Since 2020, the COVID-19 pandemic has been spreading around the world. Especially since the outbreak in Shanghai in 2022, people's normal life and production have been greatly disrupted, so many enterprises had to press the "pause button". According to the data released by the Shanghai Municipal Statistics Bureau, in April 2022, Shanghai achieved a total foreign trade import and export volume of 219.149 billion yuan, a decrease of 36.5% year-on-year. In the first four months, Shanghai saw 1, 144 new foreign directly-invested enterprises, a decrease of 46.9% year-on-year. In April 2022, Shanghai's industrial enterprises above designated size completed the total industrial output value of 128.617 billion yuan, a 61.5% decrease year-on-year, and industrial enterprises completed export delivery value of 25.253 billion yuan, a 57.3% decrease year-on-year. Shanghai has almost achieved half of its economic goal only. On April 29${}^{\mathrm{t}\mathrm{h}}$, 2022, the Political Bureau of the CPC Central Committee held a meeting to emphasize that "the pandemic should be prevented, the economy should be stabilized, and the development should be safe", which is an important decision-making deployment and a clear requirement made by the Party Central Committee with Comrade Xi Jinping as the core at the critical moment to coordinate the two overall situations at home and abroad and the two major events of development and security. On May 25${}^{\mathrm{t}\mathrm{h}}$, 2022, the State Council held a national teleconference on stabilizing the economic market, and made deployment arrangements for stabilizing the national economic market, In this connection, it is important for market entities to press the "pause button" to rapidly resume production. In terms of the resumption of work and production after the outbreak of the COVID-19 pandemic, many researchers and all sectors of society have taken active actions, achieving a series of research results on the resumption of work and production after the pandemic, and put forward many constructive countermeasures and suggestions. Zhuang, et al. clearly pointed out that pandemic prevention and control and the resumption of work should be paid equal attention to^[1]. In terms of bank funds to support the resumption of work and production, Ma focused on the role of banks in the resumption of work and production, and pointed out that it is also necessary to pay attention to the risk prevention of banks^[2]. On science and technology, finance and taxation, Ding, et al. proposed that improving science and technology, fiscal and taxation, financial support and state-owned enterprises' leading roles would help the resumption of work and production^[3]. In terms of big data applications, Wang, et al. pointed out that it was necessary to use big data to help resume work and production and enhance the collaborative linkage of the industrial chain^[4]. At the same time, some scholars also focused on the practical difficulties of the resumption of work and production, and put forward countermeasures. For example, Zhu, et al. focused on the plight of small and medium-sized enterprises and policy efficiency research in light of the pandemic^[5]. Liu called for focusing on the problems of small and medium-sized enterprises, such as low resumption rate, short-term financing shortage, heavy production and operation burden, and pandemic prevention pressure, to help them overcome the difficulties^[6]. Zhao, et al. proposed that we should avoid a "one-size-fits-all" way, and implement differentiated resumption of work and production^[7]. In addition, there are also relevant studies involving political science and other related fields. For example, Wang, et al. summarized Chinese experience in coordinating pandemic prevention and control with the resumption of work and production under the new national system^[8]. Yang, et al. studied the government-led resumption of work and production mechanism from the perspective of major public health emergencies^[9]. Wu, et al. found that there were differences in policy response and spread in different regions and different enterprises^[10]. Indeed, the resumption of work and production is determined by the enterprises, and the ultimate goal is to realize the 100% resumption of work and production. However, due to the severe disruption of the COVID-19 pandemic, most market players have problems that they are afraid of investing, lack capital and elements, so they need the support of the government. Achieving the whole resumption of work and production is an evolution from 0 to 100, or an evolution of the probability of an enterprise