Information-epidemic co-evolution analysis method under the influence of dynamic multi-source information and behavioral response

Abstract

The present invention discloses an information-epidemic co-evolution analysis method under the action of dynamic multi-source information and behavioral response. First, a multi-layer temporal network model with partially coupled nodes is constructed; then, an unconscious-conscious-unconscious, susceptible-infected-susceptible model is constructed to analyze the propagation dynamics of the information-epidemic; then, the transformation of the epidemic state and information state of the node is described, and the epidemic threshold β is derived. c ; Then simulate the dynamic evolution of epidemic spread and information diffusion; Finally, count the proportion of infected nodes and conscious nodes in the steady-state network to complete the evolution of information-epidemic collaboration. The present invention considers the influence of individual time-varying self-awareness and behavioral response on information-epidemic collaboration in a multi-layer time series network with partially coupled nodes, describes the state transition of nodes through the micro-Markov chain method, and theoretically solves the critical threshold β of the epidemic. c , to provide guidance for intervention and control of other sudden epidemics that may break out in the future.

Description

Technical Field

[0001] The present invention relates to the field of information-epidemic co-evolution technology, and in particular to an information-epidemic co-evolution analysis method under the action of dynamic multi-source information and behavioral response. Background Art

[0002] During the spread of an epidemic, it is usually accompanied by the spread of epidemic-related information. Information has typical multi-source and dynamic characteristics. On the one hand, individuals can obtain information through external information transmission such as word of mouth and social media (such as WeChat, Sina Weibo, Facebook and Twitter); on the other hand, infected individuals can have different degrees of self-awareness according to the dynamic evolution of the epidemic. At the same time, the scale of information diffusion will dynamically affect the degree of behavioral response of susceptible individuals, such as wearing masks or avoiding direct contact with others to reduce the risk of individual infection, thus forming the co-evolution of information and epidemics. In the field of information-epidemic co-evolution technology, mathematical modeling and theoretical analysis are usually used to understand the dynamic mechanism of information-epidemic co-evolution. The classic information-epidemic co-evolution transmission dynamics model is the unconscious-conscious-unconscious susceptible-infected-susceptible (UAU-SIS) compartment model and its variants, which play a key role in analyzing information-epidemic co-evolution.

[0003] However, most of the existing technologies and modeling methods ignore the multi-source and dynamic characteristics of information, or ignore the information transmission between individuals, or ignore the improvement of individual self-awareness, which is dynamically related to the evolution of the epidemic. In addition, the individual behavioral response under the action of information is also dynamically evolving. Based on the above analysis, studying the information-epidemic co-evolution under the action of dynamic multi-source information and behavioral response can help understand the role of individual behavioral factors that affect the spread of epidemics under the action of information, thereby providing a reference basis and support for formulating effective strategies to suppress the spread of epidemics. In addition, most of the existing studies are based on the information-epidemic co-evolution analysis method on multi-layer static networks, ignoring the temporal characteristics of the interaction between individuals in the layer, and not considering the partial mapping relationship between the corresponding nodes between layers, which cannot accurately describe the information-epidemic co-evolution process in real life. Therefore, on partially coupled multi-layer temporal networks, studying the information-epidemic co-evolution process under the action of dynamic multi-source information and behavioral response is still an open issue. Summary of the invention

[0004] In order to overcome the shortcomings of the above-mentioned prior art, the present invention provides an information-epidemic co-evolution analysis method under the action of dynamic multi-source information and behavioral response. The influence of individual time-varying self-awareness and behavioral response on the information-epidemic co-evolution process under the condition of partial coupling of nodes in a two-layer network is theoretically analyzed, providing guidance for responding to other sudden epidemics that may break out in the future.

[0005] This method first constructs a multi-layer temporal network model with partially coupled nodes. Secondly, it constructs an unconscious-conscious-unconscious susceptible-infected-susceptible (UAU-SIS) model to analyze the propagation dynamics of information-epidemic. Then, it describes the transition of the epidemic state and information state of the node according to the micro-Markov chain method, and derives the epidemic threshold β c ; Then, the dynamic evolution process of epidemic spread and information diffusion is simulated; finally, the proportion of infected nodes and conscious nodes in the network in steady state is counted to complete the evolution process of information-epidemic collaboration.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] A method for analyzing information-epidemic co-evolution under the action of multi-source information and dynamic behavioral response is applied to the field of information-epidemic co-evolution technology under the action of multi-layer temporal networks with partially coupled nodes, dynamic multi-source information and behavioral response. The operation steps are as follows:

[0008] Step S1: construct a multi-layer temporal network model with partially coupled nodes;

[0009] Step S2: Constructing the unconscious-conscious-unconscious susceptible-infected-susceptible (UAU-SIS) model to analyze the transmission dynamics of information-epidemic;

[0010] Step S3: Describe the transition of the epidemic state and information state of the node according to the micro-Markov chain method, and derive the epidemic threshold β c ;

[0011] Step S4: Simulate the dynamic evolution of epidemic spread and information diffusion;

[0012] Step S5: Count the proportion of infected nodes and conscious nodes in the network in steady state.

