key: cord-0817979-aav3zdc4
authors: Chen, Tinggui; Peng, Lijuan; Yang, Jianjun; Cong, Guodong
title: Modeling, simulation, and case analysis of COVID‐19 over network public opinion formation with individual internal factors and external information characteristics
date: 2021-01-23
journal: Concurr Comput
DOI: 10.1002/cpe.6201
sha: 1acb3e72d1fa38c33c68e396f07d9a3f0b5cc59c
doc_id: 817979
cord_uid: aav3zdc4

With the development of information technology, the Internet has become an important channel of public opinion for expressing public interests, emotion, and ideas. Public emergency usually spreads via network. Due to the temporal and spatial flexibility and the information amplification of network, the opinions from different regions and background are easy to be represented as network public opinion, and have important impact on social and economic life. Thus, studying the formation mechanism of network public opinion has important theoretical and practical significance. Taking the formation process of network public opinion under emergencies as the research object, this paper first identifies the key factors influencing the formation of network public opinion, namely the internal characteristics (include individual education level, individual stubbornness, individual initial opinion, and so on) and external information of individuals (include external information intensity). Second, information intensity is introduced to describe the influence of external information feature on the formation of network public opinion. Individual education level, individual stubbornness, and individual initial opinion are analyzed to describe the influence of individual internal factors on the formation, and then its model is constructed. Through the simulation experiments, this paper analyzes the influence of external information intensity, individual education level, individual stubbornness, individual initial opinion, and other factors on the formation of network public opinion. The simulation results show that: (1) the greater intensity of public emergency reporting causes the easier formation of network public opinion; (2) the higher individual education level leads to the shorter time for completing the final formation and stable state of online public opinions, and after the formation of online public opinions, the opinion of the event is mainly neutral; (3) the greater individual's stubbornness makes the shorter formation time of online public opinion. When online public opinion reaches a stable state, the neutral opinion group dominates and firmly controls the development trend of public opinion; (4) the difference of opinions among individuals is the most important factor affecting the formation of network public opinion. Finally, the rationality and validity of the proposed model are verified by a real case. Compared with previous studies on the formation mechanism of network public opinion, this paper divides the formation process of network public opinion into three stages: individual information perception, individual decision making, and individual opinion transmission. Meanwhile, the influence of individual internal factors and external information characteristics on the formation process of network public opinion is also considered.

relationship between individuals but also considers the formation cycle of network public opinion formation. More importantly, it is analyzed by combining qualitative and quantitative methods.

The structure of this paper is as follows: Section 2 is literature review; Section 3 divides the formation process of network public opinion into three stages: individual information perception, individual decision making, and individual opinion communication. Also, the factors affecting each stage are quantitatively described, so as to build a network public opinion formation model. Section 4 discusses the influence of some key factors on the formation of public opinion through simulation experiment; Section 5 verifies the model proposed in this paper with practical cases. Section 6 is the summary of the whole paper and the prospect of the future work.

At The dynamics were driven by repeated small-group discussions; within each group, a local majority rule was applied to update the opinions of agents.

Iterating the dynamics leads toward one of two opposite attractors at which every agent shares the same opinion. While odd-sized groups yield a threshold at 50%, even-sized groups, which allow the inclusion of doubt in the case of an opinion tie, produce a threshold shift toward either one of the two attractors, giving rise to minority opinion spreading. Hong and Liu 14 studied the characteristics of public sentiment on mobile Internet represented by mobile phones varied in each period of the whole life cycle. The supervision department was supposed to pay close attention to dynamic participation of public sentiment from mobile terminations like mobile phone in order to grasp the law of public sentiment development.

