Evaluating the mitigation strategies of COVID-19 by the application of the CO2 emission data through high-resolution agent-based computational experiments

The negative consequences, such as healthy and environmental issues, brought by rapid urbanization and interactive human activities result in increasing social uncertainties, unreliable predictions, and poor management decisions. For instance, the Coronavirus Disease (COVID-19) occurred in 2019 has been plaguing many countries. Aiming at controlling the spread of COVID-19, countries around the world have adopted various mitigation and suppression strategies. However, how to comprehensively eva luate different mitigation strategies remains unexplored. To this end, based on the Artificial societies, Computational experiments, Parallel execution (ACP) approach, we proposed a system model, which clarifies the process to collect the necessary data and conduct large-scale computational experiments to evaluate the effectiveness of different mitigation strategies. Specifically, we established an artificial society of Wuhan city through geo-environment modeling, population modeling, contact behavior modeling, disease spread modeling and mitigation strategy modeling. Moreover, we established an evaluation model in terms of the control effects and economic costs of the mitigation strategy. With respect to the control effects, it is directly reflected by indicators such as the cumulative number of diseases and deaths, while the relationship between mitigation strategies and economic costs is built based on the CO2 emission. Finally, large-scale simulation experiments are conducted to evaluate the mitigation strategies of six countries. The results reveal that the more strict mitigation strategies achieve better control effects and less economic costs.


