Information-epidemic coupled evolution analysis method under multi-source heterogeneous social influence

Abstract

The application discloses a kind of information-epidemic coupling evolution analysis method under the influence of multi-source heterogeneous society, first, constructs unconscious U-conscious A-unconscious U-susceptible S-infected I-susceptible S model under the influence of multi-source heterogeneous society;Then, according to the micro Markov chain method, theoretically derive the epidemic threshold β c Of unconscious U-conscious A-unconscious U-susceptible S-infected I-susceptible S model under different conditions;Finally, under the framework of multilayer time sequence network, implement the information-epidemic coupling evolution process under the influence of multi-source heterogeneous society.The application considers the influence of the multi-source and heterogeneity of social influence on the information-epidemic coupling evolution process in the activity-driven multilayer time sequence network, derives the information-epidemic coupling dynamics equation by micro Markov chain method, and theoretically solves the critical threshold β c Of epidemic spread under different conditions, which can provide theoretical guidance for formulating effective intervention measures to suppress epidemic spread.

Description

Technical Field

[0001] This invention relates to the field of information-epidemic coupling dynamics, and more particularly to a method for analyzing the coupling evolution of information-epidemic under multi-source heterogeneous social influences. Background Technology

[0002] The large-scale spread of sudden epidemics is often accompanied by the dissemination of epidemic-related information on social networks. In the absence of effective treatments and with limited medical resources, people can rely on the information they receive to guide their behavioral responses, such as wearing masks, maintaining social distancing, and getting vaccinated, to reduce the risk of infection. Therefore, a better understanding of the information-epidemic coupling evolution is crucial for formulating epidemic-related policies. In the field of information-epidemic coupling evolution dynamics, information diffusion is generally considered similar to epidemic transmission, and the classic unconscious U-conscious A-unconscious U-susceptible S-infected I-susceptible S model is used to theoretically analyze the dynamic process of information-epidemic coupling evolution. However, in real life, information diffusion is often more complex than epidemic transmission. On the one hand, if people are only informed of epidemic-related information by a few friends on social networks, they may not accept it. But when more friends tell them this information, the individual's herd mentality may prompt them to accept the information, i.e., social reinforcement. On the other hand, when people observe that neighbors in their contact network have infection symptoms, their sensitivity may prompt them to become aware of the epidemic, i.e., risk perception. In summary, the social reinforcement caused by local information diffusion in social networks and the risk perception induced by contacting neighbors in contact networks are the main social influences that drive people to acquire information.

[0003] However, existing technologies and modeling methods mostly focus on only one type of social influence, namely social reinforcement or risk perception, while neglecting the multi-source and heterogeneous characteristics of social influences. This leads to insufficient understanding of the dynamics of information-epidemic coupling evolution under multi-source and heterogeneous social influences, especially when the interactions between individuals evolve dynamically over time. Based on the above analysis, analyzing the impact of the multi-source and heterogeneous nature of social influences on the information-epidemic coupling evolution process through mathematical modeling theory within an activity-driven multi-layered temporal network framework is of great significance and can provide theoretical guidance for formulating effective interventions to suppress the spread of epidemics. Summary of the Invention

[0004] To overcome the shortcomings of the existing technologies, this invention provides a method for analyzing the coupled evolution of information and epidemics under multi-source heterogeneous social influences. Theoretically, it analyzes the impact of the multi-source and heterogeneous nature of social influences on the coupled evolution of information and epidemics within an activity-driven multi-layered temporal network framework, providing theoretical guidance for formulating epidemic-related policies.

[0005] The method of this invention first constructs an unconscious U-conscious A-unconscious U-susceptible S-infectious I-susceptible S model under multi-source heterogeneous social influences; then, based on the micro-Markov chain method, it theoretically derives the epidemic threshold β of the unconscious U-conscious A-unconscious U-susceptible S-infectious I-susceptible S model under different scenarios. c Finally, within a multi-layered temporal network framework, the information-epidemic coupled evolution process under multi-source heterogeneous social influences is implemented.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A novel method for analyzing the coupled evolution of information and epidemics under multi-source heterogeneous social influences is proposed. This method is applied to the field of activity-driven multi-layer temporal networks and the coupled dynamics of information and epidemics. The operational steps are as follows:

[0008] Step S1: Construct a model of unconscious U-conscious A-unconscious U-susceptible S-infected I-susceptible S under multi-source heterogeneous social influence;

[0009] Step S2: Based on the micro-Markov chain method, theoretically derive the epidemic threshold β under different scenarios for the unconscious U-conscious A-unconscious U-susceptible S-infected I-susceptible S model. c ;

[0010] Step S3: Under the framework of a multi-layered temporal network, implement the information-epidemic coupled evolution process under the influence of multi-source heterogeneous social factors.

[0011] Further, step S1 specifically includes the following steps:

[0012] Step S1.1: Activity-Driven Multilayer Temporal Network Evolution Rule: Considering the dynamic interactions between individuals in real life, an activity-driven multilayer temporal network evolution model is constructed, where the top layer represents the information network G. V The bottom layer represents the physical contact network G. P ; Assign each node i to the physical contact network G P Activity level a i and information network G V Activity level b i The network consists of i = 1, 2, ..., N, where N is the network size, and each network follows a power-law distribution F(a) = a^n with an exponent of γ. -γ and F(b)=b -γ γ is used to adjust the heterogeneity of the network; the specific steps are as follows:

[0013] 1) At each Δt time, the instantaneous network G of the physical contact layer P In (t), node i has an activity level a i It is activated and becomes an active node, and m is randomly selected.P Establish connections between nodes;

[0014] 2) At each Δt time, the instantaneous network G of the information layer V In (t), node i has an activity level of b. i It is activated and becomes an active node, and m is randomly selected. V Establish connections between nodes;

[0015] 3) At the next time t+Δt, delete all connections in the instantaneous network of the information and physical contact layer;

[0016] 4) Repeat steps 1)-3) until the propagation in the information and physical layers reaches a steady state;

[0017] Step S1.2: Considering the multi-source and heterogeneous nature of social influences, two mechanisms of consciousness generation induced by social influences were analyzed, namely social reinforcement and risk perception, as detailed below:

[0018] Social reinforcement: In the information layer, based on the phenomenon that individuals need notifications from multiple conscious neighbors before accepting information, a threshold model is used to describe social reinforcement. Specifically, an individual's herd mentality will only prompt them to accept epidemic-related information when the proportion of conscious neighbors reaches their awareness threshold θ. Furthermore, considering the differences in individual awareness thresholds, an individual awareness threshold θ is proposed. i b, the activity level of an individual in the information layer i The three relevant mechanisms, including stochastic correlation, linear negative correlation, and linear positive correlation, are as follows:

[0019] Case 1: Consciousness threshold θ i Independent of individual activity level in the information layer i The formula is as follows:

[0020] θ i =random[0,1],i=1,2,...N. (1)

[0021] It is worth noting that individuals with the same level of activity may have different consciousness thresholds; where i represents any individual and N represents the population size.