to choose the "resumption of work and production" strategy from 0 to 100. Game theory is a theory that analyzes the optimal strategic choices of rational individuals, and classical game theory originated in Theory of Games and Economic Behavior, a book written by Neumann and Morgenstern, which was published by Princeton University Press in 1944^[11]. In 1950, Nash proposed Nash Equilibrium, which pointed out that individuals cannot improve their personal gains by changing their own strategies^[12]. In 1973, Maynard, et al. published The Logic of Animal Conflict on the journal Nature, which pointed out that conflicts between the same animal are usually of the "limited war" type, introduced the concept of evolutionary stability strategy (ESS) to describe the stable state of the game. Also, it showed that through game theory and computer simulation analysis, the "limited war" strategy is beneficial to both animal individuals and species^[13]. In 1978, Taylor, et al. proposed replicator dynamics (also commonly known as dynamic replication equations), which simulated game dynamics in continuous and discrete scenarios through systems of differential equations^[14]. In 1982, Maynard Smith published a monograph at Cambridge University Press, which systematically explained the characteristics of "limited rationality" individuals (animals or plants), which were developed in a long-term process of evolutionary game, so evolutionary game theory was born^[15]. System Dynamics (SD), which originated in the 1950s at the work of Jay W. Forrester and colleagues at the MIT Sloan School of Management^[16], is a discipline that studies the dynamic complexity of systems^[17]. System dynamics models are suitable for dealing with long-term and cyclical problems, and do long-term, dynamic, and strategic simulation analysis^[18]. Cheng listed the school of systems dynamics as one of the five university schools of complex scientific research in the United States^[19]. Senge, a modern American management master, revealed that there are many universal management laws in social and economic systems, and formed a feedback dynamic complex analysis theory and method that can reveal the nature of complex systems^[20]. Forrester, the founder of system dynamics, proposed that in the next 50 years, system dynamics research should be particularly applied to feedback theory^[21]. Leng constructed a system dynamics of basic in-tree model of evolutionary game flow rate^[22]. At present, evolutionary game has been widely used in the dynamic evolution of behavior, such as in the study of logistics enterprise strategy^[23], risk sharing strategy selection^[24], and medical behavior evolution^[25]. In order to achieve the resumption of work and production, it is necessary to increase the probability of enterprises choosing the behaviour or the proportion of participation of the behavior to 100% with the help of relevant government policies. Therefore, based on the urgency of the resumption of work and production in all walks of life under the impact of the the COVID-19 pandemic, this paper constructs a game matrix and a dynamic replication system for enterprises under the strategies of "the resumption of work and production" and "no resumption of work and production" and the government under the strategies of "helping" and "not helping". According to the construction theorems of the system dynamics evolutionary game model, the paper constructs a general model of system dynamics evolutionary game regulation for the resumption of production, gives construction theorems of the model, and analyzes the evolutionary mechanism and scenario conditions of enterprises' strategy converging to "the resumption of production" strategy. Also, it constructs the system dynamics evolutionary game regulation model of hog production restoration, simulates and verifies related regulation theorems with the example of pig farmers resuming production. In addition, a countermeasure regulation research of hog production restoration is carried out to solve the problem of "being afraid to raise, no money to raise, no land to raise", which helps explore systematic countermeasures and suggestions for the rapid convergence of farmers' strategies to the "resumption of work and production" strategy. The evolutionary game control model of resumption system dynamics provides a systematic model and method for the study of resumption countermeasures, a general control model for the resumption ratio from 0 to 1 (100%), and a systematic idea, method and model for exploring the "precise strategy" system to promote enterprises to resume production quickly.

