A method for constructing a public opinion propagation model with direct immunity to SCIR

Abstract

The present invention discloses a method for constructing a public opinion propagation model of direct immunity SCIR. First, the problem of real-time changes in the number of online users in social networks is considered, and the concepts of new rate and offline rate are introduced; secondly, the influence of social factors on the immune effect is considered, and the intervention strength of the department, the credibility of the real information and the intervention time of the department are comprehensively considered, and a direct immunity strategy is proposed; then, the differential equation of the public opinion propagation model is established to generate the final propagation model; finally, the stability of the model is analyzed. By adjusting the probability values ​​of each state in the model, the basic reproduction number can be limited to (0,1), thereby suppressing the spread of public opinion and reducing the scope of public opinion propagation.

Description

Technical Field

[0001] The present invention relates to the field of information dissemination and control, and in particular to a method for constructing a public opinion dissemination model directly immune to SCIR. Background Art

[0002] At present, most of the research on public opinion dissemination focuses on closed network topology, without considering the fluctuation of the number of network users and the impact of social factors on public opinion dissemination. However, in the process of public opinion dissemination on real social networks, network users exist in two states: online and offline, so the number of users is not completely constant; at the same time, in the process of controlling online public opinion, a three-party benign interactive relationship has not been formed between departments, media and the public. Summary of the invention

[0003] This application proposes a method for constructing a public opinion propagation model that is directly immune to SCIR by considering the fluctuations in the number of Internet users and the impact of social factors on the propagation of public opinion.

[0004] To achieve the above object, the technical solution of the present invention is: a method for constructing a public opinion propagation model directly immune to SCIR, comprising:

[0005] Obtain the real-time number of online users in the social network based on the new addition rate and offline rate;

[0006] Taking into account the department's intervention strength, the credibility of the real information and the department's intervention time, the direct immunity rate was obtained;

[0007] Establish a public opinion propagation model that is directly immune to SCIR;

[0008] The stability of the public opinion propagation model immune to SCIR is analyzed.

[0009] Furthermore, the new addition rate is the percentage of the number of new online users in the social network at a certain moment to the total number of users, represented by A, where the new addition rate only applies to susceptible users S;

[0010] The offline rate is the ratio of the number of offline users in a social network to the total number of users at a certain moment, represented by μ, where the offline rate applies to users in all states in the network;

[0011] Therefore, the number of real-time online users in the social network is:

[0012] |1+A-μ|N(t)=S(t)+C(t)+I(t)+R(t) (1)

[0013] Where S(t) is the unknown state, C(t) is the hesitant state, I(t) is the propagation state, R(t) is the immune state, and N is the number of nodes in the network.

[0014] Furthermore, the direct immunity rate P SR for:

[0015]

[0016] Among them, α represents the intervention strength of the department, that is, the density of nodes in the immune state R at the initial moment of adopting the immune strategy, α∈[0,1]; β represents the credibility of the real information, β∈[0,1]; T represents the intervention time of the department; Represents the interference of noise, which is proportional to the intervention strength α and inversely proportional to the credibility of the information β.

[0017] Furthermore, the public opinion propagation model immune to SCIR is:

[0018]

[0019] Among them, P SC P represents the probability of being exposed to public opinion but not deciding whether to spread it, that is, the internal contact rate; CI represents the probability of being exposed to public opinion and spreading it, that is, the indirect forwarding probability; P CR represents the probability that the hesitant state does not spread and turns into the immune state, that is, the indirect immunity rate; P IR It indicates the probability that the communicator does not believe the public opinion for some reason and thus becomes immune, that is, the forwarding immunity rate. Satisfy 0≤P SC ,P CI ,P CR ,P IR ≤1; S k , C k ,I k , R k Represents the state of the node at the kth iteration.

[0020] Furthermore, the stability of the public opinion propagation model immune to SCIR is analyzed, specifically:

[0021] Let the left side of equation (3) be zero, and I k =0, k=1,2,···,n, the public opinion propagation model is in a non-propagation equilibrium state, and there is a non-propagation equilibrium point at this time:

[0022]

[0023] When I>0, the local propagation equilibrium point of the public opinion propagation model is E * =(S * ,E * ,R * ) in,

[0024]

[0025] Due to S k (t)+C k (t)+I k (t)+R k (t) = 1, then equation (3) is simplified to

[0026]

[0027] Divide the x,y vectors,

[0028]

[0029] make

[0030]

[0031] The emergence rate of new communicators is:

[0032]

[0033] The individual migration rate is

[0034]

[0035] Then there is,

[0036]

[0037] right Find the Jacobian matrix,

[0038]

[0039]

[0040] The basic reproduction number is:

[0041]

[0042] in, represents the spectral radius of the matrix.