[0022] Case 2: Consciousness threshold θ i The activity level of individual i in the information layer b i They are negatively correlated, as shown in the following formula:

[0023]

[0024] Here, b max b represents the maximum activity level of all individuals in the information layer. minThis represents the minimum activity level of all individuals within the information layer;

[0025] Case 3: Consciousness threshold θ i The activity level of individual i in the information layer b i They are positively correlated, as shown in the following formula:

[0026]

[0027] Risk perception: In real life, when an unconscious individual observes that a neighbor in their physical contact layer shows symptoms of infection, the individual's sensitivity λ... i This can induce them to become aware of the epidemic and spread information; it is important to note that, unlike the social reinforcement effect, even if only one neighbor is infected, unconscious individuals may still become aware of the epidemic through risk perception.

[0028] Step S1.3: In the information layer, if individual i is aware of the epidemic, then individual i is in a conscious state A; otherwise, individual i is in an unconscious state U. In the physical contact layer, if individual i is infected, then individual i is in an infected state I; otherwise, individual i is in a susceptible state S. Considering the coupled evolution of information and the epidemic, individual i may be in the following four states: unconscious susceptible state US, conscious susceptible state AS, unconscious infected state UI, and conscious infected state AI.

[0029] Step S1.4: In the information layer, the information diffusion process is defined as follows: On the one hand, unconscious individual i becomes conscious A through the following three situations: (1) When the proportion of conscious neighbors reaches the consciousness threshold θ of individual i. i (a) When a neighbor in the physical contact layer shows symptoms of infection, the individual, with sensitivity λ i (c) When an unconscious individual i is infected, the individual becomes aware of the epidemic at a self-conscious rate κ; without loss of generality, it is assumed that all individuals have the same sensitivity, i.e. On the other hand, a conscious individual A i becomes an unconscious individual U with a forgetting rate δ.

[0030] Step S1.5: In the physical contact layer, the epidemic transmission process is defined as follows: Susceptible individual S i is infected by contact with infected individual I at an infection rate β, and infected individual I i becomes susceptible S at a recovery rate μ; In particular, when susceptible individual S i is in a conscious state A in the information layer, individual i will take behavioral responses to reduce the infection rate of the epidemic through a decay factor α.

[0031] Furthermore, step S2 specifically involves the following steps:

[0032] Step S2.1: At time t, the probabilities of node i being in the unconscious susceptible state US, the conscious susceptible state AS, the unconscious infected state UI, and the conscious infected state AI are respectively represented by... and To indicate;

[0033] Step S2.2: The probability r of unconscious individual i maintaining state U in the information layer i (t), the formula is as follows:

[0034]

[0035] In formula (4), the first term represents the probability that an unconscious individual i remains unconscious because it is not persuaded by a conscious neighbor in the information layer; the second term represents the probability that an unconscious individual i remains unconscious because it is not induced by the infection symptoms of a neighbor in the physical contact layer; considering that individuals have different preferences for information obtained from different social influences, Q is defined to represent the weight of social reinforcement; correspondingly, 1-Q represents the weight of risk perception; H(x) represents the step function, where H(x) = 1 when x > 0, and H(x) = 0 otherwise; where i represents any individual, j represents any individual other than i, and θ i b represents the consciousness threshold of individual i. i b represents the activity level of individual i in the information layer. j This indicates the activity level of individual j in the information layer. F(b) represents the probability that individual j is in the conscious state A at time t. j ) indicates that individual j has an activity level of b in the information layer. j The probability, λ represents the individual's sensitivity, m p a represents the number of edges sent by active nodes in the physical contact layer. i a represents the activity level of individual i in the physical contact layer. j This indicates the activity level of individual j in the physical contact layer. Let represent the probability that individual j is in infected state I at time t.

[0036] Step S2.3: The probabilities of unconscious state U and conscious state A individual i in the information layer maintaining susceptible state S in the physical contact layer are respectively... and The formula is as follows:

[0037]

[0038]

[0039] Wherein, formula (5) represents the contact m between an active / inactive unconsciously susceptible US individual i and an active / inactive individual i. PThe probability of an inactive / active infected individual I j not being infected; Formula (6) represents the probability that a conscious susceptible individual AS i in the information layer takes a behavioral response in the physical contact layer to reduce the infection rate β of the epidemic by the attenuation factor α and not be infected.

[0040] Step S2.4: Based on the micro-Markov chain method and combined with formulas (4)-(6), we can obtain... The dynamic evolution equation:

[0041]

[0042] Among them, normalization conditions Applicable to all time steps; taking the first equation in formula (7) as an example, the first term represents the probability r of an unconscious susceptible US individual i at time t. i (t) Maintain unconscious state U while with probability The probability of maintaining the susceptible state S; the second term represents the probability r of unintentionally infected individual i at time t. i (t) The probability of remaining in an unconscious state U while simultaneously transitioning to a susceptible state S with a recovery rate μ; the third term represents the probability at time t that an individual i in a conscious susceptible state AS transitions to an unconscious state U with a forgetting rate δ and simultaneously transitions to a susceptible state S with a recovery rate μ. The probability of remaining in the susceptible state S; the fourth term represents the probability at time t that a consciously infected AI individual i changes to an unconscious state U with a forgetting rate δ and simultaneously changes to the susceptible state S with a recovery rate μ.

[0043] Step S2.5: Based on equation set (7), the critical threshold β for epidemic transmission can be theoretically derived. c for:

[0044]

[0045] From formula (8), we can see the epidemic threshold β c It depends on the recovery rate μ, the individual's behavioral response intensity α, and the network topology of the physical contact layer, i.e., the first moment of activity. and second moment 2 >, and the number of edges m p And conscious individuals ρ in steady state A The proportion;

[0046] Step S2.6: According to formula (4), it is found that the weight Q of social reinforcement affects the conscious individual ρ at homeostasis. A The proportion is an important factor; therefore, further analysis is needed to determine the critical threshold β of multi-source social influence on epidemic transmission under the following three scenarios. c The impact;

[0047] Case 1: Individuals are fully aware of the epidemic through risk perception, i.e., Q=0, and the critical threshold β for epidemic transmission. c for:

[0048]

[0049] As can be seen from formula (9), the epidemic threshold β c Depending on the recovery rate μ, the network topology of the physical contact layer, i.e., the first moment of activity.​ and second moment 2 >, and the number of edges m p ;

[0050] Case 2: Individuals become aware of an epidemic entirely through social reinforcement, i.e., Q=1, and the critical threshold β for epidemic transmission under the condition of a homogeneous awareness threshold θ. c for:

[0051]

[0052] As can be seen from formula (10), unlike formula (9), the critical threshold β for epidemic transmission... c It also depends on the information forgetting rate δ and the critical point θ0 of the consciousness threshold; when approaching the critical point θ0 of the consciousness threshold, the epidemic threshold β... c The occurrence of mutations indicates that the impact of information diffusion on the epidemic threshold has a two-stage characteristic;

[0053] Case 3: Individuals simultaneously become aware of an epidemic through social reinforcement and risk perception, i.e., Q∈(0,1). What is the critical threshold β for epidemic transmission under the condition of a homogeneous awareness threshold θ? c for:

[0054]

[0055] As can be seen from formula (11), unlike formula (10), the critical threshold β for epidemic transmission... c It also depends on the weight Q of social reinforcement.