Introduction
Brought by the rapid urbanization, various health and environmental issues, such as urban tuberculosis (Oppong et al., 2015) and pandemics (Bai et al., 2021), pose a significant risk to citizens and a great burden to city governors. To address these issues, city governors are deliberately implementing up-to-date socio-technological advancements in their healthy city strategies. However, city as a complex adaptive system creates complex interdependencies between humans, infrastructures, and network, which will inevitably result in increasing uncertainties and poor management decisions. Current healthy city strategies are not effective enough to deal with these issues. For instance, the Coronavirus Disease (COVID-19) caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) (Tang et al., 2020), has generated 143,445, 675 cumulative incidences and 3,051,736 deaths as of April 23, 2021(WHO, 2021, which now still plagues most countries around the world. Therefore, studying the mitigation strategies of the COVID-19 epidemic is an effective supplement to the construction of healthy cities. To effectively control the spread of the COVID-19, many governments and scholars have devoted themselves to tackling this problem, and their studies can be mainly divided into the following three categories, data-based study, simulation-oriented study, pathology-related study. Some researchers analyzed the statistical data (Coccia, 2021;Gralinski and Menachery, 2020;Liu et al., 2020a;Liu et al., 2020b;WHO, 2020a;Xu, 2020) and they discovered the main characteristics of the COVID-19, such as the basic reproduction number (R 0 ) and the distribution of the incubation period. Moreover, data-driven methods were adopted in some studies (Bta et al., 2020;Peng et al., 2020;Roques et al., 2020). For instance, Roques et al. combined the SIR model with artificial intelligence methods to estimate early infection cases and mortality rates (Roques et al., 2020). Some researchers used simulation-oriented methods, such as multi-agent modeling, complex network modeling, and Monte Carlo simulation (Bock and Ortea, 2020;Niehus et al., 2020) to predict the development of the epidemic. For example, Broniec et al., (2020) explored the impact of social distance on the spread of the epidemic. As for pathology studies, some researchers focused on the pathology of the COVID-19 (Roujian et al., 2020;Veljkovic et al., 2019;Zhang et al., 2020;Zhu et al., 2020). However, the evaluation of mitigation strategies on epidemic control is a field where current research is relatively inadequate.
Currently, the evaluation on mitigation strategies is mostly assessed through the indicator of the cumulative number of infections. Dunuwila et al. (Dunuwila and Rajapakse, 2020) established a disease spread simulation model based on the multi-agent method to study blockade and detection strategies under limited resource conditions, and the control effects were evaluated through a cumulative number of patients. Based on the multi-agent method, Chang et al., (2020) constructed an individual-level computational simulation model to study the control effects of various mitigation strategies in Australia, such as restricting international air travel, quarantining cases, and closing schools. Mukherjee et al., (2021) evaluated the different restart strategies of educational institutions based on the number of patients. The above-mentioned evaluations are all based on the infection status of population, which are simple to operate, but the impact of mitigation strategies on other aspects of society, such as environmental pollution, economic development, and public psychology, is ignored.
Studies reveal that strict mitigation strategies such as travel bans and blockades of most commercial and industrial activities would lead to a significant economic decline in the short term (Commission, 2020a). For example, the GDP of Wuhan City in the first quarter of 2020 decrease by 40.5% compared with the same period of the previous year (Commission, 2020b). To avoid short-term economic recession and unemployment tide, many countries (e.g., the United States and the United Kingdom) also take the impact of mitigation strategies on economic development into account (Danielli et al., 2020). It is noteworthy that there is currently no research studying the evaluation of the control effects and economic costs of mitigation strategies in the meantime. Therefore, our study aims to design effective mitigation strategies for different countries and cities by analyzing the control effects on the epidemic and the impact on economic development.
To evaluate the mitigation strategies of the COVID-19, this paper proposes a system model, in which an artificial society and an evaluation model are established. The construction of artificial society is based on the Artificial societies, Computational experiments, Parallel execution (ACP) approach (Wang, 2007). The key to the ACP approach is to construct an artificial society and generate diversified scenarios that are consistent with scenarios in real society. Based on the artificial society, various computational experiments can be carried out (Wang et al., 2015;Wang, 2007). Artificial society cooperates with real society in many ways, such as co-evolution, closed-loop feedback, and parallel control . Specifically, the artificial society in this paper includes five aspects: geographical environment, population, contact behavior, disease spread, and mitigation strategy. Other related work can be found in our previous study (Qiu et al., 2017;Song et al., 2014;Chen et al., 2015;Chen and Zhang, 2018;Zhang et al., 2015). This paper innovatively evaluates mitigation strategies from two aspects: control effects and economic costs. Specifically, the control effect of mitigation strategies on the pandemic can be reflected by some metrics such as the cumulative number of patients and the cumulative number of deaths. However, it is challenging to directly establish a model of the impact of mitigation strategies on economic costs. Mitigation strategies restrict social production and living activities, thereby hindering the social-economic development. The reduction of commercial and industrial activities would undoubtedly lead to a reduction in the emission of pollutants such as CO 2 , PM 2.5 (Ali et al., 2020;Bolaño-Ortiz et al., 2020;WHO, 2020b;Zeng et al., 2020;Zhang, 2021). Wang et al., (2020) discovered that there is a linear relationship between the daily rate of new COVID-19 cases and the total reduction of CO 2 emission in various provinces of China. Moreover, Marjanović et al., (2016) successfully predicted the GDP level through the CO 2 emission. Inspired by the above-mentioned studies, taking the reduction amount of CO 2 emission as a bridge, this paper establishes a model of the impact of mitigation strategies on economic costs. In particular, the impact of mitigation strategies on the economy cost consists of two parts, namely the GDP loss and medical expenditure. The GDP loss refers to the reduction of GDP caused by the implementation of mitigation strategies. Medical expenditure refers to the cost of treating patients. The sum of the two parts reflects the economic costs of mitigation strategies.
Based on the artificial society, we carry out the propagation simulations of COVID-19 and the evaluation of mitigation strategies in six countries, China (CHN), South Korea (KOR), Iran (IRN), Italy (ITA), the United Kingdom (GBR), the United States (USA). Wuhan is a typical city where the COVID-19 breaks out for the first time, so we choose Wuhan as the representative city of the real society. The artificial society of Wuhan is constructed based on statistical data such as Wuhan's real population and geographic environment. In order to compare the control effect and economic costs of mitigation strategies adopted by different countries, we collect the statistics of pandemic and mitigation policies in six countries from January 1, 2020, to April 30, 2020, and model the strategies quantitatively. The results of large-scale simulation experiments reveal that mitigation strategies of strict patterns (CHN, KOR, and IRN) are more proactive than those of loose patterns (ITA, GBR, and USA). It is obviously that, in strict patterns, the epidemic is controlled and the economic costs are less.
In what follows, we introduce the system model, the artificial society modeling and the evaluation model in Section 2; in Section 3, we carry out the spread simulations of the COVID-19 and the evaluation experiments of different strategies; discussions are given in Section 4, and finally, we conclude our findings in Section 5. data, are injected into the artificial society constantly and dynamically.
Step 3: Conduct computational experiments. Since there are millions of persons in the artificial society, powerful computing power is needed in the experiments. Using a supercomputer, plenty of computational experiments are carried out to obtain the simulation data, based on the constructed artificial society.
Step 4: Implement the comprehensive evaluation. Based on the simulation data and the evaluation model, the effects and the costs of different mitigation strategies can be evaluated systematically.
Step 5: Optimize the mitigation strategies and carry out the strategies in reality. Based on the evaluation results of different strategies, decision-makers can choose a suitable strategy according to different situations of their country or city to guide the prevention and control of the epidemic in the real society.
The step 2 to 5 can be implemented circularly to achieve the iteration, interaction, evolution and feedback control between the artificial society and the real society. The diagram of the process is depicted in Fig. 1.

