A rumor information control method based on evolutionary game and multi-state

Abstract

This invention belongs to the field of online public opinion dissemination, and specifically relates to a rumor information control method based on evolutionary game theory and multi-state analysis. It acquires data sources and extracts internal factors, external factors, and message influence that affect rumor dissemination from these sources. Internal factors include user activity and user sensitivity; external factors include topic popularity and friend referral power; and message influence includes the influence of rumor messages and the influence of doubtful rumors. Based on the payoff function of message influence in terms of users believing and forwarding rumor information versus believing and forwarding doubtful rumors, evolutionary game theory is used to obtain the driving forces behind user participation in the dissemination of rumor messages and the behavioral driving forces behind user participation in the dissemination of doubtful rumors. A control system is constructed, and the optimal conversion rate of the control strategy to transform the target group into a specified group per unit time is calculated. This invention accurately describes the multi-state user rumor dissemination process in social networks and provides a theoretical basis for rumor control.

Description

Technical Field

[0001] This invention belongs to the field of online public opinion dissemination, and specifically relates to a method for controlling rumor information based on evolutionary game theory and multi-state. Background Technology

[0002] With the rapid development of online social networks (OSNs), large online social networking platforms such as Facebook, Twitter, and YouTube have become popular platforms for communication, making large-scale information dissemination a reality. On the downside, this has also led to the emergence of online rumors. Online rumors refer to the manipulation of public opinion by some internet users. The outbreak of rumors brings many problems, sometimes causing public panic and economic losses. In particularly egregious cases, they can further negatively impact social communication and the economy, posing a threat to human society. Therefore, the study of online rumors has always been a hot topic in the field of social networking.

[0003] Current research on the spread of rumors mainly focuses on two directions: First, based on infectious disease transmission models, improving existing models to study the spread of rumors on social networks, with the SIR and SIRS models being classic examples. Second, using machine learning algorithms to extract information features from social networks to detect and identify rumors.

[0004] Although significant progress has been made in research on the spread of rumors, some challenges still remain:

[0005] 1. The diversity and uncertainty of user states. As the main agents of rumor dissemination, users' states are diverse and uncertain. Their attitudes towards rumors depend not only on external environmental factors but also on their own personal circumstances. Users will make choices that maximize their own interests under the combined influence of multiple factors.

[0006] 2. The dynamism of control strategies. At different stages of rumor dissemination, the control effects and costs achieved by control strategies are not static, and most past studies have not considered time-varying factors, essentially belonging to static optimization.

[0007] 3. The difficulty of modeling rumor propagation on complex networks. Rumors spread among users through networks, and users are not isolated within the network; they are influenced by other users and even the entire network. Summary of the Invention

[0008] To address the problems existing in current technologies, this invention proposes a rumor information control method based on evolutionary game theory and multi-state theory, comprising the following steps:

[0009] S1. Obtain data source, that is, obtain the basic information and historical behavior of all users who participated in publishing rumors and suspected rumors within the life cycle of a certain topic;

[0010] S2. Extract the internal factors, external factors, and message influence that affect the spread of rumors from the acquired data sources. Internal factors include user activity and user sensitivity. External factors include topic popularity and the influence of friends. Message influence includes the influence of rumor messages and the influence of suspected rumors.

[0011] S3. Based on the payoff function of users believing rumors and forwarding rumor information, and believing doubtful rumors and forwarding doubtful rumors, evolutionary game theory is used to obtain the driving force for users to participate in the spread of rumor messages and the behavioral driving force for users to participate in the spread of doubtful rumors.

[0012] S4. Construct a control system and calculate the value of any user v. i The probability of being in a rumor-spreading state at time t, and the probability of any user v i The probability of being in a state of suspicion at time t is used to derive the dynamic equation of the rumor control model based on evolutionary game theory and multi-state. Solving the dynamic equation yields the optimal control quantity, which is the conversion rate of the target group to the specified group per unit time under the control strategy.