[0013] Furthermore, the specific steps of step S1 are:

[0014] Step S1.1: Using vector (a i ,b i ) is used to represent the activity of node i in the physical contact layer and information layer, and the indexes are γ a and γ b The power law distribution of :

[0015] Step S1.2: Use vector C = [c1, c2, ..., c N ] to represent the mapping relationship between network layers, and the interlayer coupling coefficient φ( N represents the total number of nodes). For node i, if there is an inter-layer mapping relationship (c i =1), then node i can receive multi-source information or take action in response, and vice versa;

[0016] Step S1.3: At every Δt moment, the node i in the instantaneous network is respectively active with degree a i and b i It is activated at the physical contact layer and information layer to become an active node and randomly generates m P and m V Edges; inactive nodes cannot actively send edges, but can receive edges from active nodes;

[0017] Step S1.4: The duration of all edges in the network is Δt;

[0018] Step S1.5: At the next time t+Δt, delete all the edges of the instantaneous network in the physical contact layer and the information layer, and generate the network at the next time according to step S1.3;

[0019] Step S1.6: Repeat the above steps S1.3-S1.5 until the steady-state time step T is reached. steady ;

[0020] In the above entire sequential network construction, self-loops and repeated edges are not allowed.

[0021] Furthermore, the specific steps of step S2 are:

[0022] Step S2.1: The states of nodes in the information layer are divided into unconscious state U and conscious state A; the states of nodes in the physical contact layer are divided into susceptible state S and infected state I;

[0023] Step S2.2: For information diffusion, every Δt, the unconscious U-state node i is notified by the A-state neighbor and converted to the A-state node with probability λ. In addition, once the conscious A-state node i forgets the information, it will be converted to the U-state node with the recovery rate δ. In particular, if the node i has an inter-layer mapping relationship (c i =1), the I-state node i in the physical contact layer makes the corresponding node i in the information layer generate self-awareness and P (t) spontaneously transforms into an A-state node. Considering that the self-awareness of individuals will change with the evolution of the epidemic, assuming that θ P(t) depends on the scale of the epidemic to promote the diffusion of information. Therefore, θ P (t) and p I (t) and is defined as:

[0024]

[0025] Here, θ P (t) represents the self-awareness of the individual at time t, p I (t) represents the proportion of infected individuals at time t, and P is the intensity of self-awareness;

[0026] Step S2.3: For epidemic spread, at every Δt, a susceptible S node i is transformed into an I node with probability β by contacting an I neighbor node, and an infected I node i is restored to an S node with probability μ. In particular, if there is an inter-layer mapping relationship between node i (c i = 1), the conscious node i in the information layer causes its corresponding node i in the physical contact layer to take behavioral responses to reduce the rate θ v (t) Reduce its infection rate. Similarly, considering that the degree of individual behavioral response will change with the evolution of information, assuming that θ V (t) depends on the scale of information diffusion to suppress the spread of the epidemic. Therefore, θ V (t) and p A (t) and is defined as:

[0027]

[0028] Here, θ V (t) represents the behavioral response of the individual at time t, p A (t) represents the proportion of conscious individuals at time t, and V is the intensity of behavioral response.

[0029] Furthermore, the specific steps of step S3 are:

[0030] Step S3.1: Considering the co-evolution of information diffusion and epidemic spread, individuals can be represented as the following four states: unconscious susceptible state US, unconscious infected state UI, conscious susceptible state AS, conscious infected state AI;

[0031] Step S3.2: The probability of node i being in the above four states at time t is expressed as To express;

[0032] Step S3.3: For the information layer, the probabilities of the S-state and I-state nodes i in the physical contact layer maintaining the U-state in the information layer are:

[0033]

[0034]

[0035] The second term of formula (3) represents the activity b i The m sent by the activated U-state node i V The third term represents the probability of receiving information from the U-state node i with activity b. j Formula (4) indicates that the I-state node i in the physical contact layer is not informed of the information by the A-state neighbor in the information layer, and at the same time, with probability 1-θ P (t)c i The probability of not being spontaneously aware of epidemic information;

[0036] Step S3.4: For the physical contact layer, the probabilities of the U-state and A-state nodes i in the information layer maintaining the S-state in the physical contact layer are:

[0037]

[0038]

[0039] The second term of formula (5) represents the activity level a. i The m sent by the activated S-state node i P The third term represents the probability of S-state node i receiving a message with activity a. j The probability of the activated I-state node j being infected. Formula (6) indicates that the A-state node i in the information layer takes action response at the physical contact layer with probability 1-θ V (t)c i Reduce the infection rate of the epidemic and the probability of not being infected;