Artificial society modeling
In this paper, an artificial society based on the ACP approach is constructed as the experimental environment for the spread of COVID-19 in large cities, and the structure of the artificial society is shown in Fig. 2. In the construction, we mainly consider the four elements: population, contact behavior, disease spread model, and mitigation strategies. As shown in Fig. 2, the population modeling includes attributes such as age and gender, and all of this information is obtained through statistical data. The contact behavior in the crowd contains two types: regular and random contact. Both of these are characterized via complex network models. Based on the SEIR model (Nie et al., 2021), we formulate a disease course model and a spread model for COVID-19.   Moreover, based on the policy data of relevant countries, an 8-tuple model is built for the mitigation strategy, which takes 8 elements into account, including contact quarantine, area traffic blockade, social contact restriction, etc.

Population modeling
Population modeling refers to the process of assigning attributes to individuals based on statistical data. According to the sixth national census data in 2010, the number of permanent residents in Wuhan is 9,785,392 and all of them belong to 172 subdistricts (Statistics, 2012). Using the detailed data, we generated virtual agents according to the real demographic information. In the artificial population, each individual has eight attributes, including ID, age, gender, subdistrict, housing location, social role, social relationship, and workplace as shown in Fig. 3.
The model proposed by Yuanzheng is employed to generate the artificial population (Ge, 2014), which relies on census data and annual data from the official statistics to define the role of each one in a family (Staticstics, 2012;Statistics, 2011).

Contact behavior modeling
COVID-19 is spread through breath, cough, sneeze, and so on (Tang et al., 2020). Close contact behavior for a certain period is the necessary condition for spread. In this paper, we use the complex network to model contact behavior. In the network, the nodes represent individuals, and the edges represent the contact behavior between individuals, as shown in Fig. 3.
The contact behavior includes two types, regular contact behavior, and random contact behavior. The regular contact behaviors refer to the predictable contact behaviors that occur at homes, workplaces, schools, etc., as shown in Appendix 1. All other contact behaviors are random contact behaviors, such as shopping, leisure, and others that are not listed in Appendix 1. To model the regular contact behavior, the spatiotemporal contact behavior modeling method based on the weighted bimodal network is adopted . While for the random contact behavior, we propose the Scale Distance Degree (SSD) model, which is based on the gravity model and the preferential attachment. The details of the methods to model regular contact behavior and random contact behavior are shown in Appendix 1.