In order to explore the main body of the online public opinion formation stage, Dong 15 At present, most of the studies on the formation of public opinion belong to the procedure stream, and the representative literature is as follows:

Chen et al 19 combined external information and individual characteristics to study the impact on public opinion reversal. Xu 20 described network of public opinion formation from four aspects: formation of network issues, formation of the public opinion field, formation on the axis, and formation of three-dimensional communication. Based on the life cycle theory, Liu and Tian 21 analyzed the formation path of network public opinion, and discussed its formation mechanism. After that, they analyzed the evolution mechanisms of network public opinion, including the evolution direction mechanism of topics and mutation mechanism of network public opinion. Xiang and Xu 22 conducted in-depth analysis on the evolution factors, life cycle and propagation effects of network public opinion of mass events, which was an important premise for the effective guidance of network public opinion and efficient response to mass events. Public events, Internet users and mass media were the basic evolution elements of public opinion of mass events. The life cycle of network public opinion of mass events includes formation period, diffusion period, fluctuation period and dissipation period, and each stage has its own unique communication logic. Combined with the gray statistic method and Analytic Hierarchy Process (AHP) analysis method, Liang and Ju 23 made researches on each stage of network public opinion evolution period with the risk index system, and made analysis and calculation on each risk index weight coefficient.

From the above three types of literature, for the study of formation of network public opinion although there are from the public opinion formation model and system dynamics, the dynamic equation of evolution is analyzed, 24, 25 individual internal factors and external information to influence public opinion are rarely considered. Especially, the information intensities of these factors and individual education level have important effect on network public opinion formation. In addition, in the process of exploring the formation of network public opinion, few researches subdivide it into individual information perception, individual decision making, individual opinion communication and other stages, and discuss the influence of individual internal factors and external information on different stages. 26, 27 Based on this, this paper divides the formation process of network public opinion into the above three stages, considers the influence of individual internal factors and external information characteristics, constructs a network public opinion formation model, and then explores the action mechanism of different factors in the formation process through experimental simulation.

This Tables 1 and 2 .

In order to quantitatively describe the network public opinion formation process, there will be individual views with attitude value in the interval, 1 

Campbell and Key 28 pointed out that a major influence of education on viewpoints lies in the fact that education carries various influences of a person throughout life. With the continuous expansion of educational experience, a person is more likely to be exposed to the discussion of issues during his growth, and these educational conditions will have a certain influence on the direction of public opinion, meaning the education level of an individual has an important influence on the initial formation of individual views. The RAS model discusses the dynamic change process and development trend of an individual's own views under the influence of external information, and describes the evolution process of views as: an individual may perceive or miss an external view, and may adopt or ignore the perceived views. By referring to the probability formula of information being perceived by individuals in the evolution rules of RAS model and integrating with individual education level to study their perception degree of other people's information, the probability formula of individual information perception 7 is expressed as follows:

F I G U R E 1 Network public opinion formation process The existing tendency of an individual's initial opinion

The number of individuals holding the ith opinion at time t where Inf represents the information intensity of an event, that is, the intensity of media reports after the event occurs. a 1 represents the understanding degree of the individual to the perceived information. l represents the minimum perceived ability of an individual. W c represents the view coefficient of an individual, indicating the individual's understanding of the information related content. According to individual information perception stage, individual education level will have an effect on whether to read others' views, and the different levels of education will form the subjective viewpoint, which can form a minimum perception of each individual l, meaning minimum awareness l and education level W a are lineally related: l = k 1 ×W a , including k 1 as correlation coefficient in the range of (0,1). The probability of individual information perception can be represented by the formula (2).

where different education levels are divided into different categories from 1 to 10 levels. The higher level indicates the higher individual's education level, the stronger individual's ability to receive the opinions of others, and the higher probability that the individual perceives the opinions of others.

The RI represents intensity of relationship between individual education level and P r , which is set in the range of (0,+∞). Inf is the information intensity of an event, similar to the intercept of standard regression, and is defined in the range of (0,1).

In the RAS model, individuals may adopt or ignore others' views, that is, there are different selection strategies. Assume that a new information has been perceived by an individual, according to Equation (1), the probability of an individual adopting the idea of this information decreases with the increase of W c . The probability that an individual adopts others' views is P a , which is represented by formula (3). 7 The probability of individuals' attitude change when they perceive a piece of information and change their own views is expressed by Formula (4). 7

where the parameter b 0 describes the difficulty or reliability of information, b 1 indicates the influence coefficient between inherent thought and the probability that individuals adopt others' views. b 2 indicates the influence coefficient between individual's perception and the probability that individuals adopt others' views. P i indicates the tendency of individuals to adopt information, which depends on the degree of information awareness.

