Evolutionary Game Analysis of Collaborative Prevention and Control for Public Health Emergencies

Abstract

In the context of the COVID-19 pandemic, strengthening collaborative prevention and control of public health emergencies has become an important element of social governance. In the process of collaborative prevention and control of public health emergencies, there is a complex game relationship among government agencies, the Internet media and the general public. In order to explore the evolution process of participants’ behavioral strategies, a trilateral evolutionary game model is constructed, and a system dynamics approach is further adopted to simulate the heterogeneous effect of different initial strategies and epidemic spread probability on the evolution of strategies. The results show that the tripartite equilibrium strategies are (0,0,0), (1,1,1), and (0,1,1) during the early stage, outbreak stage, and resumption stage of COVID-19, respectively. Then, taking the resumption stage as an example, the system strategy will eventually stabilize at the equilibrium point (0,1,1) when the initial probabilities of these three subjects are all equal to 0.2, 0.5 or 0.8. When the initial probability of Internet media is set to be 0.2, the public’s strategies converge faster than government agencies. As the initial probability of Internet media increases to 0.5 or 0.8, the convergence time of government agencies will be shortened from 40 weeks to 29 weeks or 18 weeks, whereas the opposite is true for the general publicWhen the epidemic spread probability $p_2=0.5$, government agencies reach the equilibrium strategy after 20 weeks. As $p_2$ increases to 0.7 and 0.9, the convergence time of government agencies becomes 27 weeks and 31 weeks, and the Internet media and the general public will converge more quickly toward the stable strategy. This paper links the theoretical study with the realistic prevention and control of COVID-19 to provide decision-making support and policy recommendations for the scientific prevention, and contributes to the sustainable development of society.

1. Introduction

The novel coronavirus (COVID-19), which broke out at the end of 2019, spread rapidly around the world in a remarkable form of human-to-human transmission, posing a serious threat to global public health. Under the leadership of the government, the prevention and control of the COVID-19 epidemic has achieved outstanding results. With the weekly deaths from COVID-19 down to the lowest since March 2020, the head of WHO said on 14 September 2022, that the end of the pandemic is now in sight. However, during the pandemic, as a result of the continuous mutation of the virus, its transmission speed and infectiveness are rapidly increasing. Currently, it is found that a single person infected with the Omicron virus may infect an average of 9.5 people without any protection, and the virus cannot be easily detected [1]. There is no doubt that epidemic prevention and control around the world are facing greater challenges, and, therefore, related strategies require further attention and investigation.

In COVID-19 prevention and control, government guidance and supervision play a critical role, but the actual effectiveness of the governance also depends on the implementation by the public. During the pandemic, it can be found that there are still some people who do not follow the epidemic-related regulations, such as wearing a mask when in public places, which to some extent adds difficulties to the epidemic governance. Furthermore, between the government and the public, Internet media also plays an important role in the transmission of the epidemic-related information and regulations. Internet media is a double-edged sword, which means that positive online comments can help enhance the effectiveness of prevention and control policies, whereas negative online comments may reduce it. In this context, the paper aims to study the collaborative prevention and control of public health emergencies among the government, Internet media, and the public.

In the existing literature regarding public health emergencies, the epidemic transmission, and epidemic prevention and control were widely studied. Several simulation models were introduced to study the problems. Taking H1N1 as an example, evolutionary game theory was used to build the epidemic situation diffusion function, in order to forecast the peak value under different evolutionary scenarios [2]. Moreover, in the literature, epidemic logistics models [3] and SEIR models [4,5,6] were applied to study the transmission and diffusion mechanisms of public health emergencies. Focusing on epidemic prevention and control, the existing literature mainly studied the effects of government intervention mechanisms, media perceptions of role, and public behavioral responses. Firstly, from the perspective of government intervention, Chinazzi et al. [7] indicated that travel restrictions on residents could contain the outbreak. The importance of government interventions was demonstrated by Wessel [8] and Mandal et al. [9]. Then, Jiao et al. [10] and Hallewell et al. [11] pointed out that strict isolation policies by the government can effectively contain the spread of infectious diseases. Huang et al. [12] believed that strengthening the emergency management performance assessment of relevant government departments is conducive to improving the emergency management efficiency of the public health emergency management system. Secondly, from the perspective of media perception of the role, during the emergency response and recovery stages of public health emergencies, social media could not only quickly convey official policies and event progress, but also served as a reference for leadership decision-making [13]. Hagen et al. [14] studied how social media can be used in crisis communication during public health emergencies. Thirdly, from the perspective of public behavioral responses, Sega et al. [15] argued that the public levels of risk perception had an important effect on the evolution of the epidemic. Klaczkowski et al. [16] investigated the effect of social distancing driven by individual’s risk attitudes on epidemics, and found that voluntarily enforcing social distancing can effectively contain the outbreak. Some scholars also believed that maintaining social distancing [17,18] and consciously wearing masks [19,20] can effectively reduce the spread of the epidemic. Overall, aiming at the prevention and control of public health emergencies, the above studies mainly focused on strategies from the perspective of only one single subject, such as the government, the media, or the public, but pays less attention to collaborative prevention and control of public health emergencies among them.

Based on utility maximization theory, the evolutionary game model is introduced in this paper, in order to study the collaborative prevention and control problem and to obtain the optimal strategies for the subjects. In fact, under the assumption of boundedly rational, the behavioral evolutionary process of participants has been widely applied in the fields of computer science [21], electronic equipment recycling management [22], engineering safety [23] and supply demand analysis [24]. Moreover, in a series of studies on public health emergencies, evolutionary game theory was also used to study the decision-making process of participants. Fan et al. [25] combined evolutionary game theory with system dynamics to analyze the interactions of behavioral strategies of the government, communities, and residents, and introduced a dynamic reward–penalty mechanism, which proved to be effective in suppressing the fluctuations in the evolutionary game process. Xiao et al. [26] applied a regional evolutionary game model to study the collaborative governance of multiple regions in public health emergencies. Xu et al. [27] analyzed the effects of the different factors on the decision-making of participants for public health emergencies by using a tripartite evolutionary game model, involving the local government, enterprises, and the public. Jia et al. [28] used the stochastic evolutionary game model to explore the public’s epidemic prevention and control strategies in an uncertain environment. Yuan et al. [29] studied the influencing factors of medical supply distribution in public health emergencies by constructing a two-sided game model between government-owned nonprofit organizations and hospitals. Liu et al. [30] explored the interaction and influence mechanisms among government rescue teams, social emergency organizations, and government support institutions based on a tripartite evolutionary game model. Therefore, according to the existing literature, there were few systematic analyses of response strategies among various subjects, and most of the research explored the effects of behavioral evolution strategies among the central government, local governments, enterprises, and the public. However, there is no quantitative analysis regarding the interactions between government agencies, the Internet media, and the general public.