[0013] Furthermore, user activity is used to describe the level of activity a user has on a social network, and is expressed as:

[0014] Act(v i )=a*Num[rev(v i )]+Num[orig(v i )]

[0015] User sensitivity is used to describe a user's sensitivity to topic information, and is expressed as:

[0016]

[0017] Among them, Act(v i ) represents user v i The number of original posts, comments, and reposts on Weibo within a certain period before the topic emerged, Num[orig(v i )], Num[rev(v i )] respectively represent user v i The number of comments, reposts, and original posts on Weibo during this period, where a∈[0,1] is a weakening factor; Sen(v i ) for user v i Sensitivity, f(v) i f represents the number of followers a user has. avg(net) represents the average number of followers a user has on the network.

[0018] Furthermore, since any topic will gradually fade away over time after it is published, the topic's popularity can be expressed as:

[0019]

[0020] The participation of a node in topic propagation is positively correlated with the activity and sensitivity of its neighboring nodes. The neighboring nodes' response to node v... i The information transmission force is represented as:

[0021]

[0022] Where t and t' represent the current time point and the message publication time point, respectively, and w is the regularization factor; Dri(v i ) indicates the influence of friends, Act(v) j ) represents the neighbor node v j activity level, Sen(v j ) represents the neighbor node v j The sensitivity is given by N, where N is the number of neighboring nodes.

[0023] Furthermore, the influence of information includes the influence of rumors, the influence of dubious rumors, the external factors influencing users of rumors, and the external factors influencing users of dubious rumors, which are respectively represented as follows:

[0024] inf(rumor) = γ1 + γ2 * fac internal (v i )+γ3*fac' external (v i )

[0025] inf(doubt) = γ1 + γ2 * fac internal (v i )+γ3*fac" external (v i )

[0026] fac internal (v i ) = Act(v i )*Sen(v i )

[0027] fac' external (v i =Pop rumor_top (t)*Dri rumor (v i )

[0028] fac” external(v i =Pop doubt_top (t)*Dri doubt (v i )

[0029] Where inf(rumor) represents the influence of the rumor; γ1, γ2, and γ3 are partial regression coefficients; Act(v i ) represents the neighbor node v i Activity level; Sen(v i ) represents the neighbor node v i sensitivity; fac internal (v i ) represents the internal influencing factors of rumors and suspected rumors on users, fac' external (v i () indicates the external factors that influence users' perception of rumors; fac" external (v i () indicates the external factors that influence users on suspected rumors; Pop top (t) represents the topic's popularity; Dri(v) i ) represents a neighbor node to node v i Information transmission power.

[0030] Furthermore, user v i The driving forces behind the spread of rumors are represented as follows:

[0031]

[0032] User v i The driving forces behind participating in the spread of suspected rumors are represented as follows:

[0033]

[0034] Inc rumor (v i ) = p1*Inf(rumor)

[0035] Inc doubt (v i = p2*Inf(doubt)

[0036] Among them, Drf vi (rumor) indicates user v i The driving force for the spread of rumors; Inf(rumor) represents the influence function of the rumor; Inf(doubt) represents the influence function of the doubtful rumor; p1 and p2 represent the proportions of neighboring nodes that participate in forwarding the rumor and the doubtful rumor, respectively, and p1+p2=1.

[0037] Furthermore, the control model includes four user states: users who have not yet been freed from rumors and are in a susceptible state; users who believe rumors and forward and spread rumors and are in an infected state; users who doubt rumors and forward and spread doubtful rumors and are in a doubtful state; and users who have been exposed to too many types of information and are immune to information and are in a removed state. In this model, susceptible users will transform into doubtful rumor nodes with a probability of α and into infected nodes with a probability of β. Infected users and doubtful rumor users will transform into removed users with probabilities of ω and ψ, respectively.

[0038] Furthermore, the dynamic equation of the rumor control model based on evolutionary game theory and multi-state is expressed as:

[0039]

[0040]

[0041]

[0042]

[0043] Where S(t) is the number of susceptible users at time t, I(t) is the number of infected users at time t, D(t) is the number of suspected rumor users at time t, and R(t) is the number of removed users at time t; v1(t) represents the conversion rate from susceptible users to removed users under the prevention strategy at time t, and v2(t) represents the conversion rate from infected users to suspected rumor users under the isolation strategy at time t.