[0056] Furthermore, step S3 specifically involves the following steps:

[0057] Step S3.1: Set the parameters for the unconscious U-conscious A-unconscious U-susceptible S-infectious I-susceptible S model under multi-source heterogeneous social influence and the activity-driven multi-layer temporal network model, including the network size N and the number of edges m of active nodes in the information layer and physical contact layer. V and m P The activity level of node i in the physical contact layer and the information layer, a i and b i The time interval Δt, the epidemic infection rate β, the epidemic recovery rate μ, the information forgetting rate δ, the awareness threshold θ, the sensitivity factor λ, the weight of social reinforcement Q, the behavioral response intensity α, the self-awareness rate κ, the total number of simulations and the maximum time step T;

[0058] Step S3.2: Randomly initialize a certain proportion of infected state I0 and conscious state A0 as seed nodes;

[0059] ​Step S3.3: At each Δt time, according to the activity-driven multilayer temporal network evolution rule in step S1.1 of claim 2, generate an activity-driven multilayer temporal network evolution model;

[0060] Step S3.4: At each Δt time, for the information diffusion process, according to step S1.4 in claim 2, node i in the information layer updates whether it is in a conscious state based on the consciousness state of its neighbors in the information layer, the infection state of its neighbors in the physical contact layer, and the infection state of node i in the physical contact layer.

[0061] Step S3.5: At each Δt time, for the epidemic transmission process, according to step S1.5 in claim 2, node i in the physical contact layer updates whether it is infected based on the consciousness state of its corresponding node in the information layer;

[0062] Step S3.6: The propagation process lasts for Δt time;

[0063] Step S3.7: Repeat steps S3.3-S3.6 until the spread of the epidemic and the diffusion of information reach a steady state;

[0064] Step S3.8: Statistically determine the conscious state ρ at steady state. A and infected state p I The proportion of nodes;

[0065] Step S3.9: Repeat steps S3.2-S3.8 above until the total number of simulations is reached;

[0066] Step S3.10: When counting the total number of simulations, the conscious state ρ A and infected state p I The average proportion of nodes indicates the end of the information-epidemic coupling evolution process.

[0067] Compared with the prior art, the present invention has the following obvious and prominent substantive features and significant advantages:

[0068] 1. This invention constructs a mathematical model based on multi-source heterogeneous social influences: Unconscious U - Conscious A - Unconscious U - Susceptible S - Infected I - Susceptible S. This model considers public acceptance preferences for multi-source social influences and describes the differences in multi-source social influences among different individuals. It provides a critical threshold β for analyzing the spread of epidemics under multi-source heterogeneous social influences. c This provides theoretical support for the coupled evolution of information and epidemics;

[0069] 2. This invention effectively verifies the accuracy of the theoretically predicted epidemic threshold through simulation experiments, and systematically studies the single or combined effects of social reinforcement and risk perception, which can provide a reference for accurately describing the coupled evolution process of information-epidemic in real life.

[0070] 3. The method proposed in this invention can provide theoretical guidance for formulating effective intervention measures to suppress the spread of epidemics. Attached Figure Description

[0071] The accompanying drawings, incorporated in and constituting a part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application. To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. The described drawings are some embodiments of the present invention; for those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0072] Figure 1 This is a schematic diagram of the information-epidemic coupled evolution analysis method under multi-source heterogeneous social influences in an embodiment of the present invention.

[0073] Figure 2 This is a schematic diagram of the information-epidemic coupling evolution model under multi-source heterogeneous social influences in an embodiment of the present invention.

[0074] Figure 3 This is a schematic diagram of the state transition probability tree of information-epidemic under multi-source heterogeneous social influence in an embodiment of the present invention. Detailed Implementation

[0075] To enable those skilled in the art to better understand the technical solutions in this application, the technical solutions in the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of this application.

[0076] To better understand this application, the embodiments of this application will be explained in detail below with reference to the accompanying drawings.

[0077] Example 1:

[0078] See Figure 1 , Figure 2 and Figure 3 A novel method for analyzing the coupled evolution of information and epidemics under multi-source heterogeneous social influences is proposed. This method utilizes activity-driven multi-layer temporal networks and the dynamics of information-epidemic coupling. The operational steps are as follows:

[0079] Step S1: Construct a model of unconscious U-conscious A-unconscious U-susceptible S-infected I-susceptible S under multi-source heterogeneous social influences, specifically as follows:

[0080] Step S1.1: Activity-Driven Multilayer Temporal Network Evolution Rule: Considering the dynamic interactions between individuals in real life, an activity-driven multilayer temporal network evolution model is constructed, where the top layer represents the information network G. V The bottom layer represents the physical contact network G. P ; Assign each node i to the physical contact network G P Activity level a i and information network G V Activity level b i The network consists of i = 1, 2, ..., N, where N is the network size, and each network follows a power-law distribution F(a) = a^n with an exponent of γ. -γ and F(b)=b -γ γ is used to adjust the heterogeneity of the network; the specific steps are as follows:

[0081] 1) At each Δt time, the instantaneous network G of the physical contact layer P In (t), node i has an activity level a i It is activated and becomes an active node, and m is randomly selected. P Establish connections between nodes;

[0082] 2) At each Δt time, the instantaneous network G of the information layer V In (t), node i has an activity level of b. i It is activated and becomes an active node, and m is randomly selected. VEstablish connections between nodes;

[0083] 3) At the next time t+Δt, delete all connections in the instantaneous network of the information and physical contact layer;

[0084] 4) Repeat steps 1)-3) until the propagation in the information and physical layers reaches a steady state;

[0085] Step S1.2: Considering the multi-source and heterogeneous nature of social influences, two mechanisms of consciousness generation induced by social influences were analyzed, namely social reinforcement and risk perception, as detailed below:

[0086] Social reinforcement: In the information layer, based on the phenomenon that individuals need notifications from multiple conscious neighbors before accepting information, a threshold model is used to describe social reinforcement. Specifically, an individual's herd mentality will only prompt them to accept epidemic-related information when the proportion of conscious neighbors reaches their awareness threshold θ. Furthermore, considering the differences in individual awareness thresholds, an individual awareness threshold θ is proposed. i b, the activity level of an individual in the information layer i The three relevant mechanisms, including stochastic correlation, linear negative correlation, and linear positive correlation, are as follows:

[0087] Case 1: Consciousness threshold θ i Independent of individual activity level in the information layer i The formula is as follows:

[0088] θ i =random[0,1],i=1,2,...N. (1)

[0089] It is worth noting that individuals with the same level of activity may have different consciousness thresholds; where i represents any individual and N represents the population size.