In light of the impact of the COVID-19 pandemic, all walks of life will urgently need to resume work and production if the pandemic is basically controlled. For enterprises, they may face many difficulties, such as the pressure of pandemic prevention and control, and the rising costs of labors and raw materials, so they ask governments to provide support. For the government, in order to realize the normal operation of society and the country, under the premise of pandemic prevention and control, it is urgently necessary for enterprises and society to carry out production to ensure the basic material needs of society, the country and individuals, as well as the stability of prices. Under the enterprises' resumption strategy $s_1$ = (the resumption of work and production, no resumption of work and production) and the government's support strategy (helping, no helping), it is assumed that the mixed strategies (the resumption of work and production, helping), (the resumption of work and production, no helping), (no resumption of work and production, helping), (no resumption of work and production, no helping) can benefit enterprises and governments in the pattern of ($Q_1$, $V_1$), ($Q_2$, $V_2$), ($Q_3$, $V_3$), ($Q_4$, $V_4$), respectively. Therefore, under the enterprises' resumption strategy (the resumption of work and production, no resumption of work and production) and the government's support strategy (helping, no helping), the benefit matrix can be seen in Table 1 below.

According to the benefit matrix, we assumed the proportion of the resumption of work and production as $x$, while the proportion of government assistance as $y$, so the proportions of "no resumption of work and production" and "no helping" are $1-x$ and $1-y$ respectively. Also, we can conclude that under the enterprises' resumption strategy of the resumption of work and production and no resumption of work and production, the average benefit $\overline{E_x}$, a mean value of expected return $E_{x1}$, $E_{x2}$, is:

At the same time, under the government's strategy of "helping" and "no helping", we can conclude that the average benefit $\overline{E_y}$, a mean value of expected return $E_{y1}$, $E_{y2}$, is:

The replication dynamic equation of the enterprises' "the resumption of work and production" proportion is $x$:

The replication dynamic equation of the government's "helping" proportion is:

Therefore, the dynamic replication system of the resumption of work and production evolutionary game is

We can get the dynamic replication system of the resumption of work and production evolutionary game:

We supposed that

So the dynamic replication system of enterprises' resumption of work and production and the government's assistance evolutionary game is

Theorem 1 is as below.

Theorem 1 Under the enterprises' resumption strategy $s_1$ = $($the resumption of work and production, no resumption of work and production$)$ and the government's support strategy $($helping, no helping$)$, it is assumed that the mixed strategies $($the resumption of work and production, helping$)$, $($the resumption of work and production, no helping$)$, $($no resumption of work and production, helping$)$, $($no resumption of work and production, no helping$)$ can benefit enterprises and the government in the pattern of $(Q_1,V_1)$, $(Q_2$, $V_2)$, $(Q_3$, $V_3)$, $(Q_4$, $V_4)$ respectively. Therefore, the dynamic replication system of the resumption of arbitrary enterprises and the assistance for both sides from the government evolutionary game is

And they can be shown as

Therein, $Q_1-Q_2-Q_3+Q_4=a$, $Q_2-Q_4=b$, $V_1-V_2-V_3+V_4=d$, $V_3-V_4=e$.

According to system dynamics evolutionary game theory, the dynamic replication system of evolutionary game (11) between the resumption of work and production and government support can be constructed as a basic flow rate in-tree model under system dynamics.

It can be seen that the system dynamics of basic in-tree model of evolutionary game flow rate based on the dynamic replication system of the resumption of work and production evolutionary game can simulate and regulate the convergence of proportion $x$ of the resumption of work and production by regulating the value of $a,b,c,d$.

Also, because

therefore, the theorem of work and production resuming behavior system dynamics evolutionary game regulation and control model is as follows.

Theorem 2 Under the enterprises' resumption strategy = $($the resumption of work and production, no resumption of work and production$)$ and the government's support strategy $($helping, no helping$)$, it is assumed that the mixed strategies $($the resumption of work and production, helping$)$, $($the resumption of work and production, no helping$)$, $($no resumption of work and production, helping$)$, $($no resumption of work and production, no helping$)$ can benefit enterprises and governments in the pattern of $(Q_1$, $V_1)$, $(Q_2$, $V_2)$, $(Q_3$, $V_3)$, $(Q_4$, $V_4)$, respectively. Therefore, the dynamic replication system of evolutionary game of the resumption of arbitrary enterprises is

They can constructed a system dynamics of basic in-tree model of evolutionary game flow rate based on the resumption of work and production Therein, $Q_1-Q_2-Q_3+Q_4=a$, $Q_2-Q_4=b$, $V_1-V_2-V_3+V_4=d$, $V_3-V_4=e$.

According to Theorem 1, the system dynamics of basic in-tree model of evolutionary game flow rate based on the resumption of work and production is also called work and production resuming behavior system dynamics evolutionary game regulation and control model.

It can be seen that on the basis of work and production resuming behavior system dynamics evolutionary game regulation and control model, we can regulate the value of $a,b,c,d$ through regulating the value of $Q_1$, $Q_2$, $Q_3$, $Q_4$ and $V_1$, $V_2$, $V_3$, $V_4$. Also, it can realize the simulation regulation and control research of the evolution and convergence of the proportion of the resumption of work and production.

At present, the nation and relevant departments have vigorously help enterprises resume work and production, and the State Council has also released 33 measures to stabilize the economy. Therefore, this paper discusses the convergence path and strategy of the strategy the resumption of work and production, help. Due to is the proportion of enterprises that adopt the strategy of "the resumption of work and production", Theorem 3 is as follows.