[0044] Furthermore, in order to obtain the optimal value of the prevention strategy v1(t) And the optimal value of isolation strategy v2(t) Construct the Hamiltonian function of the dynamic equation of the rumor control model based on evolutionary game theory and multi-state conditions. Apply Pontryagin's theorem to the Hamiltonian function to obtain its adjoint function. The optimal value is expressed as:

[0045]

[0046]

[0047] Where, λ S (t), λ D (t), λ I (t), λ R (t) are the companion functions corresponding to the number of susceptible users S(t), the number of users suspected of spreading rumors D(t), the number of infected users I(t), and the number of removed users R(t) at time t, respectively, and C2 and C3 are positive constants.

[0048] Furthermore, the Hamiltonian function of the dynamic equation of the rumor control model based on evolutionary game theory and multi-state conditions is expressed as:

[0049]

[0050] Where C1 is a positive constant, α is the probability that a susceptible user will become a rumor-suspecting user, β is the probability that a susceptible user will become an infected user, ω is the probability that an infected user will become a removed user, and ψ is the probability that a rumor-suspecting user will become a removed user.

[0051] Furthermore, the adjoint function λ corresponding to the number of susceptible users S(t), suspected users D(t), infected users I(t), and removed users R(t) at time t S (t), λ D (t), λ I (t), λ R (t) is represented as:

[0052] λ S (t)=λ S (t)(αD(t)+βI(t)+v1(t))-λ I (t)βI(t)-λ D (t)αD(t)-λ R (t)v1(t);

[0053] λ I (t)=-C1+λ S (t)βS(t)-λ I (t)(βS(t)-ω-v2(t))-λ D (t)v2(t)-λ R (t)ω;

[0054] λ D (t)=λ S (t)αS(t)-λ D (t)(αS(t)-ψ)-λ R (t)ψ;

[0055] λ R (t) = 0.

[0056] The beneficial effects of this invention are as follows:

[0057] 1. Construct multiple user states during the spread of rumors and describe the driving forces of user state transitions using evolutionary game theory. Taking into account multiple internal and external factors, as well as users' own profit-seeking psychology, and based on quantifying the influence of rumor messages, construct a driving force mechanism for user rumor spread using dynamic game theory, providing a basis for user state transitions.

[0058] 2. To suppress the spread of rumors, a hybrid control strategy combining prevention and isolation time-varying approaches was introduced, and an optimal control problem was established. To achieve the maximum control effect with the minimum cost, internal and external constraints of the control strategy were considered, a cost function was defined, and the optimal control problem was established. This problem was then solved using nonlinear optimization theory, leading to the optimal control solution.

[0059] 3. Addressing the impact of differences between nodes on rumor propagation, a user state transition equation is defined based on mean-field theory. Considering the complexity of user interactions in social networks and leveraging the simplification advantages of mean-field theory, an improved rumor propagation dynamics model is proposed using the mean-field theory to define the user state transition equation. This model not only accurately describes the multi-state user rumor propagation process in social networks but also provides a theoretical basis for rumor control. Attached Figure Description

[0060] Figure 1 This invention relates to a rumor information control model based on evolutionary game theory and multi-state theory.

[0061] Figure 2 This is the mechanism for quantifying the influence of messages in this invention;

[0062] Figure 3 This is the mechanism by which the prevention-isolation strategy in this invention controls the spread of rumors;

[0063] Figure 4 This is a schematic diagram illustrating user propagation prediction in this invention. Detailed Implementation

[0064] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0065] This invention proposes a rumor information control method based on evolutionary game theory and multi-state, comprising the following steps:

[0066] S1. Obtain data source, that is, obtain the basic information and historical behavior of all users who participated in publishing rumors and suspected rumors within the life cycle of a certain topic;

[0067] S2. Extract the internal factors, external factors, and message influence that affect the spread of rumors from the acquired data sources. Internal factors include user activity and user sensitivity. External factors include topic popularity and the influence of friends. Message influence includes the influence of rumor messages and the influence of suspected rumors.

[0068] S3. Based on the payoff function of users believing rumors and forwarding rumor information, and believing doubtful rumors and forwarding doubtful rumors, evolutionary game theory is used to obtain the driving force for users to participate in the spread of rumor messages and the behavioral driving force for users to participate in the spread of doubtful rumors.