[0040] Step S3.5: According to formulas (3)-(6), using the micro-Markov chain method, we can get The dynamic evolution equation of is:

[0041]

[0042] in, Taking the first formula in formula (7) as an example, the first term indicates that UI state node i has probability r i I (t) The probability of maintaining the U state and transforming to the S state with probability μ; the second term represents the probability of the AI ​​state node i transforming to the U state with probability δ and transforming to the S state with probability μ; the third term represents the probability of the US state node i transforming to the U state with probability r i S (t) Maintain the U state while using probability The probability of maintaining the S state; the fourth term indicates that the AS state node i is transformed into the U state with probability δ and at the same time The probability of maintaining the S state;

[0043] Step S3.6: According to formula (5), the epidemic threshold β is theoretically derived c for:

[0044]

[0045] From formula (8), we can see that the epidemic threshold β c Depends on the first-order moment of the node's activity in the physical contact layer ( ) and the second moment ( 2 >), recovery rate μ, interlayer coupling coefficient φ, node behavior response θ v , the proportion of conscious individuals p A , and the number of edges m p .

[0046] Furthermore, the specific steps of step S4 are as follows:

[0047] Step S4.1: randomly initialize a certain proportion of nodes as I-state seed nodes and A-state seed nodes;

[0048] Step S4.2: At every Δt moment, the nodes in the information layer and the physical layer evolve according to the rules of steps S1.3-S1.5;

[0049] Step S4.3: Calculate the ratio of I-state nodes to A-state nodes in the network at each moment;

[0050] Step S4.4: At each time Δt, for node i in the information layer, first calculate θ according to formula (1): P (t), then according to step S2.2, update whether it is in the conscious state according to whether the surrounding neighbors are in the state of having received messages, the corresponding relationship between the nodes in the layers, and the infection state of the corresponding nodes in the physical contact layer;

[0051] Step S4.5: At each Δt moment, for node i in the physical contact layer, first calculate θ according to formula (2): V (t), then update its own epidemic infection status according to the infection status of surrounding neighbors, the corresponding relationship between nodes in the layer, and the message status of the corresponding node in the information layer according to step S2.3;

[0052] Step S4.6: The propagation process lasts for a period of time Δt.

[0053] Furthermore, the specific steps of step S5 are as follows:

[0054] Step S5.1: Repeat steps S1-S4 until the steady-state time T is reached steady Finish;

[0055] Step S5.2: Statistical steady-state infection state I ∞ and conscious state A ∞ proportion, the information-epidemic co-evolution process ends.

[0056] Compared with the prior art, the present invention has the following obvious outstanding essential features and remarkable advantages:

[0057] ​1. This paper uses mathematical modeling to theoretically analyze the time-varying self-awareness and behavioral response of individuals, as well as the corresponding relationship between nodes in the network layers, that is, the joint effect between the inter-layer coupling coefficients, to analyze the epidemic transmission threshold β under the action of dynamic multi-source information. c The impact of infection scale is supported by the theory;

[0058] 2. The present invention verifies the correctness and rationality of the model through numerical simulation, as well as the role of individual time-varying self-awareness and behavioral response, and the influence of the interlayer coupling coefficient, which can effectively guide the control of the spread of epidemics;

[0059] 3. The method proposed in this invention can provide theoretical guidance for dealing with other sudden epidemics that may break out in the future. BRIEF DESCRIPTION OF THE DRAWINGS

[0060] The drawings herein are incorporated into the specification and constitute a part of the specification, showing embodiments consistent with the present application, and together with the specification, are used to explain the principles of the present application. In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings required for use in the embodiments or the prior art description are briefly introduced below. The drawings described are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0061] Figure 1 It is a schematic flow chart of the information-epidemic co-evolution analysis method under the action of dynamic multi-source information and behavioral response of the present invention.

[0062] Figure 2 Schematic diagram of the co-evolution model of information-epidemic under the action of dynamic multi-source information and behavioral response in an embodiment of the present invention.

[0063] Figure 3 Schematic diagram of the state transition probability tree of information-epidemic in an embodiment of the present invention. DETAILED DESCRIPTION

[0064] In order to enable those skilled in the art to better understand the technical solutions in the present application, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in the field without creative work should fall within the scope of protection of this application.

[0065] In order to better understand the present application, the implementation methods of the present application are explained in detail below with reference to the accompanying drawings.