Disease spread modeling
The disease model contains two aspects as the disease course and disease propagation. The disease course is the evolutionary process of health conditions experienced by patients , and disease propagation refers to the spread of the pathogen from patients to the susceptible. In this paper, we construct two models to characterize the two aspects of COVID-19, respectively.
Based on the SEIR model (Nie et al., 2021) and the course characteristics of the patients infected by COVID-19, the disease course model of COVID-19 is constructed, as shown in Fig. 4. In the model, there are 6 states of individuals, susceptible (S), incubation (E), symptomatic infection (I s ), asymptomatic infection (I a ), recovery (R), and death (D). If the susceptible contacts patients (E, I s , or I a ), they will become E state with the probability of P t . The duration of the incubation period is T E .
After the incubation period, with α probability, they will enter the asymptomatic infection state (I a ). Otherwise, they will enter the symptomatic infection state (I s ). Symptomatic patients may be dead with the probability of β. Otherwise, they will recover. Since the mortality rate of asymptomatic patients is 0, asymptomatic patients will inevitably enter the recovery state after a while. T IR represents the duration from the infected state to the recovery state. T ID represents the duration from the infected state to the dead state, and the infected state here includes symptomatic infection state and asymptomatic infection state.
In this paper, we take a reasonable value for the above parameters based on empirical data. P t changes according to different mitigation strategies. If no strategy works, P t is usually 0.05249 (Mossong et al., 2008;Yang et al., 2020). The proportion of asymptomatic infection is set as 31% according to the results of Nishiura et al., (2020) (i.e. α = 31%).
As the average mortality rate of the patients is 2.01% , which contains asymptomatic patients, we set the mortality rate of symptomatic patients as 3.35% by calculation (i.e. β = 3.35%). T E , T IR , T ID represent the period, these three variables follow a log-normal distribution. The mean value of T E is estimated as 5.1 days (95% CI, 4.5-5.8 days) (Lauer et al., 2020) (i.e. lnT E ∼ Normal (3.25, 0.13)). According to the work of Lewnard et al., (2020), the average time from infection to recovery is 9.3 days (95% CI, 0.8-32.9 days) (i.e. lnT IR ∼ Normal (3.63, 1.81)). The average time from infection to death is 12.7 days (95% CI, 1.6-37.7 days) (i.e. lnT ID ∼ Normal(4.48, 1.53)). Fig. 5 demonstrates the spread of the disease from one person to another. The blue boxes in the figure represent the parameters of the quantified mitigation strategy. Their specific meanings are shown in Table 1. If a susceptible person is infected after contacting the patient and is not quarantined, this person may spread the disease to others. According to whether this person is symptomatic, multiple tests are performed. If the test result is positive, this person will not spread the virus to others, but if tested negative, this person will spread the virus to others according to a certain probability. The detail of how mitigation strategies affect the spread of disease will be introduced in the next section.

Mitigation strategy modeling
To model the different mitigation strategies adopted by different countries, we quantify the strategy from eight aspects, including social distancing, personal protection, throat swab detection capability, quarantine, traffic blocked, random test, test the suspected patient, and the time of executing the mitigation strategy. The symbols and detailed explanations of each element are shown in Table 1.
The social distance is reflected by the daily average number of contacts, expressed as N t (Edmunds et al., 1997;Mossong et al., 2008). Personal protection is reflected in the probability of infection, expressed as P t Lindsay et al., 2009). Time T is a relative quantity, which is calculated from January 1, 2020.
At time t, a mitigation strategy can be expressed as Equation (1). Fig. 4. The disease course model.
m t is the quantitative strategy from time t to the next change in the mitigation strategy. All the mitigation strategies taken by a country over a period are called the mitigation strategy M. M is a collection of multiple m t . The details of the specific strategies of each strategy are presented in Appendix 2.