It can be seen from the RAS model that whether an individual adopts others' views and changes his/her own views is in the individual decision-making stage, which is divided into two sub-stages. The first is whether an individual chooses to adopt the views, and the second is whether an individual changes his/her own views after adopting the others' views.

When an individual perceives the information of others, the existing tendency of the individual, namely the degree of individual stubbornness, will have an influence on the choice of his strategy. According to the theory of "Spontaneous Symmetric Deviation", 29 once a persuasive opinion can be understood and quickly adopted by an individual, the individual's opinion will skew, and within a certain period of time, conform to the same opinion as his original one. Therefore, it can be seen that the attitude difference between individuals will affect the decision-making process of individuals, and the attitude difference between individuals exists in three situations as shown in Table 3 . Setting W i and W j (i, j = 1, 2, 3, i≠j, i and j respectively to represent the three groups of people with positive, negative and neutral views) as individual attitude values from the two groups of views. When the information of other party is perceived, the probability of individuals adopting the opinions of the other party is related to the attitude difference between them, that is, the greater attitude difference between two different types of individuals represents the smaller probability of the other party's opinions being adopted.

According to Table 3 

where x represents the credibility of the information after the individual perceives the information of others, whose range is within interval (0,1).

The more credible an individual perceives the information of others, the more likely it is to be accepted. Y represents the negative effect of individual education level on the probability of individual opinion adoption. L a represents the existing tendency of an individual's initial opinion, and its positive and negative values depend on whether the individual's initial opinion and the perceived opinion of others are of the same type. In other words, if the initial attitude value is both positive, it is of the same type. If it is the same attitude value, the value of L a is positive, whereas the value of L a is negative. Referring to the value obtained by Torgerson 30 through questionnaire and test theory, the value range of L a is set at [−5,5]. The parameter z represents the degree of individual stubbornness and is within the range of (0,1).

Since the individual views are divided into three classes, attitude difference also has three conditions after individuals with different viewpoints perceive others view. From formula (5), there are several conditions whether individuals with different viewpoints to accept others views, as shown in Table 4 . P aij (i,j = 1,2,3,i ≠ j, the initial view is the ith opinion, after perceiving the jth opinion information, the probability of its idea being adopted) 1 2 P a12 represents individuals whose initial view is positive, perceiving individual information with a negative opinion, the probability of a negative opinion being adopted 1 3 P a13 represents individuals whose initial view is positive, perceiving individual information with a neutral opinion, the probability of a neutral opinion being adopted 2 1 P a21 represents individuals whose initial view is negative, perceiving individual information with a positive opinion, the probability of a positive opinion being adopted 2 3 P a23 represents individuals whose initial view is negative, perceiving individual information with a neutral opinion, the probability of a neutral opinion being adopted 3 1 P a31 represents individuals whose initial view is neutral, perceiving individual information with a positive opinion, the probability of a positive opinion being adopted 3 2 P a32 represents individuals whose initial view is negative, perceiving individual information with a negative opinion, the probability of a negative opinion being adopted Note: P a12 = P a21 , P a13 = P a31 , P a23 = P a32 .

From formula (4), the probability of acceptance of the message and a henceforth change of attitude is equal to the product P rob = P r (W i ; a 0 ,a 1 )*P a

. When individuals adopt others' views to a certain probability, the probability of individual idea change also has three conditions, namely P rob12= P rob21 , P rob13= P rob31 , P rob23 = P rob32 .