[0066] Embodiment 1:

[0067] See also Figure 1 , Figure 2 and Figure 3 , an information-epidemic co-evolution analysis method under the action of dynamic multi-source information and behavioral response, applied to the field of information-epidemic co-evolution technology under the action of multi-layer temporal networks with partial node coupling, dynamic multi-source information and behavioral response, the operation steps are as follows:

[0068] Step S1.1: Using vector (a i ,b i ) is used to represent the activity of node i in the physical contact layer and information layer, and the indexes are γ aand γ b The power law distribution of :

[0069] Step S1.2: Use vector C = [c1, c2, ..., c N ] to represent the mapping relationship between network layers, and the interlayer coupling coefficient φ( N represents the total number of nodes). For node i, if there is an inter-layer mapping relationship (c i =1), then node i can receive multi-source information or take action in response, and vice versa;

[0070] Step S1.3: At every Δt moment, the node i in the instantaneous network is respectively active with degree a i and b i It is activated at the physical contact layer and information layer to become an active node and randomly generates m P and m V Edges; inactive nodes cannot actively send edges, but can receive edges from active nodes;

[0071] Step S1.4: The duration of all edges in the network is Δt;

[0072] Step S1.5: At the next time t+Δt, delete all the edges of the instantaneous network in the physical contact layer and the information layer, and generate the network at the next time according to step S1.3;

[0073] Step S1.6: Repeat the above steps S1.3-S1.5 until the steady-state time step T is reached. steady ;

[0074] In the above entire sequential network construction, self-loops and repeated edges are not allowed.

[0075] Step S2: Constructing the unconscious-conscious-unconscious susceptible-infected-susceptible (UAU-SIS) model to analyze the transmission dynamics of information-epidemic;

[0076] Step S2.1: The states of nodes in the information layer are divided into unconscious state U and conscious state A; the states of nodes in the physical contact layer are divided into susceptible state S and infected state I;

[0077] Step S2.2: For information diffusion, every Δt, the unconscious U-state node i is notified by the A-state neighbor and transformed into an A-state node with probability λ. In addition, once the conscious A-state node i forgets the information, it is transformed into a U-state node with a recovery rate δ. In particular, if the node i has an inter-layer mapping relationship (c i =1), the I-state node i in the physical contact layer makes the corresponding node i in the information layer generate self-awareness and P(t) spontaneously transforms into an A-state node. Considering that the self-awareness of individuals will change with the evolution of the epidemic, assuming that θ P (t) depends on the scale of the epidemic to promote the diffusion of information. Therefore, θ P (t) and p I (t) and is defined as:

[0078]

[0079] Here, θ P (t) represents the self-awareness of the individual at time t, p I (t) represents the proportion of infected individuals at time t, and P is the intensity of self-awareness;

[0080] Step S2.3: For epidemic spread, at every Δt, a susceptible S node i is transformed into an I node with probability β by contacting an I neighbor node, and an infected I node i is restored to an S node with probability μ. In particular, if there is an inter-layer mapping relationship between node i (c i = 1), the conscious node i in the information layer causes its corresponding node i in the physical contact layer to take behavioral responses to reduce the rate θ v (t) reduce its infection rate. Similarly, considering that the degree of individual behavioral response will change with the evolution of information, assuming that θ V (t) depends on the scale of information diffusion to suppress the spread of the epidemic. Therefore, θ V (t) and p A (t) and is defined as:

[0081]

[0082] Here, θ V (t) represents the behavioral response of the individual at time t, p A (t) represents the proportion of conscious individuals at time t, and V is the intensity of behavioral response.

[0083] Step S3: Describe the transition of the epidemic state and information state of the node according to the micro-Markov chain method, and derive the epidemic threshold β c ;

[0084] Step S3.1: Considering the co-evolution of information diffusion and epidemic spread, individuals can be represented as the following four states: unconscious susceptible state US, unconscious infected state UI, conscious susceptible state AS, conscious infected state AI;

[0085] Step S3.2: The probability of node i being in the above four states at time t is expressed as To express;

[0086] Step S3.3: For the information layer, the probabilities of the S-state and I-state nodes i in the physical contact layer maintaining the U-state in the information layer are:

[0087]

[0088]

[0089] The second term of formula (3) represents the activity b i The m sent by the activated U-state node i V The third term represents the probability of receiving information from the U-state node i with activity b. j Formula (4) indicates that the I-state node i in the physical contact layer is not informed of the information by the A-state neighbor in the information layer, and at the same time, with probability 1-θ P (t)c i The probability of not being spontaneously aware of epidemic information;

[0090] Step S3.4: For the physical contact layer, the probabilities of the U-state and A-state nodes i in the information layer maintaining the S-state in the physical contact layer are:

[0091]

[0092]

[0093] The second term of formula (5) represents the activity level a. i The m sent by the activated S-state node i P The third term represents the probability of S-state node i receiving a message with activity a. j The probability of the activated I-state node j being infected. Formula (6) indicates that the A-state node i in the information layer takes action response at the physical contact layer with probability 1-θ V (t)c i Reduce the infection rate of the epidemic and the probability of not being infected;