[0090] Case 2: Consciousness threshold θ i The activity level of individual i in the information layer b i They are negatively correlated, as shown in the following formula:

[0091]

[0092] Here, b max b represents the maximum activity level of all individuals in the information layer. min This represents the minimum activity level of all individuals within the information layer;

[0093] Case 3: Consciousness threshold θ i The activity level of individual i in the information layer b i They are positively correlated, as shown in the following formula:

[0094]

[0095] Risk perception: In real life, when an unconscious individual observes that a neighbor in their physical contact layer shows symptoms of infection, the individual's sensitivity λ... i This can induce them to become aware of the epidemic and spread information; it is important to note that, unlike the social reinforcement effect, even if only one neighbor is infected, unconscious individuals may still become aware of the epidemic through risk perception.

[0096] Step S1.3: In the information layer, if individual i is aware of the epidemic, then individual i is in a conscious state A; otherwise, individual i is in an unconscious state U. In the physical contact layer, if individual i is infected, then individual i is in an infected state I; otherwise, individual i is in a susceptible state S. Considering the coupled evolution of information and the epidemic, individual i may be in the following four states: unconscious susceptible state US, conscious susceptible state AS, unconscious infected state UI, and conscious infected state AI.

[0097] Step S1.4: In the information layer, the information diffusion process is defined as follows: On the one hand, unconscious individual i becomes conscious A through the following three situations: (1) When the proportion of conscious neighbors reaches the consciousness threshold θ of individual i. i (a) When a neighbor in the physical contact layer shows symptoms of infection, the individual, with sensitivity λ i (c) When an unconscious individual i is infected, the individual becomes aware of the epidemic at a self-conscious rate κ; without loss of generality, it is assumed that all individuals have the same sensitivity, i.e. On the other hand, a conscious individual A i becomes an unconscious individual U with a forgetting rate δ.

[0098] Step S1.5: In the physical contact layer, the epidemic transmission process is defined as follows: Susceptible individual S i is infected by contact with infected individual I at an infection rate β, and infected individual I i becomes susceptible S at a recovery rate μ; In particular, when susceptible individual S i is in a conscious state A in the information layer, individual i will take behavioral responses to reduce the infection rate of the epidemic through a decay factor α.

[0099] Step S2: Based on the micro-Markov chain method, theoretically derive the epidemic threshold β under different scenarios for the model of unconscious U - conscious A - unconscious U - susceptible S - infected I - susceptible S. c Specifically:

[0100] Step S2.1: At time t, the probabilities of node i being in the unconscious susceptible state US, the conscious susceptible state AS, the unconscious infected state UI, and the conscious infected state AI are respectively represented by... and To indicate;

[0101] Step S2.2: The probability r of unconscious individual i maintaining state U in the information layer i (t), the formula is as follows:

[0102]

[0103] In formula (4), the first term represents the probability that an unconscious individual i remains unconscious because it is not persuaded by a conscious neighbor in the information layer; the second term represents the probability that an unconscious individual i remains unconscious because it is not induced by the infection symptoms of a neighbor in the physical contact layer; considering that individuals have different preferences for information obtained from different social influences, Q is defined to represent the weight of social reinforcement; correspondingly, 1-Q represents the weight of risk perception; H(x) represents the step function, where H(x) = 1 when x > 0, and H(x) = 0 otherwise; where i represents any individual, j represents any individual other than i, and θ i b represents the consciousness threshold of individual i. i b represents the activity level of individual i in the information layer. j This indicates the activity level of individual j in the information layer. F(b) represents the probability that individual j is in the conscious state A at time t. j ) indicates that individual j has an activity level of b in the information layer. j The probability, λ represents the individual's sensitivity, m p a represents the number of edges sent by active nodes in the physical contact layer. i a represents the activity level of individual i in the physical contact layer. j This indicates the activity level of individual j in the physical contact layer. Let represent the probability that individual j is in infected state I at time t;

[0104] Step S2.3: The probabilities of unconscious state U and conscious state A individual i in the information layer maintaining susceptible state S in the physical contact layer are respectively... and The formula is as follows:

[0105]

[0106]

[0107] Wherein, formula (5) represents the contact m between an active / inactive unconsciously susceptible US individual i and an active / inactive individual i. P The probability of an inactive / active infected individual I j not being infected; Formula (6) represents the probability that a conscious susceptible individual AS i in the information layer takes a behavioral response in the physical contact layer to reduce the infection rate β of the epidemic by the attenuation factor α and not be infected.

[0108] Step S2.4: Based on the micro-Markov chain method and combined with formulas (4)-(6), we can obtain... The dynamic evolution equation:

[0109]

[0110] Among them, normalization conditions Applicable to all time steps; taking the first equation in formula (7) as an example, the first term represents the probability r of an unconscious susceptible US individual i at time t. i (t) Maintain unconscious state U while with probability The probability of maintaining the susceptible state S; the second term represents the probability r of unintentionally infected individual i at time t. i (t) The probability of remaining in an unconscious state U while simultaneously transitioning to a susceptible state S with a recovery rate μ; the third term represents the probability at time t that an individual i in a conscious susceptible state AS transitions to an unconscious state U with a forgetting rate δ and simultaneously transitions to a susceptible state S with a recovery rate μ. The probability of remaining in the susceptible state S; the fourth term represents the probability at time t that a consciously infected AI individual i changes to an unconscious state U with a forgetting rate δ and simultaneously changes to the susceptible state S with a recovery rate μ.

[0111] Step S2.5: Based on equation set (7), the critical threshold β for epidemic transmission can be theoretically derived. c for:

[0112]

[0113] From formula (8), we can see the epidemic threshold β c It depends on the recovery rate μ, the individual's behavioral response intensity α, and the network topology of the physical contact layer, i.e., the first moment of activity. and second moment 2 >, and the number of edges m p And conscious individuals ρ in steady state A The proportion;

[0114] Step S2.6: According to formula (4), it is found that the weight Q of social reinforcement affects the conscious individual ρ at homeostasis. A The proportion is an important factor; therefore, further analysis is needed to determine the critical threshold β of multi-source social influence on epidemic transmission under the following three scenarios. c The impact;

[0115] Case 1: Individuals are fully aware of the epidemic through risk perception, i.e., Q=0, and the critical threshold β for epidemic transmission. c for:

[0116]

[0117] As can be seen from formula (9), the epidemic threshold β c Depending on the recovery rate μ, the network topology of the physical contact layer, i.e., the first moment of activity.​ and second moment 2 >, and the number of edges m p ;

[0118] Case 2: Individuals become aware of an epidemic entirely through social reinforcement, i.e., Q=1, and the critical threshold β for epidemic transmission under the condition of a homogeneous awareness threshold θ. c for:

[0119]

[0120] As can be seen from formula (10), unlike formula (9), the critical threshold β for epidemic transmission... c It also depends on the information forgetting rate δ and the critical point θ0 of the consciousness threshold; when approaching the critical point θ0 of the consciousness threshold, the epidemic threshold β... c The occurrence of mutations indicates that the impact of information diffusion on the epidemic threshold has a two-stage characteristic;

[0121] Case 3: Individuals simultaneously become aware of an epidemic through social reinforcement and risk perception, i.e., Q∈(0,1). What is the critical threshold β for epidemic transmission under the condition of a homogeneous awareness threshold θ? c for:

[0122]

[0123] As can be seen from formula (11), unlike formula (10), the critical threshold β for epidemic transmission... c It also depends on the weight Q of social reinforcement.