After the occurrence of public emergencies, individuals with positive, negative and neutral views will change their attitude values after adopting others' views, and further interact with others, thus spreading the information. When the communication stage of individual viewpoints reaches a stable state within a certain period of time, the network public opinion forms. The Lotka-Volterra model adopted by Lan 3 in the process of information spread is used to model the interactive process of viewpoints. At the initial moment, not all individuals in the network participate in the discussion of public emergencies, but with the spread of information, more and more individuals participate in the process of view interaction. However, cyberspace does not allow unlimited individual expression, that is, the number of individuals that can accommodate different views should have limit, so the spread of public opinion stage in essence is the individuals with positive, negative, and neutral viewpoints competing for limited cyberspace resources (as shown in Figure 2 ). It is similar to the evolution mechanism in ecological science theory that species compete for limited resources: when the number of each type of species in a certain time period remains the same (balance), the individuals achieve the optimal state of competition in cyberspace. Based on the Lotka-Volterra model of population competition in ecological science, the interaction process between individuals is studied through differential equations, and the communication of three different viewpoints is described.

Individuals' views at time t may change, and the number of people with positive, negative and neutral views at time t is set as X 1 (t), X 2 (t), X 3 (t), that is, the groups with different views form a competitive relationship. Set the competition coefficient of three kinds of people as (The coefficient of competition between individuals with positive and negative views), (The coefficient of competition between individuals with negative and neutral views), and (The coefficient of competition between individuals with positive and neutral views). According to the analysis process of the individual decision-making stage, the probabilities of attitude change of three views are P rob12 , P rob13 , P rob23 , whose meanings are the same as the competition F I G U R E 2 Communication process of individuals views coefficient. Therefore, setting = P rob12 , = P rob13 , = P rob23 . r 1 , r 2 , and r 3 represent the growth rates corresponding to individuals with positive, negative and neutral views respectively, and their values are set within the range of (0,1). K 1 , K 2 , and K 3 represent the upper limit of the number of individuals holding three different viewpoints respectively, which is determined according to the number of netizens in the existing network. The number of three types of individuals at initial time (t = 0) is X 10 , X 20 , and X 30 , respectively.

When there are individuals with only one single view (no competition relations), the number of individuals holding the ith opinion at time t is

, as shown in below 10 :

After a sudden incident, three types of individuals holding different viewpoints coexist in the Internet space. Therefore, it is necessary to expand the single viewpoint competition model based on formula (6) to analyze the problem of mixture. There are three kinds of conditions: first, the "residual" space of individuals holding positive viewpoints changes, from (1-

, so the number of individuals holding positive viewpoints is

; second, the number of individuals holding negative viewpoints is

; third, the number of individuals holding neutral viewpoints is

The initial numbers are X 10 , X 20 , X 30 respectively. By integrating the above three equations, the number of individuals with different views can be obtained as follows:

In the stage of individual opinion communication, when the number of individuals with positive, negative, and neutral opinions reaches a stable state within a certain period of time, it indicates that network public opinion has formed. In order to clearly know the formation time of network public opinion and the main advantages of which views are in the stable state, it is necessary to discuss the stability of the equation set (7), and the time of reaching the stable state. In general, the stability problem is discussed by solving analytic solutions of differential equations. However, the differential equation proposed in practical problems is often very complex, so it is impossible to find the exact analytic solution. We need to judge its stability from the zero solution of the differential equation. The relevant definitions are discussed below: Definition 1. The differential equation without explicit independent variable t at the right end of the equation is called autonomous equation, as shown in Equation (8):

If the real root x = x 0 , then x = x 0 is called as the equilibrium point of the differential Equation (8).

After the equilibrium point of differential equation is obtained, it is necessary to judge the stability of the equilibrium point in order to analyze whether the equilibrium point will remain stable and unchanged in the following period of time. The following two methods for judging the stability of equilibrium point are introduced: one is the indirect method; the other is the direct method.

Starting from any value of some neighborhood of x 0 , the solution x(t) lim t→∞ x (t) = x 0 in the differential Equation (8) can be satisfied, then x 0 is stable, otherwise it is unstable.