Evaluation model on economic costs
In this section, an evaluation model on economic costs is constructed, which mainly considers two aspects: the medical expenditure and the GDP loss. The medical expenditure is measured by the sum of medical expenses caused by cured cases and fatal cases during the epidemic. The evaluation model is based on the number of symptomatic patients which we obtain both in real society and artificial society. Since there is no direct relationship between the number of the symptomatic patient and the GDP loss, we establish a mapping relationship between new cases of the symptomatic patient and the GDP loss by using the CO 2 emission as the medium. The economic costs of mitigation strategies in different countries are formulated in Equation (2). C n = Tr n + G n (2) where Tr n represents the medical expenditure, G n represents the GDP loss and n indicates different strategies. The calculation methods of Tr n and G n will be described in detail later.
where n represents mitigation strategies, j is a day, starting from the first day of the outbreak, and 121 represents the period from January 1, 2020, to April 30, 2020. On day j, the number of newly cured cases under the strategy n is denoted as N cjn . Similarly, the number of newly fatal cases under the strategy n is denoted as N fjn . μ λ or ν λ is the proportions of age groups λ in cured and fatal cases respectively (Surveillances, 2020). Ψ cλ or Ψ fλ are the medical consumption caused by treating one cured or one fatal case respectively (Bartsch et al., 2020;Thunstrom et al., 2020). The values of μ λ , ν λ , Ψ cλ and Ψ fλ are shown in Table 2.

GDP loss
In this paper, we use the CO 2 emission as a bridge to establish a mapping relationship between the mitigation strategy and GDP loss. Wang et al., (2020) found that there is a linear relationship between the daily change rate of new cases and the cumulative reduction of CO 2 emission. This paper draws on and improves its fitting indicators to make the linear relationship more obvious. Besides, the CO 2 emission is directly related to social-economic activities, so there is also an obvious linear relationship between the CO 2 emission and GDP (Marjanović et al., 2016). The monthly gridded dataset of CO 2 emission used in this paper is obtained from the Open-source Data Inventory for Anthropogenic CO 2 (ODIAC) inventory developed by the Center for Global    Wang et al., (2020), considering the influence of time and relative changes, we designed four pairs of indicators for CO 2 emission and new case, as shown in Table 3 and Table 4.
Relative changes is considered in Ω 3 j and Ω 4 j . In the following, we focus on how W 4 j and Ω 4 j are calculated, as they are the most complex indicators.
Random and volatile data of new cases show poor fitness if matched with CO 2 emission without preprocessing. Therefore, a 7-day moving window is firstly used in the new case data to weaken the influence of the random factors. The indicator W 4 j of the new case is designed as shown in Table 3, where j represents the jth day and N j represents the number of new case in the jth day.
The next step is to deal with the CO 2 emission data. The CO 2 emission data are detrended by removing a temporal trend over 2016-2019 that best fit the data in the least-squares sense, as Equation (4) shows.
Where m is a month, t is a year and ξ m is the linear regression slope of is the daily average in month m, in the unit of (gram carbon/m 2 /day).
Then, the daily reduction of CO 2 emission is calculated from January to April 2020. We assume that COVID-19 do not contribute considerably to changes in CO 2 emission in December between 2015 and 2019, which serves as a reference change in the absence of COVID-19. The equation is shown as Equation (5). Where j is a day. E j and E 0j are the daily CO 2 emission with and without COVID-19, respectively. E m,2016− 2019 is the daily detrended CO 2 emission in month m as an average for 2016-2019. E 0,2019 and E 0,2015− 2018 are the detrended CO 2 emission in December 2019 and the detrended average for December 2015-2018, respectively. CCF j is the concentration confinement factor, which is proposed in Reference . CCF j is obtained through NO 2 column concentrations and we directly use the CCF j of Wuhan.
Then calculate the indicator Ω 4 j , the calculation formula is shown in Table 4. Where j is a day and 121 denotes the last day for Apr. 30, 2020 (j = 1 for Jan. 1,2020). ΔTER j is the total CO 2 emission reduction due to COVID-19. TER 0 is the total CO 2 emission in January-April without COVID-19. ΔE d is the change in daily CO 2 emission due to COVID-19. E d and E 0d are the daily CO 2 emissions with and without COVID-19, respectively (Equation (5)).
Finally, the CO 2 emission indicator Ω 4 j and the new cases indicator W 4 j are fitted by a regression model, which is shown in Equation (6).
Through plenty of experiments, we compare the fitting results between four pairs of indicators in Tables 3 and 4 and the fitting results are shown in Fig. 6. To account for uncertainty, 95% confidence intervals of the model-averaged coefficients are also shown in the figure. In Fig. 6 (a), (b) and (c), the 95% confidence intervals range is large and R 2 is small, both of which means the linear relationship between the two indicators is not obvious. The results show that Ω 4 j and W 4 j fit best, which are adopted in the evaluation model.

