an individual with a conscious state, who takes protective measures when interacting with infected neighbors. This behavior is manifested as a certain conscious emphasis on the adjustment coefficient q in the physical contact network to reduce the probability of being infected by infected neighbors. Combining the state transition probability tree and the above formula, the three state probability evolution equations of each node i can be obtained as:

[0102]

[0103] 2. Analyze the model threshold. Since the infectious disease threshold determines whether an epidemic can break out or disappear, we analyze the effect of different parameters on the infectious disease threshold β. c The influence of is crucial. From the state transition probability tree ( Figure 3-Figure 5 ) derived from the MMCA equation, the critical epidemic threshold β can be calculated according to the threshold theory c As all nodes i and states in the system are in a stable state is a function of the other parameters. In the initial situation, there are more susceptible people S in the population, and few infected people who are aware of the infectious disease, that is, at this time Very small, let ∈ i is a small positive number; where i = 1, 2, ..., N, and N is the number of network nodes. For convenience, let According to formula (4),

[0104]

[0105] Similarly, we can get

[0106]

[0107] therefore, and Approximately and

[0108] Substituting into formula (5), we get:

[0109]

[0110] From formula (8) and the last equation in formula (5), it can be easily obtained that:

[0111]

[0112] because as well as Formula (9) can be expressed as:

[0113]

[0114] Among them, δ ji are the elements of the identity matrix.

[0115] Note that the solution of formula (12) reduces to the eigenvalue problem of the matrix H, whose elements are The occurrence of an epidemic is β c The minimum value that satisfies formula (12) is the maximum eigenvalue Λ of the matrix H max (H), whose critical point is:

[0116]

[0117] From formula (13), we can see that the epidemic threshold depends on the structure of the contact network (b ij ), parameter γ, consciousness emphasis adjustment coefficient q and consciousness density

[0118] In one embodiment, the threshold analysis of the double-layer coupled network infectious disease propagation model includes: solving the double-layer coupled network infectious disease propagation model, obtaining the state probabilities of nodes in the information propagation network and the physical contact network at different time points, and determining the infectious disease threshold through threshold theory analysis; the infectious disease threshold is used to determine whether an infectious disease has broken out or disappeared.

[0119] In one embodiment, determining the infectious disease threshold through threshold theory analysis includes: determining the infectious disease threshold through MC (MonteCarlo, Monte Carlo random simulation), MMCA and threshold theory analysis.

[0120] Specifically, in this embodiment, MC random simulation, MMCA modeling and threshold theory are used for detailed analysis and verification. Figure 6a (Shown as MMCA and MC for the proportion of conscious people ρ A ) and Figure 6b (Shown as MMCA and MC for the proportion of infected people ρ I This study compared the results of MMCA modeling and MC random simulation, effectively verifying the accuracy of MMCA-based analysis. These figures show the specific results obtained through numerical simulation, including how the diffusion of individual consciousness in the information layer after the introduction of the game evolution mechanism effectively reduces the transmission risk in the physical contact network (see Figures 7a to 7d and Figures 8a to 8d ;in, Figure 7a Shown is a comparison of information diffusion networks with and without game evolution mechanisms when μ = 0.2 and γ = 0.1; Figure 7b Shown is a comparison chart of the information dissemination network with and without the game evolution mechanism when μ = 0.2 and γ = 0.9; Figure 7c Shown is a comparison chart of the information dissemination network with and without the game evolution mechanism when μ = 0.8 and γ = 0.1; Figure 7d Shown is a comparison chart of the information dissemination network with and without the game evolution mechanism when μ = 0.8 and γ = 0.9; Figure 8a Shown is a comparison of the physical contact network with and without the game evolution mechanism when μ = 0.2 and γ = 0.1; Figure 8bShown is a comparison of the physical contact network with and without the game evolution mechanism when μ = 0.2 and γ = 0.9; Figure 8c Shown is a comparison of the physical contact network with and without the game evolution mechanism when μ = 0.8 and γ = 0.1; Figure 8d The figure shows the comparison of the physical contact network with and without the game evolution mechanism when μ = 0.8 and γ = 0.9), and how the intensity of consciousness regulation reflects the dynamic evolution of individual behavior and the actual communication characteristics (see Figures 9a to 9d ;in, Figure 9a The display is a comparison chart of different consciousness regulation intensities when μ=0.2 and γ=0.1; Figure 9b The display is a comparison chart of different consciousness regulation intensities when μ=0.2 and γ=0.9; Fig.9c The display is a comparison chart of different consciousness regulation intensities when μ=0.8 and γ=0.1; Figure 9d The comparison of different consciousness regulation intensities when μ = 0.8 and γ = 0.9 is shown in the figure). In addition, the statistical method PRCC (Partial Rank Correlation Coefficient) sensitivity analysis was used to further analyze the data, especially in processing and interpreting Fig.10 and Fig.11 The relationship between the infectious disease recovery rate (μ) and the awareness emphasis adjustment coefficient (q) and the infectious disease threshold (β c ). Finally, Fig.12 and Fig.13 The effect of the tempter parameter b on the proportion of individuals with epidemic prevention awareness ρ was discussed. A and the proportion of infected people ρ I The impact of the epidemic situation on individual epidemic prevention awareness is revealed when the cost of epidemic prevention increases. This part of the numerical simulation provides important theoretical support for understanding and controlling epidemic dynamics. The specific results of the example are as follows:

[0121] pass Figure 6a and Figure 6b The present invention compares the results of MMCA modeling and MC random simulation to verify the effectiveness of the MMCA-based analysis in the present invention. Figure 6a and Figure 6b As can be seen in Figure 1, the results based on the two simulation methods are very consistent. Therefore, in the following figures, the main results are obtained by MMCA equation simulation.

[0122] from Figures 7a to 7d , Figures 8a to 8d It can be seen that the introduction of the game evolution mechanism significantly promotes the spread of individual awareness related to infectious diseases in the information dissemination network, thereby reducing the risk of epidemic transmission in the physical contact network.

[0123] Specifically, in Figures 7a to 7dIn the paper, after the game evolution mechanism was added to the information dissemination network, the proportion of conscious individuals in the information dissemination network increased significantly, and the information exchange and decision-making process between individuals became more complex and rich. The introduction of the prisoner's dilemma game model requires individuals to consider not only their own interests when making decisions, but also the choices of other individuals and the possible impact. This game process promotes the rapid dissemination and sharing of information, allowing consciousness to spread rapidly in information dissemination. At the same time, when the recovery rate μ of infectious diseases is low, the proportion of conscious individuals in information dissemination is higher. This is because under low recovery rates, the duration of individual infection is longer, leaving more time for information dissemination, allowing more individuals to realize the existence of infectious diseases and transform into a conscious state. When the recovery rate μ of infectious diseases is high, the effect of the game evolution mechanism in information dissemination is more significant, which helps to maximize the efficiency of consciousness dissemination within a limited time. In addition, when the consciousness infection coefficient γ increases, that is, the difference in the probability of infection between unconscious and conscious states is narrowed, the game mechanism can play a better role and further enhance the individual's consciousness dissemination of infectious diseases.

[0124] Therefore, in Figures 8a to 8d The figure clearly shows the inhibitory effect of the game mechanism on the spread of infectious diseases in a two-layer coupled network. The figure shows that when the infectious disease recovery rate μ increases, the final infection scale is significantly reduced. This is because a higher recovery rate means that the infected person can recover to a susceptible state faster, thereby reducing the time and scope of the spread of infectious diseases in the network, resulting in a smaller overall infection scale. The smaller the consciousness infection coefficient γ, the higher the probability of infection in the unconscious state β U and the probability of infection in a conscious state β A The larger the gap between them, the higher the probability of infection of unconscious individuals is than that of conscious individuals. At this point, the game mechanism promotes the dissemination of information and the improvement of individual consciousness, so that more individuals can be transformed from unconscious to conscious states, thereby significantly reducing the overall probability of infection. In this state, the game mechanism effectively reduces the occurrence of high-risk behaviors and further compresses the scale of infectious disease transmission. Therefore, the smaller γ is, the stronger the inhibitory effect of the game mechanism on the spread of infectious diseases. Through the game process, people can have a deeper understanding of the importance and urgency of public health events, and thus participate more actively in the prevention and control of infectious diseases. This change in individual behavior directly leads to a reduction in the risk of epidemic transmission in physical contact networks. This innovation helps to enhance the public's awareness and participation in public health events, and has important practical significance for prevention and control work.