[0043] The basic reproduction number of the public opinion propagation model is:

[0044]

[0045] Substituting the propagation-free equilibrium point E0 in equation (4), we obtain:

[0046]

[0047] If R0≤1, it means that the maximum number of people that a communicator can infect during the average infectious period is less than 1, and the transmission point will gradually disappear. At this time, the public opinion propagation model only has a non-propagation equilibrium point, which is globally asymptotically stable.

[0048] If R0>1, it means that the maximum number of people that a communicator can infect during the average infection period is greater than 1, that is, the transmission point always exists and forms local transmission; at this time, the public opinion propagation model has a local transmission equilibrium point in addition to the no-transmission equilibrium point. The no-transmission equilibrium point is unstable, and the local transmission equilibrium point is globally asymptotically stable.

[0049] By adopting the above technical method, the present invention can achieve the following technical effects: the method constructs a public opinion propagation model that is directly immune to SCIR by considering the fluctuation of the number of network users and the influence of social factors on the propagation of public opinion, which is more in line with the propagation of public opinion in real social networks, and is conducive to supervising and controlling the propagation of public opinion, and reducing the impact of negative public opinion on society. By adjusting the probability values ​​of each state in the model, the basic reproduction number can be limited to (0,1), thereby suppressing the spread of public opinion and reducing the scope of public opinion propagation. BRIEF DESCRIPTION OF THE DRAWINGS

[0050] In order to more clearly illustrate the embodiments of the present invention or the technical solutions of the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0051] Figure 1 It is a real social network topology graph with 1000 nodes;

[0052] Figure 2 This is a diagram of the public opinion propagation model that is directly immune to SCIR;

[0053] Figure 3 This is the result diagram of the impact of the basic reproduction number on the spread of public opinion;

[0054] Figure 4 This is the result diagram of the impact of intervention intensity on the spread of public opinion;

[0055] Figure 5 This is the result diagram of the impact of information credibility on the spread of public opinion;

[0056] Figure 6 It is the influence diagram of intervention time on the spread of public opinion;

[0057] Figure 7 This is a graph showing the results of the model comparison analysis. DETAILED DESCRIPTION

[0058] In order to make the purpose, technical solution and advantages of the present invention more clear, the present invention is further described in detail below in conjunction with the accompanying drawings and specific implementation methods. The following embodiments can enable technicians in this field to understand the present invention more comprehensively, but the present invention is not limited to the scope of the embodiments.

[0059] Example 1

[0060] In the process of controlling online public opinion, the present invention forms a three-party benign interactive relationship between departments, media and the public. Departments increase their intervention and information transparency, and media disclose information in a timely manner, thereby meeting the public's information needs, protecting the public's right to know, and ultimately achieving control over the spread of public opinion on social networks. Based on the SCIR model, the present invention considers the activity of network users, introduces the concepts of new user rate and offline rate, makes the number of nodes in the network fluctuate, and establishes a public opinion propagation model that is directly immune to SCIR; proposes a public opinion direct immunity control strategy that considers social factors such as department intervention, information credibility and intervention time, so that S-state nodes directly transform into R-state after contacting public opinion without secondary propagation; analyzes the equilibrium point and basic reproduction number of the public opinion propagation model, and obtains the boundary conditions of public opinion propagation; finally, simulates and analyzes the impact of different factors on the spread of public opinion in social networks, summarizes the direct immunity laws of different factors, and provides reference for departments to deal with public opinion, thereby maintaining the security of the network and society.

[0061] This embodiment proposes a method for constructing a public opinion propagation model that is directly immune to SCIR, and the specific implementation steps are as follows:

[0062] S1: Considering the problem of real-time changes in the number of online users in social networks, the real-time number of online users in social networks is obtained based on the new addition rate and offline rate. Specifically:

[0063] (1) The new addition rate is the percentage of the number of new online users in the social network at a certain moment to the total number of users, denoted by A, where the new addition rate only applies to susceptible users S;

[0064] (2) The offline rate is the ratio of the number of offline users to the total number of users in the social network at a certain moment, denoted by μ, where the offline rate applies to users in all states in the network;

[0065] Therefore, the number of real-time online users in the social network is:

[0066] |1+A-μ|N(t)=S(t)+C(t)+I(t)+R(t) (1)

[0067] Where S(t) is the unknown state, C(t) is the hesitant state, I(t) is the propagation state, R(t) is the immune state, and N is the number of nodes in the network.