[0124] Step S3: Within a multi-layered temporal network framework, implement the information-epidemic coupled evolution process under multi-source heterogeneous social influences, specifically as follows:

[0125] Step S3.1: Set the parameters for the unconscious U-conscious A-unconscious U-susceptible S-infectious I-susceptible S model under multi-source heterogeneous social influence and the activity-driven multi-layer temporal network model, including the network size N and the number of edges m of active nodes in the information layer and physical contact layer. V and m P The activity level of node i in the physical contact layer and the information layer, a i and b i The time interval Δt, the epidemic infection rate β, the epidemic recovery rate μ, the information forgetting rate δ, the awareness threshold θ, the sensitivity factor λ, the weight of social reinforcement Q, the behavioral response intensity α, the self-awareness rate κ, the total number of simulations and the maximum time step T;

[0126] Step S3.2: Randomly initialize a certain proportion of infected state I0 and conscious state A0 as seed nodes;

[0127] ​Step S3.3: At each Δt time, according to the activity-driven multilayer temporal network evolution rule in step S1.1 of claim 2, generate an activity-driven multilayer temporal network evolution model;

[0128] Step S3.4: At each Δt time, for the information diffusion process, according to step S1.4 in claim 2, node i in the information layer updates whether it is in a conscious state based on the consciousness state of its neighbors in the information layer, the infection state of its neighbors in the physical contact layer, and the infection state of node i in the physical contact layer.

[0129] Step S3.5: At each Δt time, for the epidemic transmission process, according to step S1.5 in claim 2, node i in the physical contact layer updates whether it is infected based on the consciousness state of its corresponding node in the information layer;

[0130] Step S3.6: The propagation process lasts for Δt time;

[0131] Step S3.7: Repeat steps S3.3-S3.6 until the spread of the epidemic and the diffusion of information reach a steady state;

[0132] Step S3.8: Statistically determine the conscious state ρ at steady state. A and infected state p I The proportion of nodes;

[0133] Step S3.9: Repeat steps S3.2-S3.8 above until the total number of simulations is reached;

[0134] Step S3.10: When counting the total number of simulations, the conscious state ρ A and infected state p I The average proportion of nodes indicates the end of the information-epidemic coupling evolution process.

[0135] This embodiment analyzes the single or combined effects of social reinforcement and risk perception on the information-epidemic coupled evolution process, and further verifies the accuracy of the theoretically predicted epidemic threshold.

[0136] Example 2:

[0137] This embodiment is basically the same as the above embodiments, with the following differences:

[0138] Step S1: This step is the same as in Example 1;

[0139] Step S2: This step is the same as in Example 1;

[0140] Step S3: Within a multi-layered temporal network framework, implement the information-epidemic coupled evolution process under multi-source heterogeneous social influences, specifically as follows:

[0141] Step S3.1: Set the parameters for the unconscious U-conscious A-unconscious U-susceptible S-infectious I-susceptible S model under multi-source heterogeneous social influence and the activity-driven multi-layer temporal network model, including the network size N and the number of edges m of active nodes in the information layer and physical contact layer. V and m P The activity level of node i in the physical contact layer and the information layer, a i and b i The time interval Δt, the epidemic infection rate β, the epidemic recovery rate μ, the information forgetting rate δ, the sensitivity factor λ, the weight of social reinforcement Q, the intensity of behavioral response α, the self-awareness rate κ, the total number of simulations and the maximum time step T;

[0142] Step S3.2: Based on their willingness to accept information, individuals are categorized into activists, paranoids, and moderates. Paranoids, with a higher awareness threshold θ, are individuals with a lower willingness to accept information; they will only accept information if all their neighbors notify them. Activists, with a lower awareness threshold θ, are individuals with a higher willingness to accept information; they will accept information even if only one neighbor notifies them. In particular, moderates are individuals whose willingness to accept information falls between that of activists and paranoids.

[0143] Step S3.3: Given a consciousness threshold θ = 0, θ = 0.5 and θ = 1 represent activists, moderates and paranoids, respectively;

[0144] Step S3.4: Randomly initialize a certain proportion of infected state I0 and conscious state A0 as seed nodes;

[0145] Step S3.5: At each Δt time, according to the activity-driven multilayer temporal network evolution rule in step S1.1 of claim 2, generate an activity-driven multilayer temporal network evolution model;

[0146] Step S3.6: At each Δt time, for the information diffusion process, according to step S1.4 in claim 2, node i in the information layer updates whether it is in a conscious state based on the consciousness state of its neighbors in the information layer, the infection state of its neighbors in the physical contact layer, and the infection state of node i in the physical contact layer.

[0147] Step S3.7: At each Δt time, for the epidemic transmission process, according to step S1.5 in claim 2, node i in the physical contact layer updates whether it is infected based on the consciousness state of its corresponding node in the information layer;

[0148] Step S3.8: The propagation process lasts for Δt time;

[0149] Step S3.9: Repeat steps S3.5-S3.8 until the spread of the epidemic and the diffusion of information reach a steady state;

[0150] Step S3.10: Statistically determine the conscious state ρ at different consciousness thresholds during steady state. A and infected state p I The proportion of nodes;

[0151] Step S3.11: Repeat steps S3.4-S3.10 above until the total number of simulations is reached;

[0152] Step S3.12: Count the number of simulations with different consciousness thresholds and the resulting conscious state ρ. A and infected state p I The average proportion of nodes indicates the end of the information-epidemic coupling evolution process.

[0153] In this embodiment, the impact of different awareness thresholds on the information-epidemic coupling evolution process was explored, showing that increasing individuals' willingness to accept information will prompt more individuals to take behavioral responses to significantly suppress the spread of the epidemic.