If f(x) is expanded at x 0 and only one term is taken, the differential Equation (8) can be approximately expressed as:

Equation (9) is the approximate linear equation of Equation (8), and x 0 is the equilibrium point of Equation (9), and the general solution of Equation (9) is:

Since lim x (t)

, the stability of the equilibrium point of differential Equation (9) can be concluded as follows:

1. If f ′ (x) < 0, x 0 is the stable balance point of Equations (8) and (10);

x 0 is the unstable balance point of Equations (8) and (10).

As Equation set (7) is an autonomous equation, the stable state of individual viewpoint communication cannot be determined by analytic solutions, but only by solving the equilibrium point and analyzing the stability of the equilibrium point. Based on this, it is necessary to first find the equilibrium point of the equation set (7), and then use the equation set (7) to describe the trend of the numerical solutions of X 1 (t), X 2 (t), and X 3 (t), so as to find the stable value of X 1 (t), X 2 (t), and X 3 (t) over time. Finally, it judges whether the equilibrium point satisfies the stability condition. If so, the equilibrium point is stable, that is, the value of the stable state is equal to the equilibrium point value, and this equilibrium point is also the for- To facilitate the solution of the dynamic differential equation, the equation set (7) is rewritten into the difference equation form as follows:

where 

Seven non-zero equilibrium points can be obtained from the above Equation (12), which is represented by P i (X, Y, Z). The specific value is shown in Equation (13):

After solving the equations of equilibrium, because direct method needs to illustrate the stability state of the equations by the stability of the analytical solutions, the indirect method is adopted to determine the stability of the equilibrium point, that is: if the balance P i (X,Y,Z) meet lim

is called as stable equilibrium. And the balance at this moment is the time for forming network public opinion.

In addition, in reality, the ecosystem equilibrium conditions in the Volterra model must be satisfied, that is, X 1 (t), X 2 (t), and X 3 (t) in the equilibrium point must all be greater than zero to have practical significance. According to the above indirect method and the premise of X 1 (t) > 0, X 2 (t) > 0, and X 3 (t) > 0, the conditions for the seven equilibria to reach a stable state are solved, as shown below:

1. If the equilibrium point P 1 reaches a stable state, it shall meet > 1, > 1.

2. If the equilibrium point P 2 reaches a stable state, it shall meet > 1, > 1.

3. If the equilibrium point P 3 reaches a stable state, it shall meet > 1, > 1.

4. If the equilibrium point P 4 reaches a stable state, it shall meet 0 < < 1, 1 + < + .

5. If the equilibrium point P 5 reaches a stable state, it shall meet 1+ < + , 0< <1.

6. If the equilibrium point P 6 reaches a stable state, it shall meet 0 < < 1, 1 + < + .

7. If the equilibrium point P 7 reaches a stable state, it shall meet

Based on the above analysis, the sufficient conditions for reaching the stable state of individual viewpoint communication stage are obtained, and the relationship between the competition coefficient and the individual viewpoint decision probability is defined in the model hypothesis as = P rob12 , = P rob13 , = P rob23 . Generally speaking, the decision probability of individual opinions ranges from [0,1], so the prerequisite for the competition coefficient between the three opinions is , , ∈[0,1]. Among the seven equilibrium points obtained above, only P 7 satisfies this condition, so the following simulation part only discusses P 7 . According to the value of P 7 , when the network public opinion is formed and reaches a stable state, individuals with positive, negative, and neutral views coexist in the network, and there is no situation that the number of individuals with a certain type of views completely disappears.