[0068] S2: Considering the impact of social factors on immunization, the department's intervention strength, the credibility of real information and the department's intervention time are comprehensively considered to obtain the direct immunization rate, which is:

[0069] (1) Departmental involvement

[0070] The main purpose of the immunization strategy is to reduce the number of users who spread public opinion on the Internet. When departments take restrictive measures on the spread of public opinion, the greater the intervention, the higher the degree of attention paid to public opinion. Then the departments will take more powerful measures to reduce the impact of negative public opinion and encourage more Internet users to believe in real information, which will lead to more immune users in the initial stage when direct immunity begins to take effect. At the same time, since opinion leaders in social networks have an important influence on the spread of public opinion, increasing the intervention of departments can limit the dissemination ability of influential communicators on the network, thereby achieving the effect of suppressing the spread of public opinion.

[0071] (2) Credibility of real information

[0072] The media not only passively provides information channels, but also changes the mode of thinking. The authoritative information held by the department needs to be released to the public through the media. As an important means to combat negative public opinion, the mainstream media should seize the initiative of information release at the first time, build a bridge of communication between the public and the department, thereby improving the credibility of information and ultimately making negative public opinion completely lose the market. For example, in earthquake early warning, the seismic network has a higher credibility than other institutions or media. Therefore, the credibility of information will greatly affect the immune control of public opinion.

[0073] (3) Department intervention time

[0074] Most mass incidents caused by negative public opinion are related to the failure of departments to deal with them in a timely and effective manner. When public opinion begins to spread on the Internet, departments need to verify the authenticity of public opinion in a timely manner and estimate the possible impact of public opinion. Once the initial outbreak of public opinion is missed, negative public opinion will ferment, increasing the difficulty of public opinion control. Therefore, departments must collect rumor information in a timely and accurate manner, intervene in the spread of public opinion as soon as possible, and thus take the initiative in controlling public opinion.

[0075] At the same time, from the perspective of communication dynamics, information will inevitably be disturbed by noise during the process of dissemination, which will weaken the effect of direct immunity of departments to a certain extent. The degree of noise is related to the social factors of the information itself. The lower the credibility of the information, the greater the interference of noise; the wider the scope of information dissemination, the stronger the interference of noise. In order to reduce the spread of negative public opinion and reduce its harmfulness, we must try to increase the scope of dissemination of real information released by departments and reduce the interference of noise on the dissemination of real information in the direct immunity strategy.

[0076] Therefore, in order to control the spread of public opinion, the present invention uses social factors to intervene in the model, and considers the influence of noise interference, and changes the direct immunity rate P SR Defined as:

[0077]

[0078] Among them, α represents the intervention strength of the department, that is, the density of nodes in the immune state R at the initial moment of adopting the immune strategy, α∈[0,1]; β represents the credibility of the real information, β∈[0,1]; T represents the intervention time of the department; Represents the interference of noise, which is proportional to the intervention strength α and inversely proportional to the credibility of the information β.

[0079] S3: Establish a public opinion propagation model that is directly immune to SCIR;

[0080]

[0081] Among them, P SC P represents the probability of being exposed to public opinion but not deciding whether to spread it, that is, the internal contact rate; CI represents the probability of being exposed to public opinion and spreading it, that is, the indirect forwarding probability; P CR represents the probability that the hesitant state does not spread and turns into the immune state, that is, the indirect immunity rate; P IR It indicates the probability that the communicator does not believe the public opinion for some reason and thus becomes immune, that is, the forwarding immunity rate. Satisfy 0≤P SC ,P CI ,P CR ,P IR ≤1; S k , C k ,I k , R k Represents the state of the node at the kth iteration.

[0082] Furthermore, the stability of the public opinion propagation model is analyzed: Let the left side of equation (3) be zero, and I k =0, k=1,2,···,n, the model is in a non-propagation equilibrium state, and there is a non-propagation equilibrium point:

[0083]

[0084] When I>0, the local propagation equilibrium point of the model is E * =(S * ,E * ,R * )

[0085] in,

[0086]

[0087] Due to S k (t)+C k (t)+I k (t)+R k (t) = 1, then formula (3) can be simplified to

[0088]

[0089] Divide the x,y vectors,

[0090]

[0091] make

[0092]

[0093] The emergence rate of new communicators is:

[0094]

[0095] The individual migration rate is

[0096]

[0097] Then there is,

[0098]

[0099] right Find the Jacobian matrix,

[0100]

[0101]

[0102] The basic reproduction number is:

[0103]

[0104] in, represents the spectral radius of the matrix.