Theorem 3 Under the conditions of the strategy of Theorem 1 and its benefits, in order to rapidly realize the resumption of work and production of enterprises, it is necessary to achieve the rapid convergence of the proportion $x$ of the resumption of work and production in work and production resuming behavior system dynamics evolutionary game regulation and control model to quickly converge at 1 (100%).

Proposition 1 $(1,1)$ is the equilibrium point of evolutionary game dynamic replication system $(11)$ of the resumption of work and production and assistance of the government.

Proof If we substitute $(1,1)$ into the system (11), then $F(x)=0$, $F(y)=0$ and $(1,1)$ is the equilibrium point of the system (11).

Further, we used the partial stability of the Jacobi matrix to analyze the evolutionary stability conditions of the equilibrium point (1, 1) of the dynamic replication system (11), and we found the partial derivative of the system of differential equations of the dynamic replication system (11) in turn about the sum, and the Jacobi matrix is:

Then the determinant of the matrix is

Its trace is $\mathrm{t}\mathrm{r}J=(1-2x)(ay+b)+(1-2y)(ex+b)$. The equilibrium point $(1,1)$ is substituted into the determinant of the matrix and the trace of the matrix, and the expression of the determinant of the matrix and the trace of the matrix are as follows:

Proposition 2 The equilibrium point $(1,1)$ of the evolutionary game dynamic replication system $(11)$ is the scenario condition of the evolutionary stability point, which are $a+b>0$ and $e+d>0$.

Proof According to evolutionary game theory, when the equilibrium point satisfies the conditions that det $J>0$, tr $J>0$, the equilibrium point is the evolutionary stability point. Therefore, if det $J=(a+b)(e+d)>0$, $-$tr $J=(a+b)+(e+d)>0$, then $a+b>0$ and $e+d>0$.

Therefore, the scenario condition that the equilibrium point $(1,1)$ is the evolutionary stability point is

The game regulative theorem of the resumption of work and production is as follows.

Theorem 4 Evolutionary game dynamic replication system of the resumption of work and production of arbitrary enterprises and assistance of the government

Thus, when $0<x<1$, $0<y<1$, because $\frac{\partial F(x)}{\partial a}=x(1-x)y>0$, $\frac{\partial F(x)}{\partial b}=x(1-x)>0$, so according to the dynamic replication system, as long as we increase the arbitrary value of $a$ and $b$, we can increase $x$'s rate to converge to 1. Also, when $0<x<1$, $0<y<1$, $\frac{\partial F(y)}{\partial d}=y(1-y)x>0$, $\frac{\partial F(y)}{\partial e}=y(1-y)>0$, so as long as we increase the arbitrary value of $d$ and $e$, we can increase $y$'s rate $F(y)=\frac{\partial y}{\partial t}$ to converge to 1. Therefore, work and production behaviour evolutionary game regulation and control theorem is as follows.

Theorem 5 Arbitrary theorem in Theorem $2$ of the work and production behaviour system dynamics evolutionary game regulation and control model, under the scenario conditions that $a+b>0$ and $e+d>0$, therein, $0<x<1$, $0<y<1$, if we increase arbitrary value of $a$ and $b$, then the converging process of $x$ to $1$ $(100\mathrm{\%}$ of the resumption of work and production$)$ will be shorter. If we increase arbitrary value of $d$ and $e$, then the converging process of $y$ to $1$ $(100\mathrm{\%}$ assistance from governments$)$ will be shorter.

If under the conditions of Theorem $5$, it is not difficult to find that when $0<x<1$, $0<y<1$, because $\frac{\partial F(x)}{\partial a}=x(1-x)y>0$, $\frac{\partial F(x)}{\partial b}=x(1-x)>0$, so as long as we increase arbitrary value of $a$ and $b$, then we can increase $x$'s rate $F(x)=\frac{\partial x}{\partial t}$ of converging to 1. Also, because $\frac{\partial F(y)}{\partial x}=y(1-y)d>0$, so as long as we increase $y$'s rate $F(y)=\frac{\partial y}{\partial t}$ of converging to 1. In the same way, when $0<x<1$, $0<y<1$, and $\frac{\partial F(y)}{\partial d}=y(1-y)x>0$, $\frac{\partial F(y)}{\partial e}=y(1-y)>0$, so as long as we increase arbitrary value of $d$ and $e$, we can increase $y$'s rate $F(y)=\frac{\partial y}{\partial t}$ of converging to 1. Then because $\frac{\partial F(x)}{\partial y}=x(1-x)a>0$ at the time, so we can also increase $x$'s rate $F(x)=\frac{\partial x}{\partial t}$ of converging to 1 at the same time. Therefore, Theorem 6 of work and production behaviour evolutionary game regulation and control is as follows.