Different from the above-mentioned studies, this paper aims to examine the collaborative prevention and control of public health emergencies among the government, Internet media, and the public, and to explore the evolution process of participants’ behavioral strategies. Taking COVID-19 as an example, the research shows that there are significant differences in the tripartite equilibrium strategies during the early stage, outbreak stage and resumption stage of epidemic. Based on the evolutionary game theory, a trilateral evolutionary game model for collaborative prevention and control is constructed, and the evolutionary paths of three stages of the epidemic are simulated. In our context, the government agencies are mainly responsible for making policies and supervising the behaviors of Internet media and the public through a reward–penalty mechanism, then the government’s optional strategies are set to be “strong supervision” and “weak supervision”. Additionally, the Internet media, as the main promoters and information guiders of online public opinion, are supposed to convey the government’s policies and suppress negative public sentiment. However, the Internet media can also choose to pursue maximum utility by promoting public opinion. Then, the optional strategies for Internet media are “promoting” and “no promoting”. As for the public, they need to strictly follow the prevention and control policies and voluntarily self-isolate if needed. Therefore, the public’s optional strategies are set to be “voluntary isolation” and “free flowing”. Therefore, government agencies, Internet media, and the general public, as important subjects, play crucial roles in the collaborative prevention and control of the epidemic. How the strategies and mechanisms for epidemic prevention and control evolve is a topic worthy of in-depth study.

Moreover, a system dynamics approach is further adopted to simulate the heterogeneous effects of stochastic factors on the evolutionary of strategies. Changes in initial strategy probabilities of the game subjects are found not to affect the equilibrium results of the system, but to affect the convergence speed. Additionally, the higher the initial willingness of government agencies to supervise, the shorter the time for the Internet media and the general public to reach a steady state. However, when the initial willingness of the Internet media to promote the online public opinion is higher, the faster the public will converge to a stable state, and the slower government agencies will converge to a stable state. Furthermore, for these three game subjects, changes in the probabilities of epidemic spread are found to have the greatest impact on the evolution of government agency strategies.

Our analysis contributes to the literature on epidemic prevention and control. Different from the existing literature, the study considers the collaborative prevention and control among government agencies, the Internet media, and the general public, and emphasizes the important role played by the Internet media. Our second contribution is to introduce the evolutionary game theory to obtain the tripartite equilibrium strategies of the subjects. Moreover, the heterogeneous effects of stochastic factors on the evolutionary results are further studied, which sed light on the underlying evolutionary mechanisms. Our results provide decision-making support and policy recommendations for scientific and quantitative prevention and control of epidemics.

This study is arranged as follows. In Section 2, a trilateral evolutionary game model is constructed, and the evolutionary paths of three stages of the epidemic development are simulated. In Section 3, a system dynamics approach is further adopted to simulate the heterogeneous effect of stochastic factors on the evolutionary of strategies. In Section 4, conclusions and recommendations are summarized.

2. Model Construction

In the process of collaborative prevention and control for public health emergencies, there is a complex game relationship among government agencies, the Internet media and the general public. Therefore, in this section, a trilateral evolutionary game model is constructed with government agencies, the Internet media and the general public as the game subjects. Additionally, the replicator dynamics equation is applied to obtain the stable equilibrium point of the game subjects. Finally, the evolutionary paths of the early stage, the outbreak stage, and the resumption stage of the epidemic’s development are simulated by MATLAB.

As a convenience, it is assumed that government agencies, the Internet media, and the general public will all be involved in the process of COVID-19 epidemic prevention and control.

(1) Government agencies. Government agencies include both the central government and local governments, which are the primary leaders in the process of epidemic prevention and control. Several prevention and control policies have been issued by the government in order to effectively contain the outbreak, and reward–penalty mechanisms have also been developed to restrain the decision-making behavior of the general public and the Internet media.

(2) The Internet media. The Internet media refer to the emerging online media and social network platforms that disseminate various types of information through the Internet. The Internet media are the main promoters and information guiders of online public opinion, and their decisions are aimed at maximizing their own profits.

(3) The general public. People who live in an affected area are defined as the general public. On the basis of ensuring their own lives and health, the general public make decisions with the goal of minimizing their own losses.

2.1. Model Assumption

To objectively analyze the decision-making behavior and interactions among government agencies, the Internet media, and the general public in the process of epidemic prevention and control, the following assumptions are introduced:

Hypothesis 1 (H1).

The game subjects, including government agencies, the Internet media, and the general public, are all bounded rationality.

Hypothesis 2 (H2).

There are two main strategies for government agencies to adopt in order to contain the outbreak. One is to take the most comprehensive, rigorous and thorough measures (referred to as “strong supervision”) for enterprises, the media, and the public, and so on. It means that, in medium-risk or high-risk regions of the epidemic, government agencies will make every possible effort to curb the spread of the disease by implementing closed-loop management, shutting down production, a nationwide nucleic acid test, reward–penalty mechanisms, and other mandatory measures. The probability of government agencies applying strong supervision is denoted by$x$($0\le x\le 1$). The other is to relax regulatory policies for enterprises, the media, and the public (called “weak supervision”), which means that in low-risk regions, government agencies relax regulatory policies to minimize the impact of epidemic prevention and control measures on production and normal life and to maximize overall coordination epidemic prevention and control with economic development. The probability of weak supervision is set to be$1-x$.

Hypothesis 3 (H3).

For the Internet media, there are two strategies for preventing and controlling epidemic. Firstly, online public opinion regarding the epidemic is not promoted by the Internet media (called “no promoting”), which implies that the Internet media have given full play to the role of information dissemination, policy publicity, and public opinion supervision, as well as appeasing and channeling public sentiment by timely reporting the COVID-19 situation, conveying relevant government policies, etc. The probability is denoted by$y$($0\le y\le 1$). Secondly, online public opinion on major epidemics is promoted by the Internet media (called “promoting”), which refers to the fact that government policies and related information about COVID-19 are not reported in a timely manner. Furthermore, the epidemic is also used to generate revenue from topics of online rumors. The probability of this case is set to be$1-y$.

Hypothesis 4 (H4).