[0094] Step S3.5: According to formulas (3)-(6), using the micro-Markov chain method, we can get The dynamic evolution equation of is:

[0095]

[0096] in, Taking the first formula in formula (7) as an example, the first term indicates that UI state node i has probability r i I(t) The probability of maintaining the U state and transforming to the S state with probability μ; the second term represents the probability of the AI ​​state node i transforming to the U state with probability δ and transforming to the S state with probability μ; the third term represents the probability of the US state node i transforming to the U state with probability r i S (t) Maintain the U state while using probability The probability of maintaining the S state; the fourth term indicates that the AS state node i is transformed into the U state with probability δ and at the same time The probability of maintaining the S state;

[0097] Step S3.6: According to formula (5), the epidemic threshold β is theoretically derived c for:

[0098]

[0099] From formula (8), we can see that the epidemic threshold β c Depends on the first-order moment of the node's activity in the physical contact layer ( ) and the second moment ( 2 >), recovery rate μ, interlayer coupling coefficient φ, node behavior response θ v , the proportion of conscious individuals p A , and the number of edges m p .

[0100] Step S4: Simulate the dynamic evolution of epidemic spread and information diffusion;

[0101] Step S4.1: randomly initialize a certain proportion of nodes as I-state seed nodes and A-state seed nodes;

[0102] Step S4.2: At every Δt moment, the nodes in the information layer and the physical layer evolve according to the rules of steps S1.3-S1.5;

[0103] Step S4.3: Calculate the ratio of I-state nodes to A-state nodes in the network at each moment;

[0104] Step S4.4: At each time Δt, for node i in the information layer, first calculate θ according to formula (1): P (t), then according to step S2.2, update whether it is in the conscious state according to whether the surrounding neighbors are in the state of having received messages, the corresponding relationship between the nodes in the layers, and the infection state of the corresponding nodes in the physical contact layer;

[0105] Step S4.5: At each Δt moment, for node i in the physical contact layer, first calculate θ according to formula (2): V (t), then update its own epidemic infection status according to the infection status of surrounding neighbors, the corresponding relationship between nodes in the layer, and the message status of the corresponding node in the information layer according to step S2.3;

[0106] Step S4.6: The propagation process lasts for a period of time Δt.

[0107] Step S5: Count the proportion of infected nodes and conscious nodes in the network in steady state;

[0108] Step S5.1: Repeat steps S1-S4 until the steady-state time T is reached steady Finish;

[0109] Step S5.2: Statistical steady-state infection state I ∞ and conscious state A ∞ proportion, the information-epidemic co-evolution process ends.

[0110] This embodiment considers the individual's time-varying self-awareness and behavioral response as well as the inter-layer coupling coefficient, studies the impact of dynamic multi-source information and behavioral response on the threshold and scale of epidemic transmission, and further verifies the correctness of the theoretical threshold. ​

[0111] Embodiment 2:

[0112] This embodiment is basically the same as the above embodiment, with the following special features:

[0113] Step S1: This step is the same as that in Embodiment 1;

[0114] Step S2: This step is the same as that in Embodiment 1;

[0115] Step S3: This step is the same as that in Embodiment 1;

[0116] Step S4: Simulate the dynamic evolution of epidemic spread and information diffusion, including:

[0117] Step S4.1: Given an individual’s self-awareness and behavioral response intensity P and V;

[0118] Step S4.2: randomly initialize a certain proportion of nodes as I-state nodes and A-state nodes;

[0119] Step S4.3: At every Δt moment, the nodes in the information layer and the physical layer evolve according to the rules of steps S1.3-S1.5;

[0120] Step S4.4: Perform numerical simulation according to formula (7) to determine the average self-awareness and behavioral response of the individual: and where β max is the maximum infection rate of the epidemic, β int is the interval of epidemic infection rate, T steady is the steady-state time step;

[0121] Step S4.5: Calculate the ratio of I-state nodes to A-state nodes in the network at each moment;

[0122] Step S4.6: When the self-awareness of an individual is a time variable, at every Δt moment, for node i in the information layer, first calculate θ according to formula (1): P (t), then according to step S2.2, update whether it is in the conscious state according to whether the surrounding neighbors are in the state of having received messages, the corresponding relationship between the nodes in the layers, and the infection state of the corresponding nodes in the physical contact layer;

[0123] Step S4.7: When the individual behavior response is a time variable, at every Δt moment, for node i in the physical contact layer, first calculate θ according to formula (2): V (t), then update its own epidemic infection status according to the infection status of surrounding neighbors, the corresponding relationship between nodes in the layer, and the message status of the corresponding node in the information layer according to step S2.3;

[0124] Step S4.8: When the individual's self-awareness is a time-independent variable < θ P >, at every Δt, for node i in the information layer, it updates whether it is in the conscious state according to step S2.2 based on whether the surrounding neighbors are in the state of receiving messages, the corresponding relationship between nodes in the layers, and the infection state of the corresponding node in the physical contact layer;

[0125] Step S4.9: When the individual's behavioral response is a time-independent variable < θ V >, at every Δt, for node i in the physical contact layer, according to step S2.3, it updates its own epidemic infection status according to the infection status of its surrounding neighbors, the corresponding relationship between nodes in the layers, and the message status of the corresponding node in the information layer;

[0126] Step S4.10: The propagation process lasts for a period of time Δt.