Theorem 6 Arbitrary theorem in Theorem $2$ of the work and production behaviour system dynamics evolutionary game regulation and control model, under the scenario conditions that $a+b>0$ and $e+d>0$, if $a>0$, $d>0$, therein $0<x<1$, $0<y<1$, if we increase arbitrary value of $a,b,d,e$, the process of converging to $1$ $(100\mathrm{\%}$ of the resumption of work and production$)$ and the process of converging to $1$ $(100\mathrm{\%}$ assistance of the government$)$ will be shorter.

Next, through the resumption of work and production, we simulated work and production behaviour system dynamics evolutionary game regulation and control model and theorems, and carried out research on regulative countermeasures.

We combined existing literature researches and actual situation, and made the following assumptions. We supposed that the one-time cost at an early stage of the resumption of work and production is $c_0$, which includes the equipment investment, the additional cost input brought by the re-recruitment, etc., referred to as $c_0$. The cost of pandemic prevention and control (non-productive pandemic prevention cost) of the resumption of work and production is $c$, the production cost of a single product (including the cost of productive pandemic prevention) is $c_1$, the saleable price of a single product is $p$, and the production size is $n$. After the resumption of work and production, the year of production and operation is $T$, and the production cycle can be completed within $T$ years. If the government adopts the "helping" strategy, it can provide a one-time subsidy $w_1$. Under the strategies of "helping" and "no helping", the products' passing rates are $\beta$, $\beta +{\beta }_1$ respectively. Under the government's "helping" strategy, the government's investment in the construction of the pandemic prevention system is $w_2$, and the investment in research and development in production and environmental protection technology is $w_3$. Under the government's "no helping" strategy, the business cycle of enterprises has decreased to $m+m_0$, and the income guarantee of a single product has dropped to $(p-c_1)\gamma$, of which is the income guarantee coefficient, $\gamma <1$. The government mainly focuses on the stability of the supply chain and the market, if the market prices of products are stable at $p_0$ that everyone can be satisfied with, the basic benefit of the government is $w_0$, and the market prices of a single product under the strategy of "the resumption of work and production" and "no resumption of work and production" are respectively, and $p_0<p<p_1$. At this time, the performances of the government are $w_0\frac{\partial p_0}{\partial p_0+|p-p_0|}$, $w_0\frac{\partial p_0}{\partial p_0+|p_1-p_0|}$, respectively. Under the strategy of "no resumption of work and production", the benefits bought by other activities is $Q$. Therefore, under the strategies of "the resumption of work and production, no resumption of work and production" and "helping, no helping", the benefit matrix is as follow.

We supposed that

According to evolutionary game dynamic replication system of the resumption of work and production of arbitrary enterprises and assistance of the government

The replication dynamic equation for the proportion $x$ of the resumption of work and production

The replication dynamic equation for the proportion $y$ of assistance of the government

According to Theorem 1, we can further get

Then, evolutionary game dynamic replication system of the resumption of work and production of arbitrary enterprises and assistance of the government can be shown as follows

According to Theorem 5 of the system dynamics evolutionary game regulation and control model of the resumption of work and production, the system dynamics evolutionary game regulation and control model for production recovery is as follows.

Through the work and production resuming behavior system dynamics evolutionary game regulation and control model, according to the relevant theorems of game regulation of resumption of work and production, we carried out simulation tests and parameter regulation simulation studies, so as to obtain relevant regulative countermeasures for the rapid resumption of production. We simulated and verified Theorem 4, under the scenario condition $a+b>0$, $e+d>0$ that the equilibrium point $(1,1)$ is the evolutionary stability point, we supposed $a=0.1$, $b=0.001$, $d=0.002$, $e=0.01$, $x=0.03$, $y=0.1$, and carried out simulation and verification studies based on the work and production resuming behavior system dynamics evolutionary game regulation and control model. The simulation diagram of the convergence curve of strategies of enterprises and the government converging to "the resumption of work and production" and "helping" respectively is as follows.