There are two strategies that can be chosen by the general public in the process of epidemic prevention and control. One is to voluntarily enforce social distancing with others (called “voluntary isolation”). It refers to how the public actively collaborate with government agencies by initiatively reporting health conditions, and voluntarily self-isolating. The probability of this strategy is set to be$z$($0\le z\le 1$). The other is to go outside as one pleases by public transport (called “free flowing”). In other words, confirmed cases, asymptomatic patients, suspected cases, close contacts and the public from medium-risk or high-risk regions ignore laws and regulations for epidemic prevention and control, and take public transport such as buses and subways to move freely. This results in the spread of outbreak. The probability of this strategy is denoted by $1-z$.

Hypothesis 5 (H5).

During the process of epidemic prevention and control, the costs of government agencies adopting the “strong supervision” strategy are denoted as$c$. Under this strategy, reward measures of$a_1$are given to the Internet media who choose the “no promoting” strategy, and punishment measures of$b_1$are given to the Internet media who choose the “promoting” strategy and cause social panic. In addition, reward measures of$a_2$are given to the public who choose the “voluntary isolation” strategy, and administrative punishment measures of$b_2$are imposed on the public who choose the “free flowing” strategy and cause the spread of the epidemic. The spread probability is denoted as$p_1$, and the corresponding socio-economic losses are denoted as$w$, then the expected socio-economic losses is$p_{1}w$. Moreover, if government agencies adopt the “weak supervision” strategy and the public prefer the “free flowing” strategy, the large-scale spread probability is set to be$p_2$($p_2>p_1$), and the expected socio-economic losses is$p_{2}w$. At the same time, the government must also bear trust losses of the public, which are$h_1$.

Hypothesis 6 (H6).

When the “no promoting” strategy is chosen by the Internet media, the costs of manpower and material resources are$d$; at the same time, it confers additional public trust profits to the government, which are set to be$r$. When the “promoting” strategy is chosen, revenues from the topic of online rumors are denoted as$e$. However, the Internet media must bear trust losses of the public, which are$h_2$.

Hypothesis 7 (H7).

When the general public choose the “voluntary isolation” strategy, if the Internet media fail to push online public opinion regarding the epidemic, then a personal loss caused by social isolation is denoted as$f_1$; if the Internet media prefer to push public opinion about the epidemic, the public will panic and the demand for supplies will increase, resulting in a surge in price. At this time, the personal loss will increase to$f_2$($f_2>f_1$). When the general public choose the “free flowing” strategy, because of the negative externality of the large-scale spread of the epidemic, the public have to bear their share of the socio-economic losses, that is,$p_{1}w/n$or$p_{2}w/n$. The population of the affected area is denoted by$n$.

To simplify the description of the methodology approach, a flowchart is shown in Figure 1. The symbols of the relevant parameters are shown in

Table 1. The symbols of the relevant parameters.

Symbol	Definition
$x$	the probability of government agencies choosing the “strong supervision” strategy
$y$	the probability of the Internet media choosing the “no promoting” strategy
$z$	the probability of the general public choosing the “voluntary isolation” strategy
$c$	costs of government agencies choosing the “strong supervision” strategy
$a_1$	reward measures for the Internet media choosing the “no promoting” strategy
$b_1$	punishment measures for the Internet media choosing the “promoting” strategy
$a_2$	reward measures for the public choosing the “voluntary isolation” strategy
$b_2$	punishment measures for the public choosing the “voluntary isolation” strategy
$p_1$	the spread probability when government choose strong supervision and the public is free to flow
$p_2$	the large-scale spread probability when government choose weak supervision strategy and the public is free to flow
$w$	socio-economic losses when the public is free to flow
$h_1$	trust losses of public in government choosing the “weak supervision” strategy
$d$	costs of the Internet media choosing the “no promoting” strategy
$r$	additional public trust profits to the government when media choosing the “no promoting” strategy
$e$	revenues of the Internet media choosing the “no promoting” strategy
$h_2$	trust losses of public in Internet media choosing the “no promoting” strategy
$f_1$	personal loss caused by social isolation when Internet media choose the “no promoting” strategy
$f_2$	personal loss caused by social isolation when Internet media choose the “promoting” strategy
$n$	the population of the affected area

.

2.2. Construction of a Tripartite Game Model

Based on the above assumptions, the strategy combination and payoff matrix of the tripartite evolutionary game among government agencies, the Internet media, and the general public are obtained, as shown in

Table 2. Payoff matrix of the game subjects.

Game Subjects		General Public
Government Agencies	Internet Media	Voluntary Isolation ($\mathit{z}$)	Free Flowing $\mathbf{(}\mathbf{1}\mathbf{-}\mathit{z}$)
strong supervision ($x$)	no promoting ($y$)	$-c-a_1-a_2+r$ $-d+a_1$ $-f_1+a_2$	$-c-a_1+b_2-p_{1}w$ $-d+a_1$ $-b_2-p_{1}w/n$
	promoting $(1-y$)	$-c+b_1-a_2$ $-d+e-h_2-b_1$ $-f_2+a_2$	$-c+b_1+b_2-p_{1}w$ $-d+e-b_1$ $-b_2-p_{1}w/n$
weak supervision $(1-x$)	no promoting ($y$)	$-h_1+r$ $-d$ $-f_1$	$-p_{2}w$ $-d$ $-p_{2}w/n$
	promoting $(1-y$)	$-h_1$ $-d+e-h_2$ $-f_2$	$-p_{2}w$ $-d+e$ $-p_{2}w/n$

.

2.2.1. Evolutionary Path Analysis of Government Agencies

According to the game payoff matrix in Table 2, the expected payoff of government agencies under different strategies is calculated, and then the replicator dynamics equation of the evolutionary game can be obtained. Let $E_{x_1}$ be the expected payoff when government agencies adopt the “strong supervision” strategy, and the formula is as follows:

$$\begin{array}{cc}\hfill E_{x_1}& =yz(-c-a_1-a_2+r)+y(1-z)(-c-a_1+b_2-p_{1}w)\hfill \\ & +z(1-y)(-c+b_1-a_2)+(1-y)(1-z)(-c+b_1+b_2-p_{1}w)\hfill \\ & =yzr-y{a}_1-y{b}_1-z{a}_2-z{b}_2+z{p}_{1}w-c+b_1+b_2-p_{1}w\hfill \end{array}$$

(1)

The expected payoff of “weak supervision” strategy for government agencies is $E_{x_2}$:

$$\begin{array}{cc}\hfill E_{x_2}& =yz(-h_1+r)+y(1-z)(-p_{2}w)+z(1-y)(-h_1)\hfill \\ & +(1-y)(1-z)(-p_{2}w)\hfill \\ & =yzr-z{h}_1+z{p}_{2}w-p_{2}w\hfill \end{array}$$

(2)

The average expected payoff of government decision-making behavior is ${\overline{E}}_x$:

$${\overline{E}}_x=x{E}_{x_1}+(1-x)E_{x_2}$$

(3)