[0127] Step S5: Count the proportion of infected nodes and conscious nodes in the network in the steady state, specifically:

[0128] Step S5.1: Repeat steps S1-S4 until the steady-state time T is reached steady Finish;

[0129] Step S5.2: Count the individual's self-awareness and behavioral responses respectively <θ V > and <θ P >, steady state infection state I ∞ and conscious state A ∞ proportion;

[0130] Step S5.3: Statistical analysis of the individual's self-awareness and behavioral responses as time-varying variables, steady-state infection state I ∞ and conscious state A ∞ proportion;

[0131] In this embodiment, the expected value when the individual's self-awareness and behavioral response are constants is <θ P > and <θ V >Time is used as a benchmark model to study the impact of individuals' time-varying self-awareness and behavioral responses on the spread of epidemics.

[0132] Embodiment three:

[0133] This embodiment is basically the same as the above embodiment, with the following special features:

[0134] Step S1: This step is the same as that in Embodiment 1;

[0135] Step S2: This step is the same as that in Embodiment 1;

[0136] Step S3: This step is the same as that in Embodiment 1;

[0137] Step S4: Simulate the dynamic evolution of epidemic spread and information diffusion, including:

[0138] Step S4.1: Given the information diffusion rate λ and the epidemic infection rate β, set the reaction intensity P and V of individual self-awareness and behavioral response from 0 to 1;

[0139] Step S4.2: randomly initialize a certain proportion of nodes in the physical contact layer as I-state nodes and A-state nodes;

[0140] Step S4.3: At every Δt moment, the nodes in the information layer and the physical layer evolve according to the rules of steps S1.3-S1.5;

[0141] Step S4.4: Calculate the ratio of I-state nodes to A-state nodes in the network at each moment;

[0142] Step S4.5: At each time Δt, for node i in the information layer, first calculate θ according to formula (1): P (t), then according to step S2.2, update whether it is in the conscious state according to whether the surrounding neighbors are in the state of having received messages, the corresponding relationship between the nodes in the layers, and the infection state of the corresponding nodes in the physical contact layer;

[0143] Step S4.6: At each Δt moment, for node i in the physical contact layer, first calculate θ according to formula (2): V (t), then update its own epidemic infection status according to the infection status of surrounding neighbors, the corresponding relationship between nodes in the layer, and the message status of the corresponding node in the information layer according to step S2.3;

[0144] Step S4.7: The propagation process lasts for a period of time Δt.

[0145] Step S5: This step is the same as that in the first embodiment;

[0146] In this embodiment, when the information dissemination rate and the epidemic infection rate are fixed, increasing the individual's self-awareness strength P and behavioral response strength V can further suppress the spread of the epidemic.

[0147] Embodiment 4:

[0148] This embodiment is basically the same as the above embodiment, with the following special features:

[0149] Step S1: This step is the same as that in Embodiment 1;

[0150] Step S2: This step is the same as that in Embodiment 1;

[0151] Step S3: This step is the same as that in Embodiment 1;

[0152] Step S4: This step is basically the same as that of the third embodiment, except that:

[0153] Step S4.1: Given the individual's self-awareness and the reaction strength of behavioral response P and V, set the information propagation rate λ and the epidemic infection rate β to change from 0 to 1;

[0154] Step S5: This step is the same as that in the first embodiment;

[0155] In this embodiment, when the individual's self-awareness intensity P and behavioral response intensity V are fixed, the interaction of information and epidemic co-evolution will no longer be obvious after reaching the conditions for full dissemination of each other.

[0156] Embodiment five:

[0157] This embodiment is basically the same as the above embodiment, with the following special features:

[0158] Step S1: This step is basically the same as that of the first embodiment; the differences include:

[0159] Step S1.2: Set the interlayer coupling coefficient φ between the physical contact layer and the information layer from 0 to 1. According to the interlayer coupling coefficient φ ( N represents the total number of nodes), using the vector C = [c1, c2, ..., c N ] to represent the inter-layer mapping relationship. For node i, if there is an inter-layer mapping relationship (c i =1), then node i can receive multi-source information or take action in response, and vice versa;

[0160] Step S2: This step is the same as that in Embodiment 1;

[0161] Step S3: This step is the same as that in Embodiment 1;

[0162] Step S4: This step is basically the same as that of the third embodiment, except that:

[0163] Step S4.1: Set the epidemic infection rate β, self-awareness and behavioral response intensity P and V from 0 to 1;

[0164] Step S5: This step is the same as that in the first embodiment;

[0165] In this embodiment, the interactions between the interlayer coupling coefficient φ and the epidemic infection rate β, the self-awareness intensity P, and the behavioral response intensity V are studied respectively to provide a basis for determining the factors that inhibit the spread of the epidemic.