[0154] Example 3:

[0155] This embodiment is basically the same as the above embodiments, with the following differences:

[0156] Step S1: This step is the same as in Example 1;

[0157] Step S2: This step is the same as in Example 1;

[0158] Step S3: Within a multi-layered temporal network framework, implement the information-epidemic coupled evolution process under multi-source heterogeneous social influences, specifically as follows:

[0159] Step S3.1: Set the parameters for the unconscious U-conscious A-unconscious U-susceptible S-infectious I-susceptible S model under multi-source heterogeneous social influence and the activity-driven multi-layer temporal network model, including the network size N and the number of edges m of active nodes in the information layer and physical contact layer. V and m P The activity level of node i in the physical contact layer and the information layer, a i and b i The time interval Δt, the epidemic infection rate β, the epidemic recovery rate μ, the information forgetting rate δ, the weight of social reinforcement Q, the intensity of behavioral response α, the self-awareness rate κ, the total number of simulations and the maximum time step T;

[0160] Step S3.2: Set the individual sensitivity factor λ and awareness threshold θ to vary from 0 to 1;

[0161] Step S3.3: Randomly initialize a certain proportion of infected state I0 and conscious state A0 as seed nodes;

[0162] Step S3.4: At each Δt time, according to the activity-driven multilayer temporal network evolution rule in step S1.1 of claim 2, generate an activity-driven multilayer temporal network evolution model;

[0163] Step S3.5: At each Δt time, for the information diffusion process, according to step S1.4 in claim 2, node i in the information layer updates whether it is in a conscious state based on the consciousness state of its neighbors in the information layer, the infection state of its neighbors in the physical contact layer, and the infection state of node i in the physical contact layer.

[0164] Step S3.6: At each Δt time, for the epidemic transmission process, according to step S1.5 in claim 2, node i in the physical contact layer updates whether it is infected based on the consciousness state of its corresponding node in the information layer;

[0165] Step S3.7: The propagation process lasts for Δt time;

[0166] Step S3.8: Repeat steps S3.4-S3.7 until the spread of the epidemic and the diffusion of information reach a steady state;

[0167] Step S3.9: Statistically determine the conscious state ρ at steady state. A and infected state p I The proportion of nodes;

[0168] Step S3.10: Repeat steps S3.3-S3.9 above until the total number of simulations is reached;

[0169] Step S3.11: When counting the total number of simulations, the conscious state ρ A and infected state p I The average proportion of nodes indicates the end of the information-epidemic coupling evolution process.

[0170] In this embodiment, the combined effect of individual sensitivity factor λ and awareness threshold θ was explored, and it was found that comprehensively considering social reinforcement and risk perception helps to formulate effective strategies for responding to sudden epidemics.

[0171] Example 4:

[0172] This embodiment is basically the same as the above embodiments, with the following differences:

[0173] Step S1: This step is the same as in Example 1;

[0174] Step S2: This step is the same as in Example 1;

[0175] Step S3: Within a multi-layered temporal network framework, implement the information-epidemic coupled evolution process under multi-source heterogeneous social influences, specifically as follows:

[0176] Step S3.1: Set the parameters for the unconscious U-conscious A-unconscious U-susceptible S-infectious I-susceptible S model under multi-source heterogeneous social influence and the activity-driven multi-layer temporal network model, including the network size N and the number of edges m of active nodes in the information layer and physical contact layer. V and m P The activity level of node i in the physical contact layer and the information layer, a i and b i The time interval Δt, the information forgetting rate δ, the sensitivity factor λ, the weight of social reinforcement Q, the behavioral response intensity α, the self-awareness rate κ, the total number of simulations and the maximum time step T;

[0177] Step S3.2: Given different epidemic recovery rates μ, set the epidemic infection rate β and awareness threshold θ to vary from 0 to 1;

[0178] Step S3.3: Randomly initialize a certain proportion of infected state I0 and conscious state A0 as seed nodes;

[0179] Step S3.4: At each Δt time, according to the activity-driven multilayer temporal network evolution rule in step S1.1 of claim 2, generate an activity-driven multilayer temporal network evolution model;

[0180] Step S3.5: At each Δt time, for the information diffusion process, according to step S1.4 in claim 2, node i in the information layer updates whether it is in a conscious state based on the consciousness state of its neighbors in the information layer, the infection state of its neighbors in the physical contact layer, and the infection state of node i in the physical contact layer.

[0181] Step S3.6: At each Δt time, for the epidemic transmission process, according to step S1.5 in claim 2, node i in the physical contact layer updates whether it is infected based on the consciousness state of its corresponding node in the information layer;

[0182] Step S3.7: The propagation process lasts for Δt time;

[0183] Step S3.8: Repeat steps S3.4-S3.7 until the spread of the epidemic and the diffusion of information reach a steady state;

[0184] Step S3.9: Statistical analysis of conscious state ρ under different epidemiological recovery rates μ at steady state. A and infected state p I The proportion of nodes;

[0185] Step S3.10: Repeat steps S3.3-S3.9 above until the total number of simulations is reached;

[0186] Step S3.11: When counting the total number of simulations, the conscious state ρ under different epidemic recovery rates μ. A and infected state p I The average proportion of nodes indicates the end of the information-epidemic coupling evolution process.

[0187] This embodiment explores the combined effect of epidemic infection rate β and consciousness threshold θ under different epidemic recovery rates μ.

[0188] Example 5:

[0189] This embodiment is basically the same as the above embodiments, with the following differences:

[0190] Step S1: This step is the same as in Example 1;

[0191] Step S2: This step is the same as in Example 1;

[0192] Step S3: Within a multi-layered temporal network framework, implement the information-epidemic coupled evolution process under multi-source heterogeneous social influences, specifically as follows:

[0193] Step S3.1: Set the parameters for the unconscious U-conscious A-unconscious U-susceptible S-infectious I-susceptible S model under multi-source heterogeneous social influence and the activity-driven multi-layer temporal network model, including the network size N and the number of edges m of active nodes in the information layer and physical contact layer. V and m P The activity level of node i in the physical contact layer and the information layer, a i and b i The time interval Δt, the epidemic infection rate β, the epidemic recovery rate μ, the information forgetting rate δ, the sensitivity factor λ, the weight of social reinforcement Q, the intensity of behavioral response α, the self-awareness rate κ, the total number of simulations and the maximum time step T;

[0194] Step S3.2: Based on the individual's activity level b in the information layer i Using formulas (1)-(3) as described in claim 2, the consciousness threshold θ of an individual under random correlation, linear negative correlation, and linear positive correlation can be calculated. i ;

[0195] Step S3.3: Randomly initialize a certain proportion of infected state I0 and conscious state A0 as seed nodes;

[0196] Step S3.4: At each Δt time, according to the activity-driven multilayer temporal network evolution rule in step S1.1 of claim 2, generate an activity-driven multilayer temporal network evolution model;

[0197] Step S3.5: At each Δt time, for the information diffusion process, according to step S1.4 in claim 2, node i in the information layer updates whether it is in a conscious state based on the consciousness state of its neighbors in the information layer, the infection state of its neighbors in the physical contact layer, and the infection state of node i in the physical contact layer.