This section discusses the influence of external information intensity, individual education level, individual stubbornness, and individual initial opinions on the formation process of network public opinion, so as to reveal its internal evolutionary mechanism. In addition, the initial attitude value of the individual was set to be within the range of [−1,1] and to follow the normal distribution of N ∼ (0,0.03876). The sum of the three individuals with positive, negative, and neutral views at the initial time is N = 500. In the individual information perception stage, the relationship strength RI between education level and information perception probability P r is set as 1. In addition, the correlation coefficient k 1 of minimum information perception ability and education level was set as 0.1. Only the interaction of two different categories of views is considered, that is, the views of each two categories of individuals are different. For example, if the individuals with a positive view and the individuals with a negative view interact, the existing tendency of the initial views of these two types of individuals is different, one is positive, the other is negative. In this paper, it is defined that the existing tendency of the initial views of the same class is positive, and the existing tendency of the initial views of different classes is negative. The interaction of two different types of initial views is discussed, so the existing tendency of the initial views of the local individuals is negative. Based on literature, 4 the value range of L a is [−5,5], the initial viewpoint tends to be negative, the value range of L a is [5, 0) . In the initial state, the value of L a only has minor influence on the result of the final public opinion formation with its initial set value as 2. The perceived confidence level x = 0.1, the negative function of individual education level for the adoption probability of the individual viewpoint is y = 0.1. Set K 1 = 6000, K 2 = 4000, K 3 = 10,000, to ensure that the group with neutral viewpoints accounts for the majority. While reflecting opinion distribution in the real world, the most initial viewpoint is neutral and only a small group of people holding extreme viewpoints. In addition, other parameters are set as follows: r 1 = 0.5, r 2 = 0.8, r 3 = 1. It should be noted that in this section, in addition to Section 4.4, which discusses the influence of individual opinion differences on the formation process of network public opinion, Sections 4.1-4.3 fix the difference between the three types of attitudes, and make W 12 = W 23 = W 13 = 0.6081 according to the range of the three types of attitudes. In the simulation results, X 1 (t), X 2 (t), and X 3 (t) (X 1 , X 2 , and X 3 mentioned below are equal to X 1 (t), X 2 (t), and X 3 (t)) respectively represent the number of individuals with positive, negative, and neutral views.

The equilibrium point P 7 described above reached a stable state under the conditions of {0 < , , < 1; 1 + > + ; 1 + > + ; 1 + > + }, the competitive coefficients of, and satisfy the conditions {0 < , , < 1; 1 + > + ; 1 + > + ; 1 + > + } indicates that P 7 is in a stable state, and the value of its equilibrium point is consistent with that of X 1 (t), X 2 (t), and X 3 (t). Based on this, the value of equilibrium P 7 is used to represent the stable state of network public opinion formation in the following content of this paper. The simulation results show that the higher information intensity promises the higher individual information perception probability under the same education level. With the improvement of individual education level, the probability of individual information perception is also higher. In real life, generally speaking, the higher an individual's education level is, the broader his mental state and vision are, the easier he is to accept others' opinions, the more willing he is to listen to others' opinions and opinions, and the more comprehensive he is in his view. On the contrary, the less educated an individual is, the more closed his mind is, the less he communicates with others, and the more extreme and biased his views on events are. Therefore, with the increase of information intensity, the number of people holding positive, negative and neutral opinions decreases when network public opinions are formed, and the time required for the final formation of network public opinions also decreases accordingly. 

In the stages of individual information perception and individual decision making, the change of individual education level will affect the probability of individual opinion change, that is to say, changing competition results among individuals with positive, negative, and neutral views. Also, the change of competition process will affect the formation time of network public opinion and the number of individuals with three views. Based on this, this section discusses the influence of W a of different individual education levels on the formation process of public opinion, and sets the value of Inf of information intensity as 0.1. The simulation results are shown in Figures 7-9 .

It can be seen from Figure 7 that the higher an individual's education level is, the greater the probability of information perception is, showing an "S-shaped" increase. It can be seen from Figure 8 that the probability of an individual adopting the views of others decreases with the increase of individual education level, and the overall trend of monotony decreases. As can be seen from Figure 9 , the greater level of individual education makes the probability of individual opinion first increase and then decrease. In other words, if the education level of an individual is at a low level, the more likely an individual is to change his or her viewpoint. If the education level of an individual is at a high level, the probability of his or her viewpoint changing gradually decreases, and he or she will not change own viewpoint easily. According to the relationship between the competition coefficient and the individual opinion change probability in the above model hypothesis in Section 3.3.1, it can be seen that = P rob12 , = P rob13 , = P rob23 , the individual opinion change probability will affect the competition coefficient among the three types of individuals. Therefore, the following simulation is conducted for the variation trend of the number of individuals with different opinions, and the results are shown in Figures 10-12 .