Therefore, substituting into Equations (1)–(3), the replicator dynamics equation for government agencies to choose the “strong supervision” strategy can be obtained as follows:

$$\begin{array}{l}F(x)=\frac{dx}{dt}=x(E_{X_1}-{\overline{E}}_X) =x(1-x)(-y{a}_1-y{b}_1-z{a}_2-z{b}_2\\ +z{p}_{1}w-c+b_1+b_2-p_{1}w+z{h}_1-z{p}_{2}w+p_{2}w)\end{array}$$

(4)

From stability theorems of the replicator dynamics equation, we know that:

(1) When $z=z^{*}=\frac{p_{1}w-p_{2}w+c-b_1-b_2+y{a}_1+y{b}_1}{p_{1}w-p_{2}w-a_2-b_2+h_1}$, we obtain $F(x)\equiv 0$. Therefore, the game is in a stable state regardless of the value of $x$; that is, the strategy choice of government agencies does not change over time.

(2) When $z\ne \frac{p_{1}w-p_{2}w+c-b_1-b_2+y{a}_1+y{b}_1}{p_{1}w-p_{2}w-a_2-b_2+h_1}$, let $F(x)=0$, we obtain $x=0$ or $x=1$, and the game is in a stable state. Firstly, we calculate the derivative of $F(x)$:

$$\begin{array}{l}{F}^{\prime }(x)=(1-2x)(-y{a}_1-y{b}_1-z{a}_2-z{b}_2+z{p}_{1}w-c\\ +b_1+b_2-p_{1}w+z{h}_1-z{p}_{2}w+p_{2}w)\end{array}$$

(5)

Then, based on Equation (5), the following two cases are discussed:

(i) When $0<z<\frac{p_{1}w-p_{2}w+c-b_1-b_2+y{a}_1+y{b}_1}{p_{1}w-p_{2}w-a_2-b_2+h_1}$, $F^{\prime }(x)|{}_{x=1}>0$, $F^{\prime }(x)|{}_{x=0}<0$, at this time, $x=0$ is the stable equilibrium point in the evolution of government behavior; that is, it is stable for government agencies to choose “weak supervision” strategy in the process of epidemic prevention and control.

(ii) When $\frac{p_{1}w-p_{2}w+c-b_1-b_2+y{a}_1+y{b}_1}{p_{1}w-p_{2}w-a_2-b_2+h_1}<z<1$, $F^{\prime }(x)|{}_{x=1}<0$, $F^{\prime }(x)|{}_{x=0}>0$, at this time, $x=1$ is the stable equilibrium point in the evolution of government behavior; that is, it is stable for government agencies to choose the “strong supervision” strategy in the process of epidemic prevention and control.

According to the above analysis, the above conclusions are expressed in the three-dimensional coordinate system, and the dynamic evolution trend of the government behavior is obtained, as shown in Figure 2.

2.2.2. Evolutionary Path Analysis of the Internet Media

According to the game payoff matrix in Table 2, the expected payoff of the Internet media under different strategies is calculated, and then the replicator dynamics equation of the evolutionary game can be obtained. Let $E_{y_1}$ be the expected payoff when the Internet media adopt the “no promoting” strategy, and the formula is as follows:

$$\begin{array}{ll}{E}_{y_1}& =xz(-d+a_1)+x(1-z)(-d+a_1)+z(1-x)(-d)+(1-x)(1-z)(-d)\hfill \\ & =a_{1}x-d\hfill \end{array}$$

(6)

The expected payoff of the “promoting” strategy is $E_{y_2}$:

$$\begin{array}{ll}{E}_{y_2}& =xz(-d+e-h_2-b_1)+x(1-z)(-d+e-b_1)+\hfill \\ & \hspace{1em}z(1-x) (-d+e-h_2)+(1-x)(1-z)(e-d)\hfill \\ & =e-d-x{b}_1-z{h}_2\hfill \end{array}$$

(7)

The average expected payoff is ${\overline{E}}_y$:

$${\overline{E}}_y=y{E}_{y_1}+(1-y)E_{y_2}$$

(8)

Therefore, substituting into Equations (6)–(8), the replicator dynamics equation for the Internet media to choose the “no promoting” strategy can be obtained as follows:

$$F(y)=\frac{dy}{dt}=y(E_{y_1}-{\overline{E}}_y) =y(1-y)(x{a}_1+x{b}_1+z{h}_2-e)$$

(9)

According to Equation (9), we have:

(1) When $x=x^{*}=\frac{e-z{h}_2}{a_1+b_1}$, we obtain $F(y)\equiv 0$. Therefore, the game is in a stable state regardless of the value of $y$, that is, the strategy choice of the Internet media does not change over time.

(2) When $x\ne \frac{e-z{h}_2}{a_1+b_1}$, let $F(y)=0$, we obtain $y=0$ or $y=1$, and the game is in a stable state. We obtain the derivative of $F(y)$:

$$F^{\prime }(y)=(1-2y)(x{a}_1+x{b}_1+z{h}_2-e)$$

(10)

Based on Equation (10), two cases are discussed as follows:

(i) When $0<x<\frac{e-z{h}_2}{a_1+b_1}$, $F^{\prime }(y)|{}_{y=1}>0$, $F^{\prime }(y)|{}_{y=0}<0$, at this time, $y=0$ is the stable equilibrium point in the evolution of the Internet media behavior, that is, it is stable for the Internet media to adopt “promoting” strategy in the process of epidemic prevention and control.

(ii) When $\frac{e-z{h}_2}{a_1+b_1}<x<1$, $F^{\prime }(y)|{}_{y=1}<0$, $F^{\prime }(y)|{}_{y=0}>0$, at this time, $y=1$ is the stable equilibrium point in the evolution, that is, it is stable for the Internet media to choose a “no promoting” strategy in the process of epidemic prevention and control.

According to the above analysis, the above conclusions are expressed in the three-dimensional coordinate system, and the dynamic evolution trend of the Internet media behavior is obtained, as shown in Figure 3.