[0125] from Figures 9a to 9dIt can be seen that the consciousness regulation mechanism introduced, the data in the figure clearly shows that the increase in the intensity of consciousness regulation can significantly reduce the proportion of infected people, especially in the case of high consciousness infection coefficient. The three curves (q = 0, 0.5, 1) show that the proportion of infected people decreases significantly with the increase in the intensity of consciousness regulation. When the q value increases from 0 to 1, the decrease in the proportion of infected people indicates that strengthening individual consciousness has a significant effect on the prevention and control of infectious diseases. This shows that improving individual awareness of infectious disease prevention and control is a key strategy to control the spread of the epidemic. At the same recovery rate, but with a higher consciousness infection coefficient, the impact of consciousness regulation is more significant. The curve interval shows that with the increase of q value, the proportion of infected people further decreases, indicating that under high consciousness infection coefficient, strengthening consciousness regulation can more effectively control the spread of the epidemic. While the higher infectious disease recovery rate μ itself can effectively reduce the proportion of infected people, but combined with the increase in consciousness regulation intensity, the epidemic control effect can be further enhanced. These findings emphasize the importance of integrating consciousness regulation mechanisms in epidemic prevention and control strategies, and provide a scientific basis for designing more effective public health intervention measures. By effectively managing and improving public awareness of infectious disease prevention and control, the spread of the epidemic can be significantly slowed down or even prevented.

[0126] Fig.10 , Fig.11 By deeply exploring the effects of the infectious disease recovery rate μ and the awareness emphasis adjustment coefficient (q) on the infectious disease threshold (β c), providing important theoretical support for the understanding and control of epidemic dynamics. The high correlation between the infectious disease recovery rate and the infectious disease threshold (correlation strength of 0.99401) shows that improving the infectious disease recovery rate can significantly increase the threshold of epidemic transmission, that is, reduce the risk of large-scale outbreaks of infectious diseases. This finding has direct practical significance for formulating effective epidemic prevention and control strategies, such as strengthening medical resource investment and optimizing treatment plans. Secondly, the strong correlation between the consciousness regulation intensity and the infectious disease threshold (correlation strength of 0.86087) shows that by adjusting the consciousness regulation intensity, the epidemic transmission dynamics can also be effectively affected. This finding provides new ideas and methods for epidemic prevention and control by adjusting the sensitivity of consciousness to infectious diseases. For example, when an epidemic breaks out, enhancing individuals' perception of the threat of infectious diseases can prompt them to take more cautious epidemic prevention behaviors, such as improving personal hygiene habits, avoiding large gatherings, or taking the initiative to get vaccinated. These changes adjust the individual's behavior patterns at the micro level, which in turn affects the path and speed of infectious disease transmission in the entire social network. In addition, the adjustment of the consciousness regulation intensity coefficient can promote more effective dissemination of public health information. Through education and public publicity, timely conveying infectious disease-related information to the public, improving the public's response speed to emerging health threats and acceptance of prevention and control measures, helps to quickly control the spread of the epidemic. In short, the research results of the present invention are of great significance for a deep understanding of the evolution of infectious diseases in different environments. By analyzing the changes in infectious disease thresholds under different parameter settings, the development trend of the epidemic can be predicted more accurately, providing a scientific basis for formulating targeted prevention and control measures.