In Figures 10-12 From the above simulation, it can be seen that the higher the individual education level is, the longer the formation time of online public opinion will be, and the more individuals with positive, negative and neutral opinions will be formed when public opinion is formed. 

Due to significant differences in personality characteristics, behavioral intention and other aspects, different individuals will have different degrees of acceptance for new matters, new information, and new ideas. Therefore, individual stubbornness will have an impact on the formation of network public opinion. By simulation experiment, the impact of different individual stubbornness z (z ∈ [0.1, 0.9]) on network public opinion formation process is discussed with the setting for the initial state of Inf is 0.1, W a is 1.

When the individual's stubbornness changes, it will have an impact on the probability that the individual adopts others' opinions and the probability that the individual's opinions change. The following part analyzes the influence of individual stubbornness on individual decision-making stage by simulating individual's adoption probability of others' opinions. Assumes that the initial condition of information intensity Inf is 0.1, the individual education level W a is defined as 1. When the value of individual stubbornness is in the range of [0.1,0.9], the values of individual viewpoint changing probability will change, but individual viewpoint changing probability will influence the competition between the individual coefficient, so that the individual views tend to be stable. In addition, the views held by three types of individuals are defined as positive, negative and neutral respectively, and the probability of change of individual views is also divided into three types, including the transformation between positive and negative views, the transformation between negative and neutral views, and the transformation between positive and neutral views. Based on this, the three cases are discussed respectively, and the simulation results are shown in Figures 13-15 . When the individual stubbornness is 0.1, X 1 , X 2 , and X 3 reach the equilibrium point P 7 (4874, 3249, 8123). Among them, the number of individuals with positive, negative and neutral views gradually tends to be stable after t = 18, 40 and 30 respectively, and shows a monotonously increasing trend. With the increase of individual stubbornness from 0.1 to 0.9, the number of individuals from three viewpoints X 1 , X 2 , and X 3 increases to P 7 (4928, 3286, 8214). The time for individuals with positive views to reach a stable state changed from t = 18 to t = 33, that is, the duration for the number of individuals with positive and neutral views to reach a stable state is longer, while the duration for the number of individuals with negative views to reach a stable state is shorter. To sum up, with the increase of individual stubbornness, it takes longer time for network to form public opinion, and more people take part in discussion when it reaches a stable state, that is, more and more individuals participate in the process of viewpoint interaction and gradually form network public opinion.

If the differences of opinions between individuals are too large, people may not participate in the communication, and there will be no fierce collision of various opinions. Instead, they will only have scattered discussions, which cannot form online public opinions. This shows that initial opinion In addition, from the model hypothesis, competition coefficient and the relationship between the individual opinion change probability, it shows: = P rob12 , = P rob13 , = P rob23 , and individual opinion change probability will influence coefficient of three kinds of competitions. Therefore, the The simultaneous changes of W 12 , W 13 , W 23 will affect the individual's competition coefficient. The simulation results of the corresponding network public opinion formation process is shown in Figure 22 : the blue shaded part represents the change of X 3 when ∈ [minP rob12 , maxP rob12 ]. The red shaded part represents the change of X 1 when ∈ [minP rob13 , maxP rob13 ]. The green shaded part represents the change of X 2 when ∈ [minP rob23 , maxP rob23 ]. It can be seen from the figure that the blue shaded part is much larger than the other two types, indicating that when three types of individuals compete with each other, the number of individuals holding a neutral view changes greatly. That is because the individuals holding a neutral F I G U R E 22 The influence of simultaneous changes of , , on the trend of X 1 (t)), X 2 (t), and X 3 (t)

view are more likely to be influenced by other individuals' views, thus making their own views biased. When the initial viewpoint difference of the three types of individuals all takes the minimum value, the number tends to be P 7 (4913, 3276, 8041). Among them, the number of positive, negative, and neutral individuals gradually tends to be stable after t = 37, 30, and 26 respectively, and generally increases monotonically. When the initial opinion difference among the three types of individuals gradually increases to the maximum value, the number tends to be P 7 (5094, 3421, 8306), that is, when the network public opinion forms and reaches a stable state, the number of people participating in the discussion of public emergencies increases, and the time required for the formation of network public opinion also increases.