2.2.3. Evolutionary Path Analysis of the General Public

Similarly, let $E_{z_1}$ be the expected payoff when the general public adopt “voluntary isolation” strategy, let $E_{z_2}$ be the expected payoff when the general public choose the “free flowing” strategy, and ${\overline{E}}_z$ denotes the average expected payoff. The formulas are as follows:

$$\begin{array}{ll}{E}_{z_1}& =xy(-f_1+a_2)+x(1-y)(-f_2+a_2)+y(1-x)(-f_1)+(1-x)(1-y)(-f_2)\hfill \\ & =a_{2}x+y{f}_2-y{f}_1-f_2\hfill \end{array}$$

(11)

$$\begin{array}{ll}{E}_{z_2}& =xy(-b_2-p_{1}w/n)+x(1-y)(-b_2-p_{1}w/n)+ y(1-x) (-p_{2}w/n)+(1-x)(1-y) (-p_{2}w/n)\hfill \\ & =x(p_{2}w/n-p_{1}w/n-b_2)-p_{2}w/n\hfill \end{array}$$

(12)

$${\overline{E}}_z=z{E}_{z_1}+(1-z)E_{z_2}$$

(13)

Therefore, substituting into Equations (11)–(13), the replicator dynamics equation for the general public can be obtained as follows:

$$F(z)=\frac{dz}{dt}=z(E_{z_1}-{\overline{E}}_z)=z(1-z)\left[y{f}_2-y{f}_1+x(p_{2}w/n-p_{1}w/n+a_2-b_2)-f_2+p_{2}w/n\right]$$

(14)

According to Equation (14), we have:

(1) When $y=y^{*}=\frac{f_2-p_{2}w/n-x(p_{2}w/n-p_{1}w/n+a_2-b_2)}{f_2-f_1}$, $F(z)\equiv 0$. Therefore, the game is in a stable state regardless of the value of $z$, that is, the strategy choice of the general public does not change over time.

(2) When $y\ne \frac{f_2-p_{2}w/n-x(p_{2}w/n-p_{1}w/n+a_2-b_2)}{f_2-f_1}$, let $F(z)=0$, we obtain $z=0$ or $z=1$, and the game is in a stable state. We obtain the derivative of $F(z)$:

$$F^{\prime }(z)=(1-2z) \left[y{f}_2-y{f}_1+x(p_{2}w/n-p_{1}w/n+a_2-b_2)-f_2+p_{2}w/n\right]$$

(15)

Then, based on Equation (15), two following cases are discussed:

(i) When $0<y<\frac{f_2-p_{2}w/n-x(p_{2}w/n-p_{1}w/n+a_2-b_2)}{f_2-f_1}$, $F^{\prime }(z)|{}_{z=1}>0$, $F^{\prime }(z)|{}_{z=0}<0$, at this time, $z=0$ is the stable equilibrium point in the evolution of the general public behavior, that is, it is stable for the general public to adopt “free flowing” strategy in the process of epidemic prevention and control.

(ii) When $\frac{f_2-p_{2}w/n-x(p_{2}w/n-p_{1}w/n+a_2-b_2)}{f_2-f_1}<y<1$, $F^{\prime }(z)|{}_{z=1}<0$, $F^{\prime }(z)|{}_{z=0}>0$, at this time, $z=1$ is the stable equilibrium point in the evolution, that is, it is stable for the general public to choose “voluntary isolation” strategy in the process of epidemic prevention and control.

According to the above analysis, the above conclusions are expressed in the three-dimensional coordinate system, and the dynamic evolution trend of the general public’s behavior is obtained, as shown in Figure 4.

2.3. Stability Analysis of Model

Based on the above analysis, the three-dimensional dynamic system of the evolutionary game is obtained as follows:

$$\{\begin{array}{l}F(x)=x(1-x)(-y{a}_1-y{b}_1-z{a}_2-z{b}_2 +z{p}_{1}w-c +b_1+b_2-p_{1}w+z{h}_1-z{p}_{2}w+p_{2}w)\\ F(y)=y(1-y)(x{a}_1+x{b}_1+z{h}_2-e)\\ F(z)=z(1-z) [y{f}_2-y{f}_1+x(p_{2}w/n-p_{1}w/n+a_2-b_2) -f_2+p_{2}w/n]\end{array}$$

(16)

Let $F(x)=F(y)=F(z)=0$; there are eight local equilibrium points of this evolutionary system: (0,0,0), (0,0,1), (0,1,0), (1,0,0), (1,1,0), (1,0,1), (0,1,1), (1,1,1). According to the idea proposed by Friedman [31], the stability of each equilibrium point can be analyzed by using eigenvalues of the Jacobian matrix. If the eigenvalues of an equilibrium point are all negative numbers, the equilibrium point is the evolutionary stable strategy (ESS). The Jacobian matrix of this system is as follows:

$$J=\left[\begin{array}{ccc}\frac{\partial F(x)}{\partial x}& \frac{\partial F(x)}{\partial y}& \frac{\partial F(x)}{\partial z}\\ \frac{\partial F(y)}{\partial x}& \frac{\partial F(y)}{\partial y}& \frac{\partial F(y)}{\partial z}\\ \frac{\partial F(z)}{\partial x}& \frac{\partial F(z)}{\partial y}& \frac{\partial F(z)}{\partial z}\end{array}\right]=\left[\begin{array}{ccc}(1-2x)A& x(1-x)(-a_1-b_1)& x(1-x)(p_{1}w-p_{2}w+h_1-a_2-b_2)\\ y(1-y)(a_1+b_1)& (1-2y)(x{a}_1+x{b}_1+z{h}_2-e)& y{h}_2(1-y)\\ z(1-z)(p_{2}w/n-p_{1}w/n+a_2-b_2)& z(1-z)(f_2-f_1)& (1-2z)B\end{array}\right]$$

(17)

which is $A=-y{a}_1-y{b}_1-z{a}_2-z{b}_2 +z{p}_{1}w-c+b_1+b_2-p_{1}w+z{h}_1-z{p}_{2}w+p_{2}w$, $B=y{f}_2-y{f}_1+x(p_{2}w/n-p_{1}w/n+a_2-b_2)-f_2+p_{2}w/n$.

From Equation (17), the eigenvalues are obtained corresponding to each equilibrium point in the evolutionary system, and then the stability is analyzed, as shown in

Table 3. Eigenvalues of the Jacobian matrix for equilibrium points.