[0198] Step S3.6: At each Δt time, for the epidemic transmission process, according to step S1.5 in claim 2, node i in the physical contact layer updates whether it is infected based on the consciousness state of its corresponding node in the information layer;

[0199] Step S3.7: The propagation process lasts for Δt time;

[0200] Step S3.8: Repeat steps S3.4-S3.7 until the spread of the epidemic and the diffusion of information reach a steady state;

[0201] Step S3.9: Statistically determine the conscious state ρ at the heterogeneous consciousness threshold during steady state. A and infected state p I The proportion of nodes;

[0202] Step S3.10: Repeat steps S3.3-S3.9 above until the total number of simulations is reached;

[0203] Step S3.11: When counting the total number of simulations, the number of conscious states ρ below the heterogeneous consciousness threshold. A and infected state p I The average proportion of nodes indicates the end of the information-epidemic coupling evolution process.

[0204] This embodiment focuses on the individual consciousness threshold θ. i The study investigated the impact of heterogeneous awareness thresholds on the information-epidemic coupling evolution process under three mechanisms: no correlation, negative correlation, and positive correlation with activity level. This research can provide a basis for formulating effective policies to suppress the spread of epidemics.

[0205] In summary, the above-described method for information-epidemic coupled evolution analysis under multi-source heterogeneous social influence first constructs an unconscious U-conscious A-unconscious U-susceptible S-infected I-susceptible S model under multi-source heterogeneous social influence; then, based on the micro-Markov chain method, it theoretically derives the epidemic threshold β of the unconscious U-conscious A-unconscious U-susceptible S-infected I-susceptible S model under different scenarios. c Finally, within a multi-layered temporal network framework, the information-epidemic coupling evolution process under multi-source heterogeneous social influences is implemented. The above embodiments of the present invention consider the impact of the multi-source and heterogeneous nature of social influences on the information-epidemic coupling evolution process in an activity-driven multi-layered temporal network. The information-epidemic coupling dynamic equation is derived using the micro-Markov chain method, and the critical threshold β for epidemic transmission under different scenarios is theoretically solved. c This can provide theoretical guidance for formulating epidemic-related policies.

[0206] The embodiments of the present invention have been described above in conjunction with the accompanying drawings. However, the present invention is not limited to the above embodiments. Various changes can be made according to the purpose of the invention. Any changes, modifications, substitutions, combinations or simplifications made based on the spirit and principle of the technical solution of the present invention shall be equivalent substitutions. As long as they meet the purpose of the invention and do not deviate from the technical principle and inventive concept of the present invention, they shall fall within the protection scope of the present invention.

Claims

1. A method for coupled evolutionary analysis of information and epidemics under multi-source heterogeneous social influences, characterized in that, The steps are as follows: Step S1: Construct a model of unconscious U-conscious A-unconscious U-susceptible S-infected I-susceptible S under multi-source heterogeneous social influence; Step S2: Based on the micro-Markov chain method, theoretically derive the epidemic thresholds of the unconscious U-conscious A-unconscious U-susceptible S-infected I-susceptible S model under different scenarios. ; Step S3: Under the framework of a multi-layered temporal network, implement the information-epidemic coupled evolution process under multi-source heterogeneous social influences; The specific steps of step S1 are as follows: Step S1.1: Activity-Driven Multilayer Temporal Network Evolution Rule: Considering the dynamic interactions between individuals in real life, an activity-driven multilayer temporal network evolution model is constructed, where the top layer represents the information network. The bottom layer represents the physical contact network. For each node i Assigned to physical contact network Activity in and information networks Activity in , N For network size, respectively, they follow the exponent of . power-law distribution and ,in, Used to adjust the heterogeneity of the network; the specific steps are as follows: 1) Each At any moment, the physical contact layer instantaneous network Nodes in i Based on activity level Activated to become an active node, and randomly selected Establish connections between nodes; 2) Each Moment, instantaneous network of information layer Nodes in i Based on activity level Activated to become an active node, and randomly selected Establish connections between nodes; 3) In the next moment Remove all connections from the transient network in the information and physical contact layers; 4) Repeat steps 1)-3) until the propagation in the information and physical layers reaches a steady state; Step S1.2: Considering the multi-source and heterogeneous nature of social influences, two mechanisms of consciousness generation induced by social influences were analyzed, namely social reinforcement and risk perception, as detailed below: Social reinforcement: In the information layer, based on the phenomenon that individuals need notifications from multiple conscious neighbors before receiving information, a threshold model is used to describe social reinforcement; specifically, social reinforcement only occurs when the proportion of conscious neighbors reaches the individual's awareness threshold. θ At that time, individuals' herd mentality will prompt them to accept information related to the epidemic; in addition, considering the differences in individual awareness thresholds, an individual awareness threshold is proposed. The activity level of individuals in the information layer The three relevant mechanisms, including stochastic correlation, linear negative correlation, and linear positive correlation, are as follows: Case 1: Consciousness Threshold Independent of individual activity levels within the information layer The formula is as follows: (1)； Individuals with the same level of activity may have different thresholds of consciousness; among them, i Represents any individual, N Indicates the size of the population; Case 2: Consciousness Threshold With individuals i Activity in the information layer They are negatively correlated, as shown in the following formula: (2)； here, This represents the maximum activity level of all individuals within the information layer. This represents the minimum activity level of all individuals within the information layer; Case 3: Consciousness Threshold With individuals i Activity in the information layer They are positively correlated, as shown in the following formula: (3) ； Risk perception: In real life, when an unconscious individual observes that a neighbor in their physical contact layer shows symptoms of infection, the individual's sensitivity... It will induce them to become aware of the epidemic and spread the information; unlike the social reinforcement effect, even if only one neighbor is infected, unconscious individuals will still become aware of the epidemic through risk perception. Step S1.3: In the information layer, if the individual i Be aware of the epidemic, then individuals i In a conscious state A Otherwise, the individual i In an unconscious state U In the physical contact layer, if the individual i If infected, then the individual i In an infected state I Otherwise, the individual i In a susceptible state S Considering the coupled evolution of information and epidemics, individuals i In the following four states: unconscious susceptible state US Consciously susceptible state AS Unconscious infection state UI and conscious infection AI ; Step S1.4: In the information layer, the information diffusion process is defined as follows: On the one hand, unconscious state U individual i Becoming conscious through the following three situations A (a) When the proportion of conscious neighbors reaches the individual i consciousness threshold (a) When a neighbor in the physical contact layer shows symptoms of infection, the individual is susceptible. (c) when an unconscious individual is aware of the epidemic; i When infected, individuals exhibit a high rate of self-awareness. Recognizing the epidemic; without loss of generality, assuming all individuals have the same susceptibility, i.e. On the other hand, conscious state A individual i With forgetting rate Become unconscious U ; Step S1.5: In the physical contact layer, the epidemic transmission process is defined as follows: Susceptible state S individual i Through contact with infected individuals I Individuals based on infection rate β Infected, infected state I individual i With recovery rate μ Become susceptible S When susceptible state S individual i In a conscious state at the information layer A At that time, individual i A behavioral response will be adopted through a decay factor. α To reduce the infection rate of the epidemic.