[0127] Fig.12 , Fig.13 The tempter parameter b and the proportion of conscious people ρ were studied in depth. A and the proportion of infected people ρ I , it can be found that when the tempter parameter b increases, that is, the cost of epidemic prevention increases, the number of individuals with epidemic prevention awareness will decrease. This finding provides a new perspective for a deeper understanding of the public's epidemic prevention behavior. In real life, the increase in epidemic prevention costs may include rising vaccine prices, cumbersome epidemic prevention measures, etc., all of which may reduce the public's enthusiasm for epidemic prevention. Therefore, when formulating epidemic prevention policies, the government and relevant departments should fully consider the impact of epidemic prevention costs on the public's awareness of epidemic prevention, take reasonable measures to reduce epidemic prevention costs, and improve the public's awareness and participation in epidemic prevention. Secondly, the increase in epidemic prevention costs will accelerate the spread of infectious diseases. This finding emphasizes the importance of optimizing epidemic prevention cost control. Excessive epidemic prevention costs will not only reduce the public's willingness to prevent epidemics, but may also aggravate the spread of infectious diseases and pose a threat to social public health security. Therefore, by reducing epidemic prevention costs and improving epidemic prevention efficiency, it is possible not only to enhance the public's awareness of epidemic prevention, but also to effectively curb the spread of infectious diseases and protect the public's health and safety.

[0128] According to the above technical scheme, the present invention proposes a method for constructing a two-layer coupled network UAU-SIS model based on game strategy, which mainly includes two innovative mechanisms: the game evolution mechanism of individual evolution in the information propagation network, and the broken edge reconnection mechanism of individuals in the physical contact network; by combining evolutionary game theory, MC, MMCA analysis, etc. to simulate the propagation process of infectious diseases and information, and analyze the coupled interaction relationship between the two, this model is closer to the complexity of individual behavior and information propagation in the real society. This method can more accurately simulate the spread process of the epidemic at different social network levels, thereby providing a more adaptable epidemic prediction and control strategy.

[0129] Firstly, the present invention constructs a double-layer network and a game evolution mechanism and a consciousness regulation mechanism according to complex network theory; secondly, it uses MMCA (model schematic diagram, such as Figure 3-Figure 5 The UAU-SIS model is constructed by using the method shown in the figure, which can not only consider the propagation law of infectious diseases, but also fully consider the dynamic influence of individual game psychology on behavior caused by the process of infectious disease information propagation, so as to provide more effective epidemic prediction and control strategies; by analyzing the Jacobian matrix of the system at the equilibrium point, the propagation threshold of infectious diseases is obtained through rigorous mathematical derivation according to the stability theory; finally, the model and evolution mechanism are simulated by MC (wherein, the simulation iteration number of random simulation MC is 20 times), and the effectiveness of simulating the evolution mechanism by the MMCA model is verified by comparing with the model constructed by MMCA; due to the adoption of the above technical scheme, the present invention comprehensively explores the complex law of interaction between infectious diseases and information revealed by the model through the construction method of dynamic evolution of double-layer coupled networks based on game strategies, and provides a new construction method and analysis angle for public health management, which can more effectively study the interaction between the propagation dynamics behavior of infectious diseases and individual behavior and information propagation, and provide theoretical and technical support for public health decision-making, which not only considers the propagation of infectious diseases, but also especially considers the propagation of information and the game evolution of individual behavior, which provides a new perspective and tool for understanding and controlling the epidemic.

[0130] The present invention aims to use the MMCA method to integrate the mechanism module on the basis of the network module to build a unified analysis framework. One of the core tasks is to construct the UAU-SIS Markov chain stochastic equation considering the game strategy mechanism and feedback mechanism, which aims to capture the complex interaction and dynamic evolution process of information dissemination and disease propagation in the network. Under the game strategy, the two-way feedback mechanism between information dissemination and disease propagation is further elaborated, revealing how information dissemination can serve as an early warning system to indirectly regulate disease propagation by changing individual behavior patterns; at the same time, how the actual situation of disease propagation is fed back to the information dissemination process, affecting the update and diffusion range of information content. Based on the above analysis, a series of optimization strategies based on network structure and disease characteristics are proposed, aiming to effectively inhibit disease propagation and promote public health safety by adjusting information dissemination strategies, enhancing public awareness, optimizing social policies and other means.