[0166] In summary, the information-epidemic co-evolution analysis method under the action of dynamic multi-source information and behavioral response in the above embodiment constructs a multi-layer temporal network model with partially coupled nodes; secondly, an unconscious-conscious-unconscious susceptible-infected-susceptible (UAU-SIS) model is constructed to analyze the propagation dynamics of the information-epidemic; then, the micro-Markov chain method is used to describe the transformation of the epidemic state and information state of the node, and the epidemic threshold β is derived. c ; Then, simulate the dynamic evolution process of epidemic spread and information diffusion; Finally, count the proportion of infected nodes and conscious nodes in the steady-state network to complete the evolution process of information-epidemic collaboration. The above embodiment method considers the influence of individual time-varying self-awareness and behavioral response on the information-epidemic collaboration evolution in a multi-layer time series network with partially coupled nodes, describes the state transition of nodes by micro-Markov chain method, and theoretically solves the critical threshold β of epidemic. c The above-mentioned embodiment method can provide guidance for intervention and control of other sudden epidemics that may break out in the future.

[0167] The above describes the embodiments of the present invention in conjunction with the accompanying drawings, but 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 according to the spirit and principle of the technical solution of the present invention should be equivalent replacement methods. As long as they meet the purpose of the invention and do not deviate from the technical principles and inventive concepts of the present invention, they belong to the protection scope of the present invention.

Claims

1. A method for analyzing information-epidemic co-evolution under the action of dynamic multi-source information and behavioral response, characterized by: The steps are as follows: Step S1: construct a multi-layer temporal network model with partially coupled nodes; Step S2: Construct the unconscious-conscious-unconscious susceptible-infected-susceptible UAU-SIS model to analyze the transmission dynamics of information-epidemic; Step S3: Describe the transition of the epidemic state and information state of the node according to the micro-Markov chain method, and derive the epidemic threshold β c ; Step S4: Simulate the dynamic evolution of epidemic spread and information diffusion; Step S5: Count the proportion of infected nodes and conscious nodes in the network in steady state; The specific steps of step S1 are: Step S1.1: Using vector (a i ,b i ) is used to represent the activity of node i in the physical contact layer and information layer, and the indexes are γ a and γ b The power law distribution of : Step S1.2: Use vector C = [c1, c2, ..., c N ] is used to represent the mapping relationship between network layers, and the interlayer coupling coefficient φ between the physical contact layer and the information layer can be obtained. N represents the total number of nodes; for node i, if there is an inter-layer mapping relationship c i =1, then node i can receive multi-source information or take action in response, and vice versa; Step S1.3: At every Δt moment, the node i in the instantaneous network is respectively active with degree a i and b i It is activated at the physical contact layer and information layer to become an active node and randomly generates m P and m V Edges; inactive nodes cannot actively send edges, but can receive edges from active nodes; Step S1.4: The duration of all edges in the network is Δt; Step S1.5: At the next time t+Δt, delete all the edges of the instantaneous network in the physical contact layer and the information layer, and generate the network at the next time according to step S1.3; Step S1.6: Repeat the above steps S1.3-S1.5 until the steady-state time step T is reached. steady ; In the above entire temporal network construction, self-loops and repeated edges are not allowed; The specific steps of step S2 are: Step S2.1: The states of nodes in the information layer are divided into unconscious state U and conscious state A; the states of nodes in the physical contact layer are divided into susceptible state S and infected state I; Step S2.2: For information diffusion, at every Δt, the unconscious U-state node i is notified by the A-state neighbor and transformed into an A-state node with probability λ; in addition, once the conscious A-state node i forgets the information, it will be transformed into a U-state node with a recovery rate δ; in particular, if the node i has an inter-layer mapping relationship c i = 1, the I-state node i in the physical contact layer makes the corresponding node i in the information layer generate self-awareness and P (t) spontaneously transforms into an A-state node; considering that the self-awareness of individuals will change with the evolution of the epidemic, assuming that θ P (t) depends on the scale of the epidemic to promote the diffusion of information; therefore, θ P (t) and p I (t) and is defined as: Here, θ P (t) represents the self-awareness of the individual at time t, p I (t) represents the proportion of infected individuals at time t, and P is the intensity of self-awareness; Step S2.3: For epidemic spread, at every Δt, a susceptible S node i is transformed into an I node with probability β by contacting an I neighbor node, and an infected I node i is restored to an S node with probability μ; In particular, if node i has an inter-layer mapping relationship c i = 1, the conscious node i in the information layer causes its corresponding node i in the physical contact layer to take behavioral responses to reduce the rate θ v (t) reduce their infection rate; Similarly, considering that the degree of individual behavioral response will change with the evolution of information, assuming that θ V (t) depends on the scale of information diffusion to suppress the spread of the epidemic; therefore, θ V (t) and p A (t) and is defined as: Here, θ V (t) represents the behavioral response of the individual at time t, p A (t) represents the proportion of conscious individuals at time t, and V is the intensity of behavioral response.