[0069] S4. Construct a control system and calculate the value of any user v. i The probability of being in a rumor-spreading state at time t, and the probability of any user v i The probability of being in a state of suspicion at time t is used to derive the dynamic equation of the rumor control model based on evolutionary game theory and multi-state. Solving the dynamic equation yields the optimal control quantity, which is the number of infected individuals who become rumor-suspects per unit time.

[0070] Figure 1 The diagram shows the overall flow of an embodiment of the present invention, as follows: Figure 1 As shown, the input of this invention is a user relationship network, user historical behavior data, and rumor topic data under a certain rumor propagation topic. After processing, the intrinsic and extrinsic attributes of users participating in rumor propagation are extracted. Using this information, the influence of rumor information and the influence of suspected rumor information are calculated. Based on the goal of suppressing rumor propagation, a prevention-isolation hybrid control strategy is designed to establish an optimal control problem. The propagation driving force of rumor information and suspected rumor information is calculated according to dynamic game theory. The propagation driving force of rumor information and suspected rumor information, along with the control coefficients obtained through optimal control, are input into the SDIR propagation model. This model can output the user's propagation result, rumor propagation trend, and user state transformation coefficient. In this way, the probability of any user propagating rumor information or suspected rumor information at any time can be effectively obtained, forming a propagation trend, which is more conducive to relevant institutions or departments controlling information propagation according to their needs.

[0071] This embodiment mainly consists of three parts in the process of implementing the method of the present invention:

[0072] (1: Data Acquisition. Data can be acquired from publicly available data websites or using APIs provided by widely used social networking platforms. What is needed here is the basic information and historical behavior of all users who participated in posting rumors or suspected rumors within the lifecycle of a specific topic.)

[0073] (2: Extract relevant attributes. Extract the internal and external factors that affect the spread of rumors from the preprocessed data, and construct the message influence accordingly.)

[0074] (3: Model Building. Based on quantifying the influence of rumors, the psychological game played by users during the cognitive process is quantified according to dynamic game theory; and the driving force of user state transition is measured according to the payoff function, providing a basis for the state transition of users in the rumor-mongering state. Secondly, a prevention-isolation hybrid control strategy is introduced to limit the spread of rumor information, an optimal control problem is established, and the optimal control with the minimum cost after control is calculated. Finally, combined with the mean field equation, a state transition equation based on multi-user states and optimal control is defined, and an improved rumor propagation dynamics model is proposed.)

[0075] (1: Obtain the data source.)

[0076] S11: Obtain raw data. Raw data can be obtained through the data query API provided by the enterprise or by directly downloading existing data sources.

[0077] S12: Simple Data Cleaning. Raw data is often unstructured and cannot be directly used for data analysis. Simple data cleaning can structure most unstructured data. For example, removing duplicate data and cleaning up invalid information.

[0078] (2: Extract the required attributes.)

[0079] Exploring the propagation process of various types of rumors, primarily purported rumors and suspected rumors, essentially involves extracting relevant features from both internal and external factors and performing modeling analysis. This invention focuses on the rumor information propagation network, extracting relevant attributes influencing rumor information propagation from both internal and external factors, thereby constructing message influence and analyzing the dynamic causes driving rumor information propagation. Specifically:

[0080] S21: Internal Factors

[0081] S211: User Activity Act(v) i )

[0082] User activity is used to describe a user's level of activity on a social network. Generally speaking, the higher the user's activity level, the greater the likelihood of them participating in the dissemination of topics. This article defines user activity level as follows:

[0083] Act(v i )=a*Num[rev(v i )]+Num[orig(v i (1)

[0084] Among them, Act(v i) represents user v i The number of original posts, comments, and reposts on Weibo within a certain period before the topic emerged, Num[rev(v i )]、Num[orgi(v i )] respectively represent user v i The number of comments, reposts, and original posts on Weibo during this period. Typically, the number of user comments and reposts far exceeds the number of original posts; therefore, this embodiment defines a weakening factor a∈[0,1] before the number of comments and reposts on Weibo.

[0085] S212: User Sensitivity Sen(v) i )

[0086] This term describes a user's sensitivity to topical information, which is largely determined by their online social network. Therefore, this paper defines user sensitivity as follows:

[0087]

[0088] Where, f(v) i ) represents the number of followers a user has, f avg (net) represents the average number of people a user follows on the network, which reflects the likelihood that a user will be exposed to online rumors.