[0131] The protection scope of the method for constructing a double-layer coupled network infectious disease propagation model based on game strategy described in the embodiment of the present invention is not limited to the execution order of the steps listed in this embodiment. All solutions implemented by adding, reducing or replacing steps in the prior art based on the principles of the present invention are included in the protection scope of the present invention.

[0132] An embodiment of the present invention also provides a system for constructing a double-layer coupled network infectious disease propagation model based on a game strategy. The system for constructing a double-layer coupled network infectious disease propagation model based on a game strategy can implement the method for constructing a double-layer coupled network infectious disease propagation model based on a game strategy described in the present invention. However, the implementation device of the method for constructing a double-layer coupled network infectious disease propagation model based on a game strategy described in the present invention includes but is not limited to the structure of the system for constructing a double-layer coupled network infectious disease propagation model based on a game strategy listed in this embodiment. All structural deformations and replacements of the prior art made according to the principles of the present invention are included in the protection scope of the present invention.

[0133] like Fig.14 As shown, in one embodiment, the present invention provides a system for constructing a double-layer coupled network infectious disease propagation model based on a game strategy, wherein the double-layer coupled network infectious disease propagation model is applied to the analysis of the evolutionary dynamics of infectious disease propagation, and the double-layer coupled network infectious disease propagation model includes: an information propagation network of individual consciousness evolution and a physical contact network of infectious disease propagation; the information propagation network layer and the physical contact network include the same nodes; each of the nodes represents an individual; the edges in the information propagation network indicate that there is information propagation behavior between the two nodes connected by the edges; the edges in the physical contact network indicate physical contact between the two nodes connected by the edges; the construction system includes:

[0134] The network construction module 141 is used to construct the information dissemination network and the physical contact network.

[0135] The evolution modeling module 142 is used to model the evolution of individual consciousness using the UAU model according to the individual state in the information dissemination network, and to model the evolution of individual state using the SIS infectious disease model in the physical contact network.

[0136] The mechanism introduction module 143 is used to introduce the game strategy mechanism of individual consciousness into the information dissemination network.

[0137] The mechanism construction module 144 is used to construct a feedback mechanism of individual behavior in the physical contact network.

[0138] The model construction module 145 is used to construct a double-layer coupled network infectious disease propagation model based on the MMCA method, the information propagation network introducing the game strategy mechanism, and the physical contact network constructing the feedback mechanism, and to perform threshold analysis on the double-layer coupled network infectious disease propagation model.

[0139] It should be noted that the structures and principles of the network construction module 141, the evolutionary modeling module 142, the mechanism introduction module 143, the mechanism construction module 144 and the model construction module 145 correspond one to one with the steps (steps S1 to S5) in the above-mentioned method for constructing a two-layer coupled network infectious disease propagation model based on game strategy. The specific working principle can also be referred to the introduction to the method for constructing a two-layer coupled network infectious disease propagation model based on game strategy in the above-mentioned embodiment, so it will not be repeated here.

[0140] The descriptions of the processes or structures corresponding to the above-mentioned figures have different emphases. For parts that are not described in detail in a certain process or structure, please refer to the relevant descriptions of other processes or structures.

[0141] The above embodiments are merely illustrative of the principles and effects of the present invention, and are not intended to limit the present invention. Anyone familiar with the art may modify or alter the above embodiments without departing from the spirit and scope of the present invention. Therefore, all equivalent modifications or alterations made by a person of ordinary skill in the art without departing from the spirit and technical concept disclosed by the present invention shall still be covered by the claims of the present invention.