From Figure 4, we can see that under the scenario conditions $a+b>0$, $e+d>0$ and the initial value setting $x=0.03$, $y=0.1$, enterprises' strategy will converge to the "the resumption of work and production" strategy when $t=380$. When $t=780$, the government's strategy will converge to "helping", and enterprises will resume work and production. This further verified Theorem 4: when, the equilibrium point $(1,1)$ is the evolutionary stability point for evolutionary game dynamic replication system of the resumption of work and production of arbitrary enterprises and assistance of the government. Further, through the work and production resuming behavior system dynamics evolutionary game regulation and control theorem, policy simulation and parameter regulation and control, we observed the impact of different policies on the evolutionary path of enterprises' strategy converging to "the resumption of work and production". 1) Countermeasure 1: Encouraging the implementation of national policies. In the case of other variables remaining unchanged, through the implementation of national and relevant local policies, we increased the initial value of $y$ to $y=0.5$, and the convergence curve simulations of enterprise and government strategies converging to "the resumption of work and production" and "helping" respectively are shown in Figure 5.

Through Figure 5(a), we found that if the government can rapidly implement policies, and increase the proportion of implementing national policies from $y=0.1$ to $y=0.5$, the time for enterprises to engage in the convergence strategy of "the resumption of work and production" can be shorter from $t=380$ to $t=150$, which can improve the speed of the resumption of production. This is the line we often hear about that national policies are beneficial, but the implementation is not satisfied (the implementation on grass-roots level is not satisfied). Therefore, how can local policies be implemented quickly? We further simulated and validated Theorem 6 and performed regulative analysis. We found that there is a positive correlation between ${\beta }_1$, $w_0$ and $e$, $d$, and we increased the pass rate to ${\beta }_1$ under the government support policy. At the same time, in order to attract the attention of the grass-root government, it is indeed necessary to keep a whole-picture mind, strengthen assessment, supervision, and publicity, so that the grass-root government can realize the goal of stabilizing product price at about $p_0$, which can be accepted by the society and enterprises, avoiding great ups and downs. The performance of increasing basic utility of the government to stabilize the price of products is $w_0$, and then because there is a positive correlation between ${\beta }_1$, $w_0$ and $e$, $d$, in the case that $p-c_1$ is positive, ${\beta }_1$ and $a$ also in a positive correlation. Through increasing the value of ${\beta }_1$, $w_0$, we increased $d=0.002$, $e=0.01$ to $d=0.002$, $e=0.11$, and increased a from $a=0.1$ to $a=0.11$. Therefore, the convergence curve simulation table is shown in Figure 5(b).

We found if we enhanced the basic perception effect of local government in stabilizing the resumption of work and production, and enhanced the effect of pandemic prevention and control, through the government's investment to further improve the product qualification rate, we can increase the value of $a$, $d$, $e$ to $d=0.002$, $e=0.01$, $a=0.11$. In the case that other conditions remain unchanged, enterprises' time engaged in the "the resumption of work and production" convergence strategy can be shorter from about $t=380$ to $t=280$, which can improve the speed of the resumption of production. So this further validated Theorem 6: Under the scenario conditions that $a+b>0$ and $e+d>0$, if $a>0$, $d>0$, thereinto, $0<x<1$, $0<y<1$, if we increase arbitrary value of $a$, $b$, $d$, $e$, the process of convergence to 1 (100% of the resumption of work and production) and the process of convergence to 1 (100% assistance from governments) will be shorter.