[0105] The basic reproduction number of the model is:

[0106]

[0107] Substituting the propagation-free equilibrium point E0 into formula (4), we obtain:

[0108]

[0109] If R0≤1, it means that the maximum number of people that a communicator can infect during the average infectious period is less than 1, and the transmission point will gradually disappear. At this time, the public opinion propagation model only has a non-propagation equilibrium point, which is globally asymptotically stable.

[0110] If R0>1, it means that the maximum number of people that a communicator can infect during the average infection period is greater than 1, that is, the transmission point always exists and forms local transmission; at this time, the public opinion propagation model has a local transmission equilibrium point in addition to the no-transmission equilibrium point. The no-transmission equilibrium point is unstable, and the local transmission equilibrium point is globally asymptotically stable.

[0111] From formula (15), we can see that the basic reproduction number is related to the state probability of the public opinion propagation model. Therefore, by adjusting the values ​​of each state probability in the public opinion propagation model, the basic reproduction number can be limited to (0,1), thereby suppressing the spread of public opinion and reducing the scope of public opinion propagation.

[0112] Considering the generality and universality of the public opinion propagation model, most of the research on the propagation of public opinion in social networks is based on the BA scale-free network. In order to verify the effectiveness and feasibility of the public opinion propagation model based on the reinforcement effect SCIR network proposed in this invention, as shown in Figure 1, a BA network with 1000 nodes was established to simulate the real social network, with an average degree of 7.981, an average path length of 3.233, and an average clustering coefficient of 0.029. In order to make the propagation evolution process of nodes in different states in the network reach a stable state, the number of iterations is set to 100 times.

[0113] (1) The impact of the basic reproduction number on the spread of public opinion

[0114] In order to analyze the impact of the basic reproduction number R0 on the spread of public opinion, under the premise that the total number of nodes in the network fluctuates finitely around N, that is, A = μ, simulation analysis is performed for two cases, R0 < 1 and R0 > 1. The simulation results are shown in the attached figure. Figure 3 shown.

[0115] By the attached Figure 3 It can be seen that when R0>1, after 60 hours of public opinion propagation, the network reaches a stable state, with the node density in the immune state R being about 0.5 and the node density in the propagation state I being about 0.37, indicating that public opinion propagators always exist in the network, and public opinion will continue to propagate in the network, showing a spreading trend. Figure 6 (b) It can be seen that when R0 is less than 1, there is a peak in the number of communicators. After reaching the peak, the I-state node density will show a downward trend. When the public opinion propagation reaches a stable state, the I-state node density is almost close to 0, and most nodes are in an immune state, indicating that public opinion is difficult to continue to spread in the social network. Similar to local communication, public opinion will disappear in the network.

[0116] (2) Change the intensity of intervention

[0117] In order to analyze the impact of intervention intensity α on the spread of public opinion, under the premise that other variables are the same, α = 0, 0.1, 0.3, 0.5, and 0.7 are taken respectively to apply direct immune analysis to the public opinion propagation model. The simulation results are shown in the attached figure. Figure 4 shown.

[0118] By the attached Figure 4 It can be seen that the magnitude of the intervention strength is reflected in the number of nodes in the unknown state S and immune state R at the initial state of public opinion dissemination. Among them, the magnitude of the intervention strength α is negatively correlated with the node density of the unknown state S, and positively correlated with the node density of the immune state R, that is, the greater the intervention strength α, the fewer S state users and the more R state users at the initial dissemination. At the same time, the greater the intervention strength α, the slower the speed of decrease of the node density in the S state and the speed of increase of the node density in the R state, indicating that the intervention strength α can suppress the fluctuation of the number of nodes in different states in the network and maintain the stability of the network. Figure 4 (b) It can be seen that the greater the intervention intensity α, the slower the growth rate of the hesitant state C in the process of public opinion propagation, which delays the time when the density of the hesitant state C node reaches the peak, and also reduces the corresponding peak value, reducing the proportion of hesitant people in the process of public opinion propagation. Figure 4 (c) It can be seen that the greater the intervention intensity α, the slower the growth rate of the initial propagation state I of public opinion, indicating that increasing the intervention intensity α can slow down the outbreak of public opinion in the network; at the same time, the time required for the propagation state I to reach the peak is extended, and the corresponding number of peaks is reduced. In the stable state, when the intervention intensity α = 0.7, the node density of the propagation state is reduced by 65.97% compared with that when the intervention intensity α = 0. The above situations all show that increasing the intervention intensity α can reduce the time and scope of public opinion propagation in the network, thereby effectively inhibiting the spread of public opinion.