Claims

1. A method for constructing a double-layer coupled network infectious disease propagation model based on game strategy, characterized in that: The double-layer coupled network infectious disease propagation model is applied to the analysis of the evolutionary dynamics of infectious disease propagation. The double-layer coupled network infectious disease propagation model includes: an information propagation network of individual consciousness evolution and a physical contact network of infectious disease propagation; the information propagation network layer and the physical contact network include the same nodes; each of the nodes represents an individual; the edges in the information propagation network indicate that there is information propagation behavior between the two nodes connected by the edges; the edges in the physical contact network indicate physical contact between the two nodes connected by the edges; the construction method includes: constructing the information dissemination network and the physical contact network; In the information dissemination network, the UAU model is used to model the evolution of individual consciousness according to the individual state, and in the physical contact network, the SIS infectious disease model is used to model the evolution of individual state; Introducing a game strategy mechanism of individual consciousness into the information dissemination network; Building a feedback mechanism for individual behavior in the physical contact network; According to the MMCA method, a double-layer coupled network infectious disease propagation model is constructed by introducing the information propagation network of the game strategy mechanism and constructing the physical contact network of the feedback mechanism, and a threshold analysis is performed on the double-layer coupled network infectious disease propagation model.

2. The method for constructing a double-layer coupled network infectious disease propagation model based on game strategy according to claim 1 is characterized in that: The game strategy mechanism for introducing individual consciousness into the information dissemination network includes: individuals corresponding to nodes in the information dissemination network play games with individuals corresponding to adjacent nodes, and calculate the strategy imitation probability according to the payoff matrix, so as to influence the state of individuals in the information dissemination network based on the strategy imitation probability; the strategy imitation probability is used to guide the strategy selection of the consciousness state of nodes in the information dissemination network.

3. The method for constructing a double-layer coupled network infectious disease propagation model based on game strategy according to claim 1 is characterized in that: The feedback mechanism for building individual behaviors in the physical contact network includes: in the physical contact network, the nodes of the physical contact network adjust the edges of the nodes in the physical contact network according to the awareness of the nodes in the information dissemination network.

4. The method for constructing a double-layer coupled network infectious disease propagation model based on game strategy according to claim 1 is characterized in that: The double-layer coupled network infectious disease propagation model constructed according to the MMCA method, the information propagation network introducing the game strategy mechanism, and the physical contact network constructing the feedback mechanism includes: Based on the game strategy mechanism, the transition probability and benefit matrix between different states of each node in the information dissemination network and the physical contact network are set; Based on the states of each node in the information propagation network and the physical contact network and the transition probability, the double-layer coupled network infectious disease propagation model is constructed; the double-layer coupled network infectious disease propagation model describes the dynamic process of the states of all nodes in the information propagation network and the physical contact network changing over time; The threshold analysis of the double-layer coupled network infectious disease propagation model includes: solving the double-layer coupled network infectious disease propagation model, obtaining the state probabilities of nodes in the information propagation network and the physical contact network at different time points, and determining the infectious disease threshold through threshold theory analysis; the infectious disease threshold is used to determine whether an infectious disease breaks out or disappears.

5. A system for constructing a double-layer coupled network infectious disease propagation model based on game strategy, characterized in that: The double-layer coupled network infectious disease propagation model is applied to the analysis of the evolutionary dynamics of infectious disease propagation. The double-layer coupled network infectious disease propagation model includes: an information propagation network of individual consciousness evolution and a physical contact network of infectious disease propagation; the information propagation network layer and the physical contact network include the same nodes; each of the nodes represents an individual; the edges in the information propagation network indicate that there is information propagation behavior between the two nodes connected by the edges; the edges in the physical contact network indicate physical contact between the two nodes connected by the edges; the construction system includes: A network construction module, used to construct the information dissemination network and the physical contact network; An evolution modeling module, used to model the evolution of individual consciousness using the UAU model according to the individual state in the information dissemination network, and to model the evolution of individual state using the SIS infectious disease model in the physical contact network; A mechanism introduction module, used to introduce a game strategy mechanism of individual consciousness into the information dissemination network; A mechanism building module, used for building a feedback mechanism of individual behavior in the physical contact network; The model construction module is used to construct a double-layer coupled network infectious disease propagation model based on the MMCA method, the information propagation network introducing the game strategy mechanism, and the physical contact network constructing the feedback mechanism, and to perform threshold analysis on the double-layer coupled network infectious disease propagation model.

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