2. The information-epidemic co-evolution analysis method under the action of dynamic multi-source information and behavioral response according to claim 1 is characterized in that: The specific steps of step S3 are: Step S3.1: Considering the co-evolution of information diffusion and epidemic spread, individuals can be represented as the following four states: unconscious susceptible state US, unconscious infected state UI, conscious susceptible state AS, conscious infected state AI; Step S3.2: The probability of node i being in the above four states at time t is expressed as To express; Step S3.3: For the information layer, the probabilities of the S-state and I-state nodes i in the physical contact layer maintaining the U-state in the information layer are: The second term of formula (3) represents the activity b i The m sent by the activated U-state node i V The third term represents the probability of receiving information from the U-state node i with activity b. j The probability that the activated A-state node j is connected and informed of the information; Formula (4) indicates that the I-state node i in the physical contact layer is not informed of the information by the A-state neighbor in the information layer, and at the same time with probability 1-θ P (t)c i The probability of not being spontaneously aware of epidemic information; Step S3.4: For the physical contact layer, the probabilities of the U-state and A-state nodes i in the information layer maintaining the S-state in the physical contact layer are: The second term of formula (5) represents the activity level a. i The m sent by the activated S-state node i P The third term represents the probability of S-state node i receiving a message with activity a. j The probability of the connected edge of the activated I-state node j being infected; Formula (6) represents the probability that the A-state node i in the information layer takes action response at the physical contact layer with probability 1-θ V (t)c i Reduce the infection rate of the epidemic and the probability of not being infected; Step S3.5: According to formulas (3)-(6), using the micro-Markov chain method, we can get The dynamic evolution equation of is: in, Taking the first formula in formula (7) as an example, the first term indicates that UI state node i has probability r i I (t) The probability of maintaining the U state and transforming to the S state with probability μ; the second term represents the probability of the AI ​​state node i transforming to the U state with probability δ and transforming to the S state with probability μ; the third term represents the probability of the US state node i transforming to the U state with probability r i S (t) Maintain the U state while using probability The probability of maintaining the S state; the fourth term indicates that the AS state node i is transformed into the U state with probability δ and at the same time The probability of maintaining the S state; Step S3.6: According to formula (5), the epidemic threshold β is theoretically derived c for: From formula (8), we can see that the epidemic threshold β c Depends on the first-order moment of the node's activity in the physical contact layer ( ) and the second moment ( 2 >), recovery rate μ, interlayer coupling coefficient φ, node behavior response θ v , the proportion of conscious individuals p A , and the number of edges m p .​ 3. The information-epidemic co-evolution analysis method under the action of dynamic multi-source information and behavioral response according to claim 1 is characterized in that: The specific steps of step S4 are: Step S4.1: randomly initialize a certain proportion of nodes as I-state seed nodes and A-state seed nodes; Step S4.2: At every Δt moment, the nodes in the information layer and the physical layer evolve according to the rules of steps S1.3-S1.5; Step S4.3: Calculate the ratio of I-state nodes to A-state nodes in the network at each moment; Step S4.4: At each time Δt, for node i in the information layer, first calculate θ according to formula (1): P (t), then according to step S2.2, update whether it is in the conscious state according to whether the surrounding neighbors are in the state of having received messages, the corresponding relationship between the nodes in the layers, and the infection state of the corresponding nodes in the physical contact layer; Step S4.5: At each Δt moment, for node i in the physical contact layer, first calculate θ according to formula (2): V (t), then update its own epidemic infection status according to the infection status of surrounding neighbors, the corresponding relationship between nodes in the layer, and the message status of the corresponding node in the information layer according to step S2.3; Step S4.6: The propagation process lasts for a period of time Δt.

4. The information-epidemic co-evolution analysis method under the action of dynamic multi-source information and behavioral response according to claim 1 is characterized in that: The specific steps of step S5 are as follows: Step S5.1: Repeat steps S1-S4 until the steady-state time T is reached steady Finish; Step S5.2: Statistical steady-state infection state I ∞ and conscious state A ∞ The information-epidemic co-evolution process ends.

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