[0089] S22: External Factors

[0090] S221: Popularity of the Topic top (t)

[0091] Any topic, once posted, will gradually fade away over time. Therefore, we borrow the half-life function from physics to describe the changing popularity of a topic, and assign new meanings to its parameters. Thus, the definition of topic popularity is:

[0092]

[0093] Where t and t' represent the current time and the message publication time, respectively, and w is the regularization factor, which is set to 100.

[0094] S222: Dri(v) - Motivation from Friends i )

[0095] This describes the information-driving force of a user's friends on that user. A user's friends play an indispensable role in the dissemination of information. Clearly, a node's participation in topic dissemination is positively correlated with the activity and sensitivity of its neighboring nodes. Therefore, this embodiment defines the information-driving force of neighboring nodes on a node as follows:

[0096]

[0097] Among them, Act(v j ),Sen(v j ) represent neighbor node v i Activity level, neighbor node v i The sensitivity is given by N, where N is the number of neighboring nodes.

[0098] S23: News Influence

[0099] The influence of a message on a user involves multiple factors, including the user themselves and the external environment. Therefore, this paper quantifies the user's internal factors from the aspects of user activity and user perception, and quantifies the external factors from the aspects of information transmission power of neighboring nodes and message popularity, in order to construct the influence of rumor messages.

[0100] like Figure 2 As shown, considering both internal and external factors, this paper uses multiple linear regression to quantify the influence of messages. Therefore, the influence function of rumor messages and suspected rumor messages is defined as follows:

[0101]

[0102] Among them, γ1, γ2, and γ3 are partial regression coefficients, obtained by fitting using a multiple linear regression method, and γ2 and γ3 are the weight coefficients of internal and external elements, reflecting their proportion in the overall influence of the rumor; fac internal (v i ) refers to the internal factors that influence users' perceptions of rumors and misinformation; these factors are only related to the user themselves. external (v i ), fac" external (v i The term "rumored information" and "doubtful information" refer to external factors that influence users. Doubtful information is defined as follows:

[0103]

[0104] The above step S3 establishes the model. It mainly consists of the following three steps.

[0105] The model consists of three main stages: quantifying the driving force of rumor propagation, calculating the optimal control coefficient using a multi-state rumor control method, and providing the dynamic equations for the rumor control model. In the first stage, the driving force for the final user state transformation is calculated by combining the message's influence with the payoff function obtained using evolutionary game theory. In the second stage, a prevention-isolation hybrid control strategy is introduced based on the traditional infectious disease model to establish an optimal control problem. Pontryagin's theorem is then used to find an optimal control solution, achieving the maximum control effect at the minimum cost. In the third stage, a rumor information control model based on evolutionary game theory and multi-state principles is established to predict and analyze the spread of rumors and misleading information.

[0106] (3: Establish a model.)

[0107] S31: Driving Forces of Rumor Spread

[0108] When rumors emerge, people either believe them or question them. The driving force behind these decisions is the pursuit of self-interest; under this influence, users tend to gravitate towards the side that benefits them the most. Therefore, to quantitatively analyze the driving force behind users spreading rumors, this paper defines two game strategies: 1 represents believing the rumor and forwarding it, and 2 represents doubting the rumor and forwarding it. Let p1 and p2 represent the proportions of neighboring nodes that participate in forwarding the rumor and the doubtful rumor, respectively. Ignoring nodes that do not forward the topic, p1 + p2 = 1. Therefore, the payoff functions for the two strategies are:

[0109]

[0110] Inf(rumor) and Inf(doubt) are the influence functions for rumors and doubtful rumors, respectively.

[0111] Using evolutionary game theory to determine the driving forces behind user participation in the spread of rumors:

[0112]

[0113] Among them, Inc rumor (v i ), Inc doubt (v i The benefits are calculated as follows: (1) for rumors and (2) for dubious rumors. Similarly, the driving force behind user Vi's participation in the spread of dubious rumors is:

[0114]

[0115] S32: Multi-State Rumor Control Methods

[0116] This paper introduces a new model based on the traditional model by incorporating a state of doubt, and introduces a control strategy to study the spread trend of rumor information under a prevention-isolation hybrid control strategy. The proposed model includes four user group states: Susceptible (S: users who have not yet been exposed to rumor information), Infected (I: users who believe in rumors and forward and spread them), Doubted (D: users who doubt rumors and forward and spread them), and Removed (R: users who have been exposed to too many types of information and are immune to it). This model is based on the following assumptions:

[0117] 1. Due to the time-limited and explosive nature of topic information dissemination, this paper assumes that the number of nodes in the social network is equal at any time during the information dissemination process, that is, the sum of the state ratios in the model at any time is S+D+I+R=1.