[0119] (3) Changing the credibility of information

[0120] In order to analyze the impact of information credibility β on the spread of public opinion, under the premise that other variables are the same, β = 0, 0.1, 0.3, 0.5, 0.7 is used to apply direct immune analysis to the propagation model. The simulation results are shown in the attached Figure 5 shown.

[0121] By the attached Figure 5It can be seen that as the information credibility β increases, the peak value of the node density in the hesitant state C decreases significantly. When the information credibility β = 0.7, the node density in the hesitant state C decreases by 49.23% compared with when β = 0. This shows that increasing the information credibility β can reduce the number of hesitants in the network and further reduce the conversion of nodes to the propagation state I, thereby inhibiting the spread of public opinion. Figure 5 (c) It can be seen that with the increase of information credibility β, the peak value of node density in propagation state I decreases significantly. When information credibility β = 0.7, the node density in propagation state I decreases by 38.74% compared with β = 0, indicating that increasing information credibility β can reduce the node density in propagation state I and inhibit the further spread of public opinion. Figure 5 (d) It can be seen that as the information credibility β increases, the growth rate of the immune state R node density also accelerates. At the same time, in the stable state, the number of immune state nodes also increases, indicating that increasing the information credibility β can reduce the scope of public opinion dissemination.

[0122] (4) Change the intensity of intervention

[0123] In order to analyze the impact of intervention time T on the spread of public opinion, under the premise that other variables remain the same, direct immune analysis is applied to the propagation model at time nodes T=3, 10, 20, 30, and 40 respectively. The simulation results are shown in the attached figure. Figure 6 shown.

[0124] By the attached Figure 6 It can be seen that before direct immunity is applied, the node density of hesitant state C reaches a peak at T=9, and when direct immunity is applied at T=3, the propagation of hesitant state C is blocked, so that the peak value corresponding to hesitant C at the intervention time T=3 is much smaller than the peak value when direct immunity is not applied, thereby effectively reducing the number of hesitant states turning into propagation states and inhibiting the spread of public opinion. Figure 6 (c) It can be seen that when direct immunity is introduced at T=3, the peak value of the node density of the corresponding propagation state I is 45.82% lower than that of other states, which effectively suppresses the spread of public opinion; when direct immunity is introduced at T=10, the node density of the corresponding propagation state I is just at the peak value of the theoretical case without direct immunity. At this time, after direct immunity is applied, the node density of propagation state I drops sharply, suppressing the large-scale spread of public opinion; when the intervention time is T=20, 30, 40, it also has an inhibitory effect on the spread of public opinion, but the intensity of the effect decreases successively. Figure 6 (d) It can be seen that the earlier the intervention time, the earlier the node density of the immune state R enters a stable state, the shorter the propagation time of public opinion, and the worse the propagation effect.

[0125] (5) Comparative analysis of models

[0126] In order to analyze the different effects of the model established by the present invention on the spread of public opinion compared with other models, the public opinion spread model of the present invention directly immune to SCIR is compared with the SIR model and the SCIR model. The simulation results are shown in the attached figure. Figure 7 shown.

[0127] By the attached Figure 7 It can be seen that, since the model of the present invention takes into account the role of intervention strength, the node density of the unknown state S and the immune state R is not 0 at the beginning. In the initial stage of public opinion propagation, there is a certain proportion of immune users, which enables the unknown state S and the immune state R to enter a stable state earlier, thus reducing the time for public opinion to propagate in the network. Figure 7 (b) It can be seen that the SIR model does not consider the existence of the hesitant state C. The model of the present invention significantly reduces the peak value of the hesitant state C node density, thereby effectively reducing the number of hesitant states turning into propagation states and inhibiting the spread of public opinion. Figure 7 (c) It can be seen that the peak value of the propagation state I in the SIR model is the largest, followed by the SCIR model, with a peak value decrease of 25.74%, and the smallest is the model of the present invention, with a peak value decrease of 59.12%. At the same time, in the above three models, the time required for the propagation state I to reach the peak value also decreases successively, indicating that the SCIR model with direct immunity can significantly reduce the number of communicators and the propagation time in the network, thereby effectively inhibiting the spread of public opinion in the network.