The relationship between CO 2 emission and GDP.
In this subsection, the linear relationship between CO 2 emission and GDP is obtained through data analysis. Since the GDP data are quarterly reported generally in China, we fit the relationship between the daily CO 2 emission and the average daily GDP in the first and second quarters from 2016 to 2019. Table 5 shows CO 2 emission data and GDP data in Wuhan.
We fit the CO 2 emission and GDP in different cities, such as Wuhan, Beijing, Guangzhou and Wenzhou. The fitting results are shown in Fig. 7. E first and E second represent the average daily CO 2 emission in the first quarter and the second quarter respectively. G first and G second represent the average daily GDP value in the first quarter and the second quarter, respectively. Among the three equations with the same color, the first one is the fitting formula; the second one and the third one show the value of R 2 and P respectively, which indicate the quality of the fitting results. According to the results, it is concluded that there exists a linear relationship between CO 2 emission and GDP to some extent.
The relationship between CO 2 emission and GDP in Wuhan is shown in Equation (7) and Equation (8).
According to the above fitting results, the following two steps can be used to evaluate the impact of different mitigation strategies on GDP loss.
1. Based on the fitting results in Fig. 6, the CO 2 emission reduction can be obtained through the cases data.

Table 3
Indicator of new case. Table 4 Indicator of CO 2 emission.
2. Based on the fitting results in Equation (7) and CO 2 emission reduction data, GDP loss can be calculated.

Experiments
Based on the constructed artificial society, we conduct propagation simulations of COVID-19, and evaluate the control effects and the economic costs of mitigation strategies in six countries. Here, 7-group experiments are carried out, among which 6-group experiments are for mitigation strategies in six countries respectively and the last one is for no strategy.
The experiments of each strategy are run 1000 times to alleviate the influence of random factors, such as the infection probability and the length of the incubation period. To actuate an artificial society with millions of population, we carry out experiments based on the Tianhe supercomputer, which is a high-performance computer and ranked 6th in the world in 2020 (Top 500, 2020). All software and models are developed based on XSim-Studio, which is a simulation experiment platform.

Validation and sensitivity analysis
Firstly, validation experiments are designed to calibrate the input parameters of artificial society and validate the evaluation model respectively. Secondly, the sensitivity analysis is carried out to test the influence of input parameters on the selected output indicator (e.g., R 0 , T gen ).
The main output of the artificial society is the incidence data of COVID-19, so we select three indicators that reflect the characteristics of disease propagation to verify the accuracy of the artificial society. These three indicators are reproductive number (R 0 ), generation period (T gen ) and growth rate of the cumulative case (Ċ) (Chang et al., 2020). Many studies estimated these indicators and published the values as shown in Table 6. In addition, we analyze the number of COVID-19 cases and the growth rate of the cumulative case Ċ averages 0.216 per day during the first 3 weeks at the beginning of January 16, 2020 in China.  Then, we validate the accuracy of the evaluation model by comparing the GDP loss based on the evaluation model with the GDP loss based on the trend forecast. Firstly, we obtain the GDP loss based on the evaluation model by evaluating the real epidemic data of COVID-19 in the first 4 months of 2020. Secondly, we obtain the GDP loss based on the trend forecast by using the historical GDP data from 2016 to 2019. The difference between the two kinds of GDP loss is about 9.14%, indicating that the evaluation model is reliable.
Finally, a sensitivity analysis is conducted to test the influence of input parameters on the selected indicators. We choose five parameters in the sensitivity analysis, including P t , α, β, T E , and T IR . The sensitivity of the parameters is reflected by three indicators, including R 0 , T gen andĊ. We applied the elementary effects (EE) method proposed by Morris, (1991) to obtain sensitivity measures σ i and μ * i (Canpolongo and Saltelli, 1997), and the results are concluded in Table 8. The smaller values of σ i and μ * i represent a lower sensitivity of the input parameters. Results reveal that our model is robust to the changes in the input parameters, with the highest sensitivity detected in R 0 and T gen , in response to the incubation period (T E ). Even for the most affected variables, the resulting variations are limited within their expected ranges. The details