Equilibrium Points	Eigenvalues
	${\mathit{\lambda }}_1$	${\mathit{\lambda }}_2$	${\mathit{\lambda }}_3$
(0,0,0)	$-(c-b_1-b_2+p_{1}w-p_{2}w)$	$-e$	$p_{2}w/n-f_2$
(0,0,1)	$-(a_2+c-b_1-h_1)$	$h_2-e$	$-(p_{2}w/n-f_2)$
(0,1,0)	$-(a_1+c-b_2+p_{1}w-p_{2}w)$	$e$	$p_{2}w/n-f_1$
(1,0,0)	$c-b_1-b_2+p_{1}w-p_{2}w$	$a_1+b_1-e$	$2p_{2}w/n-p_{1}w/n+a_2-b_2-f_2$
(1,1,0)	$a_1+c-b_2+p_{1}w-p_{2}w$	$-(a_1+b_1-e)$	$2p_{2}w/n-p_{1}w/n+a_2-b_2-f_1$
(1,0,1)	$a_2+c-b_1-h_1$	$a_1+b_1-e+h_2$	$-(2p_{2}w/n-p_{1}w/n+a_2-b_2-f_2)$
(0,1,1)	$-(a_1+a_2+c-h_1)$	$-(h_2-e)$	$-(p_{2}w/n-f_1)$
(1,1,1)	$a_1+a_2+c-h_1$	$-(a_1+b_1-e+h_2)$	$-(2p_{2}w/n-p_{1}w/n+a_2-b_2-f_1)$

and

Table 4. Stability analysis of equilibrium points.

Equilibrium Points	Stability Conditions
(0,0,0)	$c>b_1+b_2$$, f_2>p_{2}w/n$
(0,0,1)	$a_2+c>b_1+h_1$$, e>h_2$$, p_{2}w/n>f_2$
(0,1,0)	unstable point
(1,0,0)	$b_1+b_2>c$$, e-b_1>a_1$$,-2p_{2}w/n+b_2>-f_2+a_2-p_{1}w/n$
(1,1,0)	$b_2>a_1+c$$, a_1>e-b_1$$,-2p_{2}w/n+b_2>-f_1+a_2-p_{1}w/n$
(1,0,1)	$b_1+h_1>a_2+c$$, e-b_1>a_1+h_2$$,-f_2+a_2-p_{1}w/n>-2p_{2}w/n+b_2$
(0,1,1)	$a_1+a_2+c>h_1$$, h_2>e$$, p_{2}w/n>f_1$
(1,1,1)	$h_1>a_1+a_2+c$$, a_1+h_2>e-b_1$$,-f_1+a_2-p_{1}w/n>-2p_{2}w/n+b_2$

.

From the stability conditions in Table 4, it is evident that the difference between profits and costs determines the choice of three subjects. Considering the uncertainty of COVID-19, game subjects have different decision-making behaviors at different stages of the epidemic’s development. Therefore, we divide the development process of COVID-19 into three stages [32]: the early stage of the epidemic, the outbreak stage, and the resumption stage, and analyze the stability of equilibrium points at each stage.

(1) The early stage of the epidemic. At this time, COVID-19 is a new unknown virus, and there are few confirmed cases and deaths. Considering the needs of economic development, government agencies tend to choose the “weak supervision” strategy. To maximize their own interests, the Internet media prefer the “promoting” strategy to obtain revenues from hot topics regarding the epidemic. The “free flowing” strategy is adopted since the general public have limited knowledge about the epidemic and less awareness of prevention. Therefore, this stage corresponds to the equilibrium point (0,0,0). From Table 4, to achieve the equilibrium point (0,0,0) as a stable point, two conditions are supposed to be satisfied: (i) $c>b_1+b_2$, that is, if the costs of strong supervision by the government are greater than their profits, then the “weak supervision” strategy is preferred by government agencies; (ii) $f_2>p_{2}w/n$, that is, if personal loss from the “voluntary isolation” strategy exceeds the socio-economic losses of the “free flowing” strategy, then the “free flowing” strategy is chosen by the general public. The system evolution path is shown in Figure 5.

(2) The outbreak stage of the epidemic. At this time, the epidemic is widespread. Due to the high infection rate and widespread impact of COVID-19, the number of confirmed cases and deaths increases rapidly at this time. In order to effectively contain the outbreak, government agencies tend to switch from a “weak supervision” strategy to a “strong supervision” strategy. Under the influence of gradually strengthening supervision by government agencies, the Internet media prefer the “no promoting” strategy for their own profits. To protect themselves and avoid the punishment from government agencies, the public will choose the “voluntary isolation” strategy. Therefore, this stage corresponds to the equilibrium point (1,1,1). Table 4 shows that to achieve the equilibrium point (1,1,1) as a stable point, three conditions are supposed to be satisfied: (i) $h_1>a_1+a_2+c$, that is, if trust losses from the “weak supervision” strategy by government agencies are greater than costs of the “strong supervision” strategy, then the “strong supervision” strategy is adopted by government agencies; (ii) $a_1+h_2>e-b_1$, that is, if the payoff of the “no promoting” strategy by the Internet media exceeds the payoff of the “promoting” strategy, then the “no promoting” strategy is preferred by the Internet media; (iii) $-f_1+a_2-p_{1}w/n>b_2-2p_{2}w/n$, that is, if the payoff of the “voluntary isolation” strategy are greater than the payoff of the “free flowing” strategy, the “voluntary isolation” strategy is chosen by the general public. The system evolution path is shown in Figure 6.

(3) The resumption stage of the epidemic. Under the leadership of government agencies, a significant progress has been achieved in the prevention and control of COVID-19, and the resumption of work and production for enterprises will be orderly promoted. If government agencies continue to implement extremely strict public health control measures, it will disrupt normal life, production, and economic development. Additionally, considering the fiscal expenditure, government agencies prefer the “weak supervision” strategy. As the public become fully aware of the epidemic, it is difficult for the Internet media to benefit from topics about the epidemic, so the Internet media will adopt the “no promoting” strategy to maximize their profits. Additionally, the general public tend to apply the “voluntary isolation” strategy to promote business recovery and reduce personal loss. Therefore, this stage corresponds to the equilibrium point (0,1,1). Table 4 shows that to achieve the equilibrium point (0,1,1) as a stable point, three conditions are supposed to be satisfied: (i) $a_1+a_2+c>h$, that is, if costs of prevention and control caused by “strong supervision” are greater than trust losses from the “weak supervision” strategy, then the “weak supervision” strategy will be adopted by government agencies; (ii) $h_2>e$, that is, if trust losses caused by “no promoting” strategy by the Internet media exceed the revenues from the “promoting” strategy, then the “no promoting” strategy is chosen by the Internet media; (iii) $p_{2}w/n>f_1$, that is, if socio-economic losses of the “free flowing” strategy exceed the personal loss of the “voluntary isolation” strategy, then the “voluntary isolation” strategy will be preferred by the general public. The system evolution path is shown in Figure 7.

3. System Dynamics Model Construction and Simulation Analysis

In Section 2, the development process of COVID-19 is divided into the early stage, the outbreak stage, and the resumption stage, and the stability of equilibrium points at each stage is analyzed. However, which factors have effects on the evolutionary process of the decision-making of three subjects needs to be further analyzed. In this section, taking the resumption stage as an example, we apply a system dynamics model to further analyze the impact of the changes in initial strategies and spread the probability of the equilibrium strategies of game subjects.