When W 13 gradually increased from minimum to maximum value, and W 23 , W 12 values were fixed at 0.6081 ( changed from small to large), trends of three kinds are shown in the simulation results in Figure 23 (A-C): the difference between green shaded area and blue shaded area represents the impact of on the formation of public opinion. If the difference is large, the change of will have large impact. As shown in Figure 23 

In this section, in order to verify the network public opinion formation model to open the sight spots before the epidemic was stabilized. Some netizens think the tourism industry will return to normal sooner or later, and it is better to resume business as soon as possible. Later, on April 4, Huangshan scenic area was crowded and closed operation immediately, which was blamed and doubted by public. Within 1 month, network public opinion was formed, forcing the government to issue subsequent policies so as to make up the deficiency. Figure 26 .

In this paper, the data after processing were analyzed, the comments from 10:00 February 19 to 0:00 February 23 were ranked according to time order, and the change trend of three types of individuals was formed, as shown in Figure 27 .

As can be seen from Figure It can be seen from the comparison between Figures 27 and 28 that, although there is a slight difference between them, the change trend of online public opinion formation process is basically the same on the whole, and when it reaches a stable state, the proportion of positive, negative and neutral individuals is basically the same.

In addition, the Lotka-Volterra model mentioned in literature 4 was used to simulate the public opinion evolution process of the "Open Scenic Spot Policy" during COVID, and the results are shown in Figure 29 .

From Figure 27 , the formation of network public opinion trend in literature 4 is not consistent with the actual reality, network public opinion formation process model in Figure 29 speeds up sharply and then slows down. This is because the competition coefficient in literature 4 takes high value, and the competition coefficient in the model cannot adjust according to the stages of network public opinion formation, so the model proposed in literature 4 cannot fully reflect the true formation process of network public opinion. Therefore, the model established in this paper is more reasonable to simulate the formation process of network public opinion. 2. The higher an individual's education level is, the higher his/her perception probability of information will be, and the probability of changing an individual's opinion will first increase and then decrease, thus shortening the time for the final formation of online public opinion and reaching a stable state. In addition, the number of individuals with positive, negative, and neutral opinions will increase in the network.

3. When the degree of individual stubbornness decreases, the probability of individual opinion change will increase. It will take longer time for network public opinion to finally form and reach a stable state. The number of individuals holding neutral opinions is greater than the number of individuals holding positive and negative opinions.

4. The competition coefficient between positive and negative opinions has the greatest influence on the formation of online public opinion, while the attitude difference between negative and neutral opinions has minor influence on the formation of online public opinion.

Compared with the influence of information intensity, individual education level and individual stubbornness on the formation of online public opinion, the attitude differences among individuals with different views have the greatest influence on the formation and stable state of online public opinion. The larger difference in opinions among individuals encourage more netizens to participate in the discussion of the event, and it takes longer time for the online public opinion to form and reach a stable state.

There are still some deficiencies in this paper:

1. The undiscussed issues in this paper, such as psychological change of Internet users, 32,33 the leading role of the media, 34, 35 and the mood of opinion leaders, 36, 37 will all affect the formation of network public opinion, but they are difficult to be quantified. Therefore, future work needs to be further integrated into the model, and studies the effect of three factors on the network public opinion formation.

2. In the simulation analysis, the influence of relevant parameters on the formation of network public opinion is highly discussed from the macro-level. 38, 39 Consequently, the discussion on the interaction mechanism of the formation of network public opinion from the micro-perspective is very limited. 40 Therefore, it is necessary to discuss various interaction mechanisms in the formation of network public opinion.

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The authors declare that they have no competing interests.

https://orcid.org/0000-0001-6061-2517