Evaluation of control effects
Aiming at exploring the control effects of prevention strategies adopted by 6 countries, including CHN, KOR, IRN, ITA, GBR, and USA, we conduct 7 groups of experiments to simulate the spread of COVID-19, among which 6 groups are for mitigation strategies adopted by these countries respectively while the last group is simulated under no strategy condition. No strategy indicates that COVID-19 spreads freely in the artificial society without any mitigation strategies against the disease. In this paper, the mitigation strategies adopted by CHN, KOR and IRN are collectively called strict patterns. Correspondingly, the mitigation strategies of ITA, GBR, and USA are collectively called loose patterns. The experimental results are drawn in Fig. 8.
The figure mainly shows the data of daily increase in incubation,   Note: The data in the table is the result after rounding. symptomatic patients, and deaths. Through the analysis of simulation under no strategy, as shown in Fig. 8(g), we obtain that the R 0 of COVID-19 in the artificial society is 2.1 by calculation, which is consistent with the results in . This finding indicates that the constructed artificial society and the disease model are reasonable enough to conduct computational experiments (see Table 9. As shown in Fig. 8, the mitigation strategies of the six countries can greatly reduce the infection of people compared with no strategy. Therefore, a major reduction in the number of accumulative incubation, accumulative symptomatic, and accumulative deaths is observed. It can be seen in Fig. 8(a)-(f) that 100 days after the beginning of the epidemic, the number of new cases in the incubation state is almost zero with mitigation strategies, indicating that the spread of the epidemic has been effectively controlled. While the figure becomes zero only after 30 days without any strategies implemented. The phenomenon reveals that the spread of COVID-19 ends earlier under no strategy condition than that under mitigation strategies. This may be because 30 days after the beginning of the epidemic, almost everyone has entered the incubation state under no strategy condition, resulting in no susceptible case entering the incubation period. Among the mitigation strategies adopted by the six countries, the number of new cases in incubation reaches a peak between 33 days and 50 days. Among them, the largest number of new infections occurs in USA strategy, and the smallest is in the KOR strategy.
Obviously, the control effects of strict patterns are generally better than that of loose patterns, which is mainly reflected in the ability to reduce the total number of new cases in incubation, and at the same time, people in all other states can be effectively reduced.