2. The information-epidemic coupled evolution analysis method under multi-source heterogeneous social influences according to claim 1, characterized in that, The specific steps of step S2 are as follows: Step S2.1: In t Time, node i In an unconscious and susceptible state US Consciously susceptible state AS Unconscious infection state UI and conscious infection AI The probabilities are respectively used as and To indicate; Step S2.2: Unconscious Individual i Maintain at the information layer U probability of state The formula is as follows: （4）； In formula (4), the first term represents an unconscious individual. i The probability of remaining unconscious without being persuaded by conscious neighbors in the information layer; the second term represents the unconscious individual. i The probability of remaining unconscious without being induced by the infection symptoms of neighbors within the physical contact layer; considering that individuals have different preferences for information obtained from different social influences, define... Q To represent the weight of social reinforcement; correspondingly, 1- Q Weights representing risk perception; Represents the step function, when hour, ,otherwise, ;in, i Represents any individual, j Indicates except i Any individual other than Represents an individual i The threshold of consciousness Represents an individual i Activity level at the information layer Represents an individual j Activity level at the information layer express t individual moment j For consciousness A The probability, Represents an individual j The activity level in the information layer is The probability, where λ represents the individual's sensitivity. This represents the number of edges sent by active nodes in the physical contact layer. Represents an individual i The activity level of the physical contact layer Represents an individual j The activity level of the physical contact layer express t individual moment j For infection state I The probability of; Step S2.3: Unconscious state U and conscious state A individuals in the information layer i Maintain a susceptible state in the physical contact layer S The probabilities are respectively and The formula is as follows: （5）； （6）； Formula (5) represents the active / inactive unconscious susceptible state. US individual i touch An inactive / active infection state I individual j The probability of not being infected; Formula (6) represents the conscious susceptibility state in the information layer. AS individual i Behavioral response is adopted at the physical contact layer, with attenuation factor α Reduce the infection rate of epidemics β And the probability of not being infected; Step S2.4: Based on the micro-Markov chain method, combined with formulas (4)-(6), we obtain... The dynamic evolution equation: （7）； Among them, normalization conditions Applicable to all time steps; taking the first equation in formula (7) as an example, the first term represents t At any moment, unconscious susceptible state US individual i With probability Maintain an unconscious state U At the same time, with probability Maintain a susceptible state S The probability; the second term represents t At any moment, unconscious infection state UI individual i With probability Maintain an unconscious state U At the same time, recovery rate μ Become susceptible S The probability; the third term represents t At any time, there is a conscious susceptible state AS individual i With forgetting rate Become unconscious U At the same time, with probability Maintain a susceptible state S The probability; the fourth term represents t At any time, there is a conscious infection state. AI individual i With forgetting rate Become unconscious U At the same time, recovery rate μ Become susceptible S The probability of; Step S2.5: Based on equation set (7), the critical threshold for the spread of an epidemic is theoretically derived. for: （8）； The epidemic threshold can be seen from formula (8). Depends on recovery rate μ Intensity of individual behavioral response The network topology of the physical contact layer, i.e., the first moment of activity. and second moment and the number of edges and conscious individuals in steady state The proportion; Step S2.6: Based on formula (4), determine the weight of social reinforcement. Q It is a conscious individual that affects homeostasis. The proportion is an important factor; therefore, further analysis is needed on the critical threshold of multi-source social influence on epidemic transmission under the following three scenarios. The impact; Case 1: Individuals are fully aware of the epidemic through risk perception, i.e. Q =0, the critical threshold for epidemic transmission for: （9）； As can be seen from formula (9), the epidemic threshold Depends on recovery rate μ The network topology of the physical contact layer, i.e., the first moment of activity. and second moment and the number of edges ; Case 2: Individuals become aware of the epidemic entirely through social reinforcement, i.e. Q =1, Homogeneity threshold θ Critical threshold for the spread of an epidemic under certain conditions for: ；（10）； As can be seen from formula (10), unlike formula (9), the critical threshold for the spread of an epidemic is... It also depends on the information forgetting rate. and the critical point of consciousness threshold When approaching the critical point of consciousness threshold At that time, the epidemic threshold The occurrence of mutations indicates that the impact of information diffusion on the epidemic threshold has a two-stage characteristic; Case 3: Individuals become aware of the epidemic simultaneously through social reinforcement and risk perception, i.e. Homogeneity threshold θ Critical threshold for the spread of an epidemic under certain conditions for: ； (11) ； As can be seen from formula (11), unlike formula (10), the critical threshold for the spread of an epidemic is... It also depends on the weight of social reinforcement. Q .

3. The information-epidemic coupled evolution analysis method under multi-source heterogeneous social influences according to claim 2, characterized in that, The specific steps of step S3 are as follows: Step S3.1: Set the parameters for the unconscious U-conscious A-unconscious U-susceptible S-infectious I-susceptible S model under multi-source heterogeneous social influence and the activity-driven multilayer temporal network model, including network size. N The number of edges connecting active nodes in the information layer and physical contact layer and ,node i Activity levels at the physical contact layer and information layer and Time interval Epidemic infection rate β Epidemic recovery rate μ Information forgetting rate Consciousness threshold θ Sensitive factors λ Social reinforcement weight Q Behavioral response intensity α Self-awareness rate Total number of simulations and maximum time step T ; Step S3.2: Randomly initialize a certain proportion of infected states. I 0 and conscious state A 0 As a seed node; Step S3.3: Each At any given time, based on the activity-driven multilayer temporal network evolution rules in step S1.1, an activity-driven multilayer temporal network evolution model is generated. Step S3.4: Each At any given moment, regarding the information diffusion process, according to step S1.4, the nodes in the information layer... i Based on the consciousness state of neighbors in the information layer and the infection state of neighbors in the physical contact layer, as well as the nodes i The infection status at the physical contact layer is used to update whether the individual is in a conscious state; Step S3.5: Each At any given moment, regarding the transmission process of an epidemic, according to step S1.5, the nodes in the physical contact layer... i It updates whether it is in an infected state based on the consciousness state of its corresponding node in the information layer; Step S3.6: The propagation process continues time; Step S3.7: Repeat steps S3.3-S3.6 until the spread of the epidemic and the diffusion of information reach a steady state; Step S3.8: Statistical analysis of conscious states during steady state and infected state The proportion of nodes; Step S3.9: Repeat steps S3.2-S3.8 above until the total number of simulations is reached; Step S3.10: Conscious state when counting the total number of simulations and infected state The average proportion of nodes indicates the end of the information-epidemic coupling evolution process.

Images