[0118] 2. Since information dissemination is a form of contact transmission, there is a certain infection rate when susceptible users come into contact with infected users or users who are suspicious of rumors.

[0119] Because information itself has a certain level of popularity and a lifespan, the popularity of information will gradually decrease over time, and users will gradually forget about it and become users who remove it. Therefore, infected users or users who doubt rumors have a certain recovery rate and become users who remove it.

[0120] Based on the above assumptions, this paper defines the following rules for the propagation of topic information in social networks:

[0121] 1. Susceptible nodes will transform into suspected rumor nodes with probability α and into infected nodes with probability β, where α and β ∈ [0,1].

[0122] 2. As time and topic popularity change, infected nodes and suspected rumor nodes are transformed into immune nodes with probabilities ω and ψ, respectively, where ω and ψ∈[0,1].

[0123] Based on the above propagation rules, the dynamic equation is obtained:

[0124]

[0125] If no measures are taken to control the spread of rumors, it could have a very negative impact on social networks and the real world. Optimal control techniques are very useful for solving the problem of information diffusion. Therefore, this embodiment proposes the following two control strategies:

[0126] Prevention: Intervention measures implemented by social authorities and education departments to disseminate the truth to susceptible users who have not yet been exposed to rumors. Users who accept preventive measures will skip the stage of spreading rumors and directly and permanently become immune users to rumors. This is represented by the prevention strategy variable v1(t).

[0127] Isolation: This is usually implemented by the administrators of social media platforms to separate infected individuals who spread rumors from users or delete related tweets. After a period of blocking, infected individuals will gradually regain their rationality and be corrected to be users who doubt the rumors. The isolation strategy variable v2(t) is used to represent this.

[0128] like Figure 3As shown, under the influence of infected individuals, susceptible users will gradually transform into infected individuals themselves. After introducing a hybrid control strategy, infected individuals are isolated, susceptible users will no longer have direct contact with infected individuals, and at the same time, preventive controls allow susceptible users to skip the infection stage and directly become removed users.

[0129] To achieve the maximum control effect at the minimum cost, this paper defines a system loss function and then establishes an optimal control problem. Since implementing an isolation control strategy for users comes at the cost of sacrificing user experience, it will inevitably result in the loss of some users. Therefore, we divide the system loss into two parts: the users spreading rumors and the cost of implementing the control strategy. The system loss function is usually approximated using a quadratic function, partly because there is no linear function that can accurately simulate reality, and partly because quadratic functions often mitigate the system's side effects. Therefore, this embodiment defines the system loss function of the intervention strategy as the following quadratic function:

[0130]

[0131] Wherein, C1, C2, and C3 represent the weights of the loss, and their values ​​are normal numbers. The specific values ​​are set by those skilled in the art based on experience or experimental data, and this invention will not discuss them in detail.

[0132] Based on the loss function above, this embodiment establishes an optimal control problem based on the spread of rumors and misinformation. The core of this problem lies in finding a solution to a set of control variables that minimizes the above function.

[0133] J(v1 * v2 * )=min{J(v1(t),v2(t))} (12)

[0134] Among them, v1 * v2 * Let v1(t) and v2(t) represent the optimal control solutions that can be taken for the optimal control problem.

[0135] The equation after introducing control variables can be described as follows:

[0136]

[0137] This system is a terminal-state-free system, subject to the following state conditions:

[0138]

[0139] Where S(0), D(0), I(0), and R(0) represent the populations S(t), D(t), I(t), and R(t) at time t = 0, respectively; fIndicates the end time, therefore S(t) f ), D(t) f ), I(t) f ), R(t) f ) represents time t f The number of hours.