Therefore, if the market price of the product is stable at the price $p_0$ that everyone can be satisfied with, the basic utility of the government is $w_0$, the product qualification rate under the government's "helping" can be raised to ${\beta }_1$, then the resumption of work and production will be improved. $w_0$ is the government's basic utility of the market price stabilizing a price that everyone can be satisfied with, that is, the utility of the government to stabilize the price. To enhance the value of $w_0$, we need to enhance the understanding of the importance of "stabilizing prices" by local governments at all levels, continuously implement responsibilities and enhance the implementation ability of local governments at all levels, and strengthen supervision, enhancing their ability to learn from good examples and overcome own weaknesses. ${\beta }_1$ is the increased value of the product qualification rate under the government's "helping" strategy, then if we want to increase ${\beta }_1$, we need to require the government to beef up efforts in the fields of basic technology and process reengineering optimization. 2) Countermeasure two: Under the premise of $(y=1)$ that the national policies can be implemented effectively, we should stabilize the market expectations of enterprises through systematic countermeasure design to solve the problem of "being afraid of investing". Due to the uncertainty of the pandemic and other factors, many enterprises have met the problem of "being afraid of investing", so we will solve the problem through control and regulation. Firstly, on the basis of the initial value setting of the simulation analysis, that is, $a=0.1$, $b=0.001$, $d=0.001$, $e=0.01$, $x=0.03$, $y=0.1$, through the premise of $(y=1)$ that the national policies can be implemented effectively, we supposed that $y=1$, and the convergence curve simulation diagrams of strategies of enterprise and government converging to "the resumption of work and production" and "helping" respectively are as shown in Figure 6(a). We found that compared with Figure 5(a), when we increased $y=0.8$ to $y=1$, the time for enterprises to engage in the convergence strategy of "the resumption of work and production" was shorter from about $t=150$ to about $t=80$.

Under the premise of $(y=1)$ that the national policies can be implemented effectively, through stabilizing the benefit of every product, we increased enterprises' business cycle $m$, survival rates $\beta$ and ${\beta }_1$, and $m$, $\beta$, ${\beta }_1$ and $a$, $b$ have a positive correlation. We increased $a=0.1$ to $a=0.2$, and $b=0.001$ to $b=0.002$, then the convergence curve simulation diagrams of strategies of enterprise and government converging to "the resumption of work and production" and "helping" respectively are as shown in Figure 6(b). Compared with Figure 6(a), the time for enterprises to engage in the convergence strategy of "the resumption of work and production" was shorter from about $t=80$ to about $t=45$, the willingness of enterprises to resume work and production increased, and the proportion of enterprises engaged in the resumption of work and production is increased, further simulating and validating Theorems 5 and 6.

Then, if we want to stabilize revenue expectations, then we must stabilize $(p-c_1)$, and we can stabilize the income expectations of enterprises through regulate parameters $p$, $c_1$, $m$, $\beta$, ${\beta }_1$.

For example, through market guidance, price index insurance, futures market innovation, we can stabilize the price of products $p$. Through reducing production costs (including pandemic prevention costs $c$) $c_1$ by production technology innovation, and we can reduce pandemic prevention costs $c$ through smooth logistics and restore supply chains, thus reducing unit product costs $c_1$. For a long-term plan, we need to try to stabilize the future operating time of enterprises, relieve the concerns of enterprises that they are concerned about the pause of production at any time due to pandemic prevention requirements, or solve technical problems through technology and process innovation, thereby improving $m$, $\beta$, ${\beta }_1$. Especially in the pandemic-hit areas, when people and logistics are almost blocked, the cost of pandemic prevention and control of the resumption of work and production is very high, and the smooth flow of people and logistics can greatly reduce the cost of pandemic prevention $c$, which in turn can greatly reduce the cost of unit products $c_1$, rapidly promoting the resumption of work and production.

3) Countermeasure three: Under the premise of $(y=1)$ that the national policies can be implemented effectively, we can help enterprises solve the problems of lacking capital and elements through a systematic design

The one-time investment at the early stage of production recovery has difficulties in lacking money for production, and some enterprises also face the problem of lacking elements due to the closure during the previous periods. On the basis of the simulation analysis of the initial value setting, that is, $a=0.1,b=0.001,d=0.002,e=0.01,e=0.01,x=0.03,y=0.1$, and under the premise of $(y=1)$ that the national policies can be implemented effectively, we help enterprises solve the problem of one-time large investment at the early stage and reducing the total investment at the early stage of $c_0$ through subsidies for enterprise construction $w_1$. We increased $a=0.1$ to $a=0.2$, and $b=0.001$ to $b=0.1$, then the convergence curve simulation diagrams of strategies of enterprise and government converging to "the resumption of work and production" and "helping" respectively are as shown in Figure 7.