3.1. System Dynamics Model

System Dynamics (SD) is a system simulation method proposed by Professor Forrester of MIT [33] in the 1950s. Based on system theory, control theory and information theory, this method studies the dynamics of complex systems and characterizes the decision-making behavior of subjects from a system perspective. In the existing literature, evolutionary game analysis is combined with system dynamics to study decision-making problems. For example, Zhu et al. [34] combined the tripartite evolutionary game with the system dynamics approach to study how the behavior strategies of government departments, restaurants, and waste disposal companies interact. For the impact of renewable portfolio standard (RPS) on the retail electricity market, Zhu et al. [35] established a system dynamics model of tripartite evolutionary game among energy regulatory authorities and two types of sales companies, analyzed the strategic interactions of stakeholders, and simulated the evolution process. According to Liu et al. [23], the long-term dynamic process of multi-player games in coal mine safety supervision was described by evolutionary game theory, and the system dynamics approach was adopted to analyze how different penalty strategies affect the game process and game equilibrium.

To systematically analyze the evolutionary trends of subjects’ strategies, VENSIM is used to build the system dynamics model for the COVID-19 collaborative prevention and control, which is based on the evolutionary game theory among government agencies, Internet media and the general public. Using the SD model, this paper conducts simulation analysis to explore their evolutionary strategies.

As shown in Figure 8, three probability variables are included, namely, “Probability of strong supervision by government agencies”, “Probability of no promoting by Internet media”, and “Probability of voluntary isolation by the general public”, as well as nine auxiliary variables and sixteen exogenous variables.

3.2. System Simulation Analysis

Taking the resumption of work and production stage as an example, we give the system simulation analysis. To achieve the evolutionary stable strategy (0,1,1) in the resumption of work and production stage, the following three conditions are supposed to be satisfied: (i) $a_1+a_2+c>h_1$, (ii) $h_2>e$, (iii) $p_{2}w/n>f_1$. Following the conditions and the existing literature [36,37], the initial values of the parameters are set as follows: $c=1$, $a_1=0.3$, $a_2=0.2$, $b_1=0.4$, $b_2=0.3$, $w=1$, $n=10$, $p_1=0.4$, $p_2=0.7$, $h_1=1.35$, $d=0.3$, $r=0.4$, $e=0.5$, $h_2=0.8$, $f_1=0.01$, $f_2=0.02$. In the simulation process, only the simulation parameters are dynamically changing, and the rest of the parameters are constants. The simulation starts at the time point 0 and ends at the time point 50, with a step size of 0.0625 per week.

3.2.1. Simulation Analysis for Initial Strategies

In this part, the effects of the distribution of initial strategies on evolutionary results are investigated. Three kinds of cases are considered: (i) $x=y=z=0.2$, (ii) $x=y=z=0.5$, (iii) $x=y=z=0.8$, and the simulation results are shown in Figure 9.

As shown in Figure 9, the strategies of government agencies, the Internet media and the general public will eventually stabilize at the equilibrium point (0,1,1) when the initial probabilities of these three subjects are all equal to 0.2, 0.5 or 0.8. The results indicate that the change of initial probabilities will not affect the final stable state of the system but will affect the time to reach it. Taking the results in Figure 9a as an example, possible explanations include: When the initial probabilities are low, the Internet media tend to trigger public sentiment to maximize profits, which will lead government agencies to strengthen corresponding supervision. Additionally, the Internet media and the general public will converge toward the “no promoting” and “voluntary isolation” strategies because of government policies. Then, as the epidemic is gradually controlled, the government’s strategies are changed to the “weak supervision” strategy due to the pressure of fiscal expenditure and the need for economic development.

It can also be found that for the Internet media and the general public, the higher the initial probability ($y$ and $z$), the shorter the time for them to reach a stable state; but for government agencies, as the initial probability increases, the time to reach a stable state will first increase and then decrease. This is mainly because of the stickiness in the policy transitions. When initial strategies of government agencies prefer “strong supervision”, it will take rather long time to change to “weak supervision” due to the time lag in the transmission and implementation between levels of government, as shown in Figure 9c.

3.2.2. Strategy Simulation of Government Agencies

According to the given initial values of parameters, the effects of initial strategies distribution for government agencies on evolutionary results are investigated. Under the condition that $y=0.5$ and $z=0.5$, $x$ is separately assumed to be 0.2, 0.5 or 0.8, and the simulation results based on the SD model are given in Figure 10.

Figure 10 shows how the strategies of all three subjects gradually converge and eventually stabilize at the equilibrium point (0,1,1). Changes in the initial strategies of government agencies will not change the final stable strategies of the Internet media and the general public, but affect the time for them to reach the stable state, which to some extent indicates that the strategies of government agencies will affect their decision-making process. Specifically, the time it takes for Internet media and the public to stabilize will be shortened as the initial probability of government agencies increases. The possible explanations are that a higher initial probability of government agencies means stronger supervision and greater reward–penalty measures for the Internet media and the public. Based on this, in order to maximize their own profits, the Internet media and the general public will converge toward the “no promoting” and the “voluntary isolation” strategy more quickly.

3.2.3. Strategy Simulation of Internet Media

In this subsection, we study the effects of the initial strategies for the Internet media on evolutionary results. Under the condition that $x=0.5$ and $z=0.5$, $y$ is separately assumed to be 0.2, 0.5 or 0.8, and the simulation results are given in Figure 11.

In Figure 11, the strategies of game subjects eventually stabilize at the equilibrium point (0,1,1). Similar to the results above, changes in the initial strategies of Internet media will not change the final stable strategies of government agencies and the general public, but will affect the time for them to reach the stable state.

When the initial strategy $y$ is set to be 0.2, which is a rather low level, the public’s strategies converge faster than government agencies. This is because, when the Internet media tend to push online rumors for profits, government agencies have to adopt the “strong supervision” strategy to curb the spread of online rumors, and to coordinate epidemic prevention and control with economic and social development; thus, government agencies are even slower to reach the “weak supervision” equilibrium strategy. On the contrary, for the general public, when the initial probability of Internet media is low, due to the influence of information asymmetry and negative sentiment, their strategies will converge toward the “voluntary isolation” strategy.

Then, as the initial probability of Internet media increases to 0.5 and 0.8, the strategies of government agencies will change to “weak supervision” based on the pressure of fiscal expenditure and the need for economic development, and it can also be found that the time for the government agencies to reach the equilibrium strategy will gradually be shortened. The general public, however, have gradually learned more about the outbreak’s dynamics due to the active reporting of epidemic-related information by the Internet media. To minimize their losses, they will converge toward the “voluntary isolation” strategy at a lower speed.