[0140] To solve this optimal control problem, we first construct the Hamiltonian function H(t):

[0141]

[0142] Where, λ S (t), λ D (t), λ I (t), λ R (t) represents the adjoint function corresponding to the number of susceptible users S(t), suspected users D(t), infected users I(t), and removed users R(t) at time t, respectively, where S, I, D, and R are abbreviations for the number of susceptible users S(t), suspected users D(t), infected users I(t), and removed users R(t) at time t. Substituting (13) into (15), we get:

[0143]

[0144] To find the optimal control variables, Pontryagin's theorem is applied to the Hamiltonian function. According to Pontryagin's theorem, the adjoint function can be obtained as follows:

[0145]

[0146]

[0147]

[0148]

[0149] Where H is a shorthand for the Hamiltonian function H(t) of the dynamic equation of the rumor control model based on evolutionary game theory and multiple states; the purpose of this optimization control problem is to reduce or even eliminate rumor information in the system, therefore, under the terminal condition:

[0150] λ S (t f )=λ I (t f )=λ R (t f )=λ D (t f )=0 (21)

[0151] Furthermore, according to Pontryagin's theorem:

[0152]

[0153] Where v1 and v2 are abbreviations for the conversion rate v1(t) from susceptible users to removed users under the prevention strategy at time t, and the conversion rate v2(t) from infected users to suspected users under the isolation strategy at time t, respectively. Therefore:

[0154]

[0155]

[0156] The concise writing format is as follows:

[0157]

[0158] It can be seen that when v1(t) and v2(t) take v1 * v2 * When the optimal control problem is solved, the optimal control solution is obtained.

[0159] S33: Dynamic Equations of a Rumor Control Model

[0160] Because the spread of rumors is unidirectional, user state transitions are also unidirectional. That is, a user's state can only move from a susceptible state to a suspicious or infected state, and ultimately to a removed state. Assume user v... i There are n neighbors, and the probability that m neighbors forward the message at time t follows a binomial distribution:

[0161]

[0162] Then any user v i The probability of being in a state of spreading rumors at time t is:

[0163]

[0164] Similarly, for any user v i The probability of being in a state of doubt at time t is:

[0165]

[0166] Combining mean-field theory, the dynamic equations of the rumor control model based on evolutionary game theory and multi-state dynamics are derived as follows:

[0167]

[0168] in, This represents the average conversion probability.

[0169] Using the dynamic equations of the above propagation model, the probability of any user participating in the propagation of rumors and misinformation at any time under the control strategy can be solved.

[0170] Figure 4 This is a schematic diagram illustrating user information propagation prediction in an embodiment of the present invention, such as... Figure 4 As shown, the SDIR model described above can be used to calculate the state of various users in the next moment.

[0171] The dynamic propagation model constructed using this invention allows the system to predict the spread trend of rumors on a specific topic on social networks, outputting user status ratios and propagation trend graphs at each moment. Furthermore, it provides valuable reference for relevant departments in controlling the spread of rumors on social networks. Based on the output data, the system can understand the spread pattern and scale of rumors, enabling early and effective control of online public opinion.