Through increasing the subsidy $w_1$ for enterprises' construction, when $a=0.1$ was increased to $a=0.2$, we found that compared with Figure 6(a), the time for the convergence strategy of "the resumption of work and production" in Figure 7 was shorter from about $t=80$ to about $t=40$. By helping enterprises solve the problem of one-time large investment at the early stage and reducing the total investment at the early stage $c_0$, when $b=0.001$ was increased $b=0.1$, compared with Figure 6(a), the time for enterprises in Figure 7 to engage in the convergence strategy of "the resumption of work and production" was shorter from about $t=80$ to about $t=45$. We found that the willingness of enterprises to resume work and production strengthened, and the proportion of enterprises engaged in the resumption of work and production increased, further simulating and validating Theorems 5 and 6.

In terms of specific countermeasures, it can help enterprises solve the problem of large investment at the early stage, various subsidies, etc., increasing $w_1$ and reducing $c_0$ to achieve the rapid recovery of production. Then, in order to increase $w_1$, it is necessary to increase the financial subsidy for the early start of the resumption of work and production of enterprises, so as to solve the problem of "lacking capital" at the start-up stage of the resumption of work and production after the suspension of work due to the pandemic.

Therefore, we found that the work and production resuming behavior system dynamics evolutionary game regulation and control model provides a set of systematic models and methods for the research and regulation of the resumption of work and production system, which can provide systematic regulation and simulation for the proportion of resumption of work and production from 0 to 1, and provide systematic ideas, methods and models for finding a "precise strategy" to promote the resumption of work and production. At the same time, through the regulation simulation, the relevant countermeasures and suggestions for the rapid resumption of work and production have also been obtained, namely the lever solution.

Based on the urgency of the resumption of work and production due to the disruption of the COVID-19, this paper constructs enterprises' game matrix and dynamic replication system under enterprises' strategy of "the resumption of work and production" and "no resumption of work and production" and the government's of "helping" and "no helping". According to the construction theorem of the system dynamic evolutionary game model, it constructs the work and production resuming behavior system dynamics evolutionary game regulation and control model and the relevant regulative theorems of the resumption of work and production, analyzes the evolutionary mechanism and scenario conditions of enterprises' strategy converging to "the resumption of work and production" (100% of the resumption of work and production) and carries out simulation and countermeasure regulation based on the work and production resuming behavior system dynamics evolutionary game regulation and control model. We found that the work and production resuming behavior system dynamics evolutionary game regulation and control model provides a set of systematic models and methods for the research and regulation of the resumption of work and production system, which can provide systematic regulation and simulation for the proportion of the resumption of work and production from 0 to 1, and provide systematic ideas, methods and models for finding a "precise strategy"to promote the resumption of work and production. The simulation of countermeasure regulation and control shows that: 1) Strengthening supervision, continuously implementing responsibilities, and improving the awareness and implementation ability of party committees and governments at all levels on the importance of "stabilizing prices" will help promote the rapid implementation of national policies and improve the speed of the resumption of work and production. 2) Through technology and process innovation, smooth logistics, and restoration of supply chains, we can reduce production costs such as pandemic prevention and control inputs, to relieve the concerns of enterprises that they are concerned about pausing production at any time due to pandemic prevention requirements to stabilize the business expectations of enterprises to solve the problem of "being afraid of investing". Especially in the pandemic-hit areas, people and logistics are almost blocked, so the smooth flow of people and logistics can greatly reduce the cost of pandemic prevention, thus greatly reducing the cost of unit products, which is conducive to the rapid resumption of work and production. 3) Efforts should be made to solve the initial start-up funds for enterprises to resume work and production, so as to solve the problem of "lacking capital and elements" at the start-up stage of the resumption of work and production after the suspension due to the pandemic. According to the study, the evolutionary game control model of resumption system dynamics provides a systematic model and method for the study of resumption countermeasures, a general control model for the resumption ratio from 0 to 1 (100%), and a systematic idea, method and model for exploring the "precise strategy" system to promote enterprises to resume production quickly. The multi-party game problem of the resumption of work and production, the evaluation of the effect of different policies on the resumption of work and production, especially the decision-making issue of the dual-goal balance between the resumption of work and production and the prevention and control of the pandemic need to be further studied deeply.