[0128] From the above simulation results, we can see that when the basic reproduction number of the model R0>1, public opinion continues to spread in the network, showing a spreading trend; when R0<1, public opinion automatically disappears after spreading in the network for a period of time, which is similar to local transmission. Social factors can effectively control the spread of public opinion. Increasing the intervention intensity α and the credibility of information β can increase the number of users in the immune state R at the initial moment and the probability of direct immunity P SR , thereby suppressing the spread of online public opinion; the smaller the intervention time T, the earlier the emotional spread can be controlled. The research results of the present invention can provide a good reference for departments to control the spread of public opinion, actively resolve the crisis of online public opinion, and have important significance for maintaining social security and stability.

[0129] The embodiments of the present invention have better practicability and are not intended to limit the present invention in any form. The technical features or combinations of technical features described in the embodiments of the present invention should not be considered isolated, and they can be combined with each other to achieve better technical effects. The scope of the preferred embodiments of the present invention may also include other implementations, and this should be understood by those skilled in the art of the invention embodiments.

Claims

1. A method for constructing a public opinion propagation model directly immune to SCIR, characterized in that: include: Obtain the real-time number of online users in the social network based on the new addition rate and offline rate; The new addition rate is the percentage of the number of new online users in the social network at a certain moment to the total number of users, denoted by A, where the new addition rate only applies to susceptible users S; the offline rate is the ratio of the number of offline users in the social network at a certain moment to the total number of users, denoted by μ, where the offline rate applies to users in all states in the network; Therefore, the number of real-time online users in the social network is: |1+A-μ|N(t)=S(t)+C(t)+I(t)+R(t) (1) Where S(t) is the unknown state, C(t) is the hesitant state, I(t) is the propagation state, R(t) is the immune state, and N is the number of nodes in the network; Taking into account the intervention strength of the department, the credibility of the real information and the intervention time of the department, the direct immunity rate is obtained; the direct immunity rate P SR for: Among them, α represents the intervention strength of the department, that is, the density of nodes in the immune state R at the initial moment of adopting the immune strategy, α∈[0,1]; β represents the credibility of the real information, β∈[0,1]; T represents the intervention time of the department; Represents the interference of noise, which is proportional to the intervention strength α and inversely proportional to the credibility of information β; A public opinion propagation model directly immune to SCIR is established; the public opinion propagation model directly immune to SCIR is: Among them, P SC P represents the probability of being exposed to public opinion but not deciding whether to spread it, that is, the internal contact rate; CI represents the probability of being exposed to public opinion and spreading it, that is, the indirect forwarding probability; P CR represents the probability that the hesitant state does not spread and turns into the immune state, that is, the indirect immunity rate; P IR It represents the probability that the communicator does not believe the public opinion for some reason and thus becomes immune, that is, the forwarding immunity rate; it satisfies 0≤P SC ,P CI ,P CR ,P IR ≤1; S k , C k ,I k , R k Indicates the state of the node at the kth iteration; The stability of the public opinion propagation model immune to SCIR is analyzed as follows: Let the left side of equation (3) be zero, and I k =0, k=1,2,···,n, the public opinion propagation model is in a non-propagation equilibrium state, and there is a non-propagation equilibrium point at this time: When I>0, the local propagation equilibrium point of the public opinion propagation model is E * =(S * ,E * ,R * )in, Due to S k (t)+C k (t)+I k (t)+R k (t) = 1, then equation (3) is simplified to Divide the x,y vectors, make The emergence rate of new communicators is: The individual migration rate is Then there is, right Find the Jacobian matrix, The basic reproduction number is: in, represents the spectral radius of the matrix; The basic reproduction number of the public opinion propagation model is: Substituting the propagation-free equilibrium point E0 in equation (4), we obtain: If R0≤1, it means that the maximum number of people that a communicator can infect during the average infectious period is less than 1, and the transmission point will gradually disappear. At this time, the public opinion propagation model only has a non-propagation equilibrium point, which is globally asymptotically stable. If R0>1, it means that the maximum number of people that a communicator can infect during the average infection period is greater than 1, that is, the transmission point always exists and forms local transmission; at this time, the public opinion propagation model has a local transmission equilibrium point in addition to the no-transmission equilibrium point. The no-transmission equilibrium point is unstable, and the local transmission equilibrium point is globally asymptotically stable.

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