[0172] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A rumor information control method based on evolutionary game and multi-state, characterized in that, The method comprises the following steps: S1, obtaining a data source, that is, obtaining basic information and historical behaviors of all users participating in publishing rumor information and rumor-doubt information under a topic in a life cycle of the topic; S2, extracting internal factors, external factors and message influence from the obtained data source, the internal factors including user activity and user sensitivity, the external factors including topic heat and friend driving force, and the message influence including rumor message influence and rumor-doubt message influence; S3, using an evolutionary game theory to obtain a driving force of the user participating in rumor message propagation and a behavior driving force of the user participating in rumor-doubt message propagation according to a benefit function of the user believing rumor information and forwarding rumor information and believing rumor-doubt information and forwarding rumor-doubt information; S4, construct a control system and calculate any user the probability of being in the rumor state at time t, any user the probability of being in the doubt state at time t, bring these two probabilities into the control system to obtain the rumor control model dynamics equation based on evolutionary game and multi-state, solve the dynamics equation to obtain the optimal control amount, which is the conversion rate of the control strategy converting the target group into the specified group per unit time; In the control model, four states of users are included, including users in a susceptible state who have not yet removed the rumor message, users in an infected state who believe the rumor and forward the rumor information for transmission, users in a rumor-doubt state who doubt the rumor and forward the rumor-doubt information for transmission, and users in a removed state who have been exposed to multiple types of information and are immune to the information; in the model, the susceptible state users will be converted into rumor-doubt nodes with a probability of , into infected nodes with a probability of , and the infected state users and the rumor-doubt state users will be converted into removed state users with probabilities of , , respectively; A dynamics equation of the rumor control model based on the evolutionary game and the multi-state is expressed as: wherein, is the number of susceptible users at time t, is the number of infected users at time t, is the number of rumor users at time t, is the number of removed users at time t; denotes the conversion rate of susceptible users to removed users at time t under the prevention strategy, denotes the conversion rate of infected users to rumor users at time t under the quarantine strategy; To calculate the conversion rate from susceptible users to removed users under the prevention strategy at time t. optimal value And the conversion rate from infected users to suspected users under the isolation strategy at time t. optimal value We construct the Hamiltonian function of the dynamic equation of a rumor control model based on evolutionary game theory and multi-state dynamics. We then use Pontryagin's theorem to find the adjoint function of the Hamiltonian function, and the optimal value is expressed as: where, , , , respectively are the number of susceptible users at time t , the number of rumor-doubt users at time t , the number of infected users at time t , the number of removed users at time t corresponding adjoint functions, , are normal numbers; is the Hamilton function of the rumor control model dynamics equation based on evolutionary game and multi-state. 2.The rumor information control method based on evolutionary game and multi-state according to claim 1, wherein, The user activity is used for describing an active degree of the user in the social network and is expressed as: The user sensitivity is used for describing a sensitivity of the user to topic information and is expressed as: in, Indicates user The number of original posts, comments, and reposts on Weibo within a certain period before the topic emerged. Representing users respectively The number of comments, reposts, and original posts on Weibo during this period. As a weakening factor; For users sensitivity, For the number of followers of a user, This represents the average number of followers a user has on the network. 3.The rumor information control method based on evolutionary game and multi-state according to claim 1, wherein, Any topic will gradually die out with time elapsing after being published, and therefore the topic heat can be expressed as: The node participates in the topic propagation and the activity and sensitivity of the neighbor node are positively correlated. The information transmission power of the neighbor node to the node is represented as: ​ wherein, respectively represent the current time point, the message publishing time point, and w is a regularization factor; represents the friend driving force, represents the activity of the neighbor node , represents the sensitivity of the neighbor node , N is the number of neighbor nodes.

4. The rumor information control method based on evolutionary game and multi-state according to claim 1, characterized in that, The message influence includes rumor message influence, rumor-doubt message influence, an external influence factor of the rumor message on the user and an external influence factor of the rumor-doubt message on the user, and is respectively expressed as: wherein, is the influence of the rumor message; is the bias regression coefficient; represents the activity of the neighbor node ; represents the sensitivity of the neighbor node ; is the internal influence factor of the rumor message and the rumor message on the user, represents the external influence factor of the rumor message on the user; represents the external influence factor of the rumor message on the user; represents the topic heat; represents the information transmission power of the neighbor node on the node .

5. The rumor information control method based on evolutionary game and multi-state according to claim 1, characterized in that, User v i The driving force of participating in rumor message propagation is represented as: User v i The driving force of the behavior participating in the rumor message propagation is represented as: wherein, represents a user v i the driving force of participating in rumor message propagation; represents an influence function of a rumor message; represents an influence function of a rumor message; p1, p2 respectively represent the proportion of participating in forwarding rumor information and forwarding rumor message in neighbor nodes, and p1+ p2=1.

6. The rumor information control method based on evolutionary game and multi-state according to claim 1, characterized in that, A Hamilton function of the dynamics equation of the rumor control model based on the evolutionary game and the multi-state is expressed as: wherein, is a normal number, is the probability of a susceptible state user converting to a rumor-susceptible state user, is the probability of a susceptible state user converting to an infected state user, is the probability of an infected state user converting to a removed state user, is the probability of a rumor-susceptible state user converting to a removed state user.

7. The rumor information control method based on evolutionary game and multi-state according to claim 1 or 6, characterized in that, the number of susceptible users at time t the number of rumor-doubting users the number of infected users the number of removed users the corresponding adjoint function 、 、 、 is represented as: ； ； ； 。

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