3.2.4. Effects of the Changes in Spread Probability $p_2$ on Evolutionary Results

In this part, the effects of the changes in spread probability $p_2$ on evolutionary results are studied. With other parameters unchanged, the value of the spread probability $p_2$ is separately set as 0.5, 0.7, and 0.9. The results of the simulation analysis are presented in Figure 12.

Following the results in Figure 12, when the value of $p_2$ increases, its effects on equilibrium strategies of government agencies, Internet media and the general public are heterogeneous. That is, government agencies converge more slowly toward the “weak supervision” strategy, whereas the Internet media and the general public converge more quickly toward the “no promoting” strategy and the “voluntary isolation” strategy. The possible explanations are that for government agencies, when $p_2$ is low, the pressure on government agencies to prevent and control the epidemic is relatively low, and therefore a “weak supervision” equilibrium strategy is reached more quickly. As the value of $p_2$ increases, in order to reduce social losses, the government agencies have to choose a stronger strategy to curb the spread of the epidemic; thus, it will take longer to reach the “weak supervision” equilibrium strategy. For the Internet media and the general public, as the supervision strengthens, they will converge more quickly toward the stable strategy to maximize profits.

4. Conclusions and Recommendations

The Internet media, as the main promoters and information guiders of online public opinion, plays a significant role in the process of epidemic prevention and control. However, there are many conflicts of interest among government agencies, the Internet media, and the general public. Therefore, this paper considers the Internet media as a game subject. Based on dynamic game theory, a trilateral evolutionary game model among government agencies, the Internet media and the general public is constructed to explore the sustainable collaborative prevention and control for public health emergencies. This paper links the theoretical study with the realistic prevention and control of COVID-19 to provide decision-making support and policy recommendations for scientific prevention.

4.1. Research Conclusions

In this paper, a trilateral evolutionary game model among government agencies, the Internet media and the general public is constructed, and the evolutionary stable strategies of game subjects are analyzed. Moreover, based on system dynamics theory, the impact of initial strategies and key factors on equilibrium strategies are further simulated. The main results are as follows:

(1) At the early stage, the outbreak stage, and the resumption stage of the epidemic, the tripartite equilibrium strategies of government agencies, the Internet media and the general public are significantly different. In order to maximize their own profits, the “weak supervision”, “promoting” and “free flowing” strategies will be adopted at the early stage; the “strong supervision”, “no promoting” and “voluntary isolation” strategies will be used at the outbreak stage; and the “weak supervision”, “no promoting” and “voluntary isolation” strategies will be applied at the resumption of work and production stage.

(2) Changes in initial probabilities will not affect the final stable state of the system but will affect the time to reach it. Taking the equilibrium strategies at the resumption of work and production stage as an example, on the one hand, as the initial probability of government agencies adopting the “strong supervision” strategy increases, the time for the Internet media and the general public to reach a stable state will be shortened. On the other hand, as the initial probability of Internet media adopting the “no promoting” strategy increases, government agencies converge faster to the “weak regulation” strategy, whereas the general public converge slower to the “voluntary isolation” strategy.

(3) When the epidemic spread probability $p_2$ increases, its effects on the equilibrium strategies of government agencies, the Internet media and the general public are heterogeneous. Government agencies converge more slowly toward the “weak supervision” strategy, whereas the Internet media and the general public converge more quickly toward “no promoting” and “voluntary isolation” strategies.

4.2. Research Recommendations

Our results shed light on the evolutionary stable strategies of government agencies, Internet media and the public during the pandemic. Based on the above analysis, the following recommendations for decision maker are proposed for preventing and controlling epidemics:

(1) As the leader of epidemic prevention and control, government agencies should pay attention to the interests of the public and supervise the behavior of Internet media to promote the coordinated prevention and control of multiple subjects. From the above analysis, it can be found that the equilibrium strategy of the subjects changes continuously with the evolutionary trend of epidemic, and the stable point changes sequentially from (0,0,0), to (1,1,1), and then to (0,1,1). Thus, in the process of epidemic prevention and control, the government cannot blindly adopt extreme strategies to simply force the public to isolate at home, but should dynamically adjust the prevention and control strategies to fit the characteristics of the epidemic and the truly needs of the public. According to our model, in the resumption stage, the stable point is (0,1,1), which recommends that the prevention and control rely more on the Internet media and the public at the time, and the supervision from the government should be appropriately relaxed to ensure the orderly resumption of production and human life. In addition, the public should strengthen their awareness of self-protection to avoid threats to their own health.

(2) In the process of epidemic prevention and control, the Internet media play a crucial role as a bridge between government agencies and the public. According to our results, in both outbreak stage and resumption stage of the epidemic, the equilibrium strategies for the Internet media are showed to be “no promoting”. Specifically, in the outbreak stage of the epidemic, various information about the epidemic is growing rapidly. Therefore, the Internet media should actively cooperate with the government in terms of disseminating prevention and control information, publicizing official policies, supervising online public opinion, and appeasing public sentiment, which can help the government improve the efficiency of epidemic prevention and control. As the epidemic enters the resumption stage and the equilibrium strategy for government gradually changes from “strong supervision” to “weak supervision”, the Internet media turns to play a much more important role in prevention and control. The Internet media is supposed to moderately promote online public opinion by timely disseminating information about the affected areas and the trajectories of confirmed cases to maintain the public’s high attention to the epidemic and daily protection. Moreover, according to system simulation analysis results, as the probability of Internet media’s initial strategy preference of “no promoting” increases, the speed of government policy shift to “weak supervision” will also gradually increase, thus enabling the government to better coordinate epidemic prevention and control with economic and social development.

4.3. Future Perspectives

In the future, there are more research directions to be explored. Firstly, in the process of prevention and control of public health emergencies, there can be more subjects in the game, whereas this paper mainly focuses on the trilateral game problem. In the following research, more game subjects can be introduced to explore the collaborative prevention and control mechanism for public health emergencies, such as hospitals, GNPOs, etc., to build an evolutionary game model.

Secondly, to explore further, researchers can also combine machine learning with an evolutionary game model, where the improved model can automatically update the evolutionary paths of game subjects when their strategies change.

In addition, this paper mainly studies the impact of initial strategies and key factors in the resumption stage of the epidemic rather than the whole process of the event. In fact, research on the early warning in the early stage of the epidemic is equally important. In the future, it is also worth discussing that how to achieve effective prevention and control by tracking the dynamic changes of relevant indicators in the early stage of the epidemic.