Evaluation of economic costs
We evaluate the economic costs of different countries' mitigation strategies, and the results are shown in Fig. 9. In particular, the economic costs of different mitigation strategies are listed in Table 10.
From the changes in economic costs, it can be seen that the decline in GDP has the greatest impact on economic costs. The curves show that the figures of GDP loss decline rapidly in the early stage, but gradually flatten out in the later stage. At the beginning of the epidemic or the later end of the epidemic, the number of cases is often small, which may lead to relatively large changes in V j in the evaluation model. Therefore, slight fluctuations in the value of GDP loss are observed. Although there are minor fluctuations, the overall downward trend remains unchanged. It is noteworthy the figure on medical expenditure is not large at the beginning, while after a period of time it becomes large. This is because it takes a period of the incubation period for COVID-19-infected patients to enter the symptomatic state and then, they will consume medical resources. Moreover, the death cases also need to go through the symptomatic period, which causes the significant change in medical expenditure to be delayed even further. The decline in GDP loss continues until the end of the epidemic, that is, when the number of new cases reaches zero, the decline stop. The explosive spread of the epidemic ends in about 100 days. However, sporadic people are infected later, so the entire epidemic lasts until about 200 days at the latest.
Comparing the economic costs of the mitigation strategies of different countries in Table 10, it is found that the economic costs of the strict patterns are generally better than that of the loose patterns. The total economic costs of the CHN strategy are 669.697 billion (¥), which is observed a 27.30% drop compared to the economic costs caused by the American strategy. Compared with the ITA strategy which is relatively better among the loose patterns, the CHN strategy also reduces the economic costs by 16.00%. The average loss of the three mitigation strategies in the strict patterns is 735.59 billion (¥), while in the loose patterns the figure is 871.277 billion (¥). The economic costs caused by the strict patterns are 15.57% lower than that of the loose patterns. In the strategy model, the key difference between strict patterns and loose patterns lies in N t and P t , that is, the average number of daily contacts and the probability of infection. The differences between the strict patterns and loose patterns can be reflected from two main aspects: the first is that people in CHN, KOR, and IRN are more likely to cooperate with the governments. Mitigation strategies, such as travel and contact restrictions, work better. While people in ITA, GBR and USA refuse to cooperate. For example, some politicians oppose restrictions and encourage people to resist the ban. Another aspect is the difference in etiquette culture in different countries. The etiquette between people in CHN et al. is relatively subtle, such as nodding, bowing, greeting, and shaking hands, while In ITA et al. face-to-face kisses and hugs are used usually. Such differences lead to different probabilities of infection.
In Table 10, compared with other strategies, the GDP loss caused by no strategy is the least, but it greatly increases the medical expenditure. The least decline in GDP may be due to reduced restrictions on social, industrial, and commercial production activities, and the short duration of the outbreak. Moreover, under the condition of no strategy, the number of symptomatic infections and deaths are significantly greater than that under mitigation strategies, and the medical cost is linearly related to the number of symptoms and deaths. Therefore, under this condition, the medical expenditure will be much higher than that under other strategies. In the loose patterns, the figures of medical expenditure and GDP loss are generally relatively large. The main reason is that the epidemic lasts for a long time since the restrictions of the loose patterns are loose, leading to an increment in GDP loss. The American strategy is the least effective of all strategies. Not only does the GDP decline the most, but also because of the large number of people suffering from the disease, its medical expenditure is also high.

Discussions
We switch the fixed mindset and evaluate the different mitigation strategies based on artificial society from two aspects: control effects and economic costs. Specifically, control effects are evaluated through indicators such as the cumulative number of cases in incubation and the cumulative number of death cases. Economic cost evaluated through medical expenditure and GDP loss refers to the impact of mitigation strategies on economic development. In this paper, three types of data are collected to establish the evaluation model of economic costs, including epidemic data of COVID-19, historical CO 2 emission data and GDP data. Both medical expenditure in the epidemic and the GDP loss are considered in economic costs. Therefore, we provide a more comprehensive evaluation of mitigation strategies from a perspective that is closer to the needs of social development. More importantly, the proposed system model is not only applicable to the COVID-19 pandemic but also applicable to other major pandemics.
From the perspective of control effects, under the strict patterns, the number of new cases in incubation, the number of symptomatic patients, and the number of the deaths are generally lower than that in the loose patterns. Among the strict patterns, the KOR strategy has the lowest cumulative number of infections and is the most effective strategy to control the epidemic. From the perspective of economic costs, countries with strict patterns can reduce the damage to their economies. Among them, the CHN strategy keeps the economic costs of the city to a minimum, followed by the KOR strategy. It is noteworthy that GDP loss accounts for the vast majority of the economic costs (except no strategy condition). Therefore, when studying how to reduce economic costs, we should focus on the impact of mitigation strategies on GDP loss. As the representatives of the loose patterns, GBR and USA have experienced repeated outbreaks of COVID-19, mainly due to the lack of strict control of the epidemic, which leads to the rapid spread of infections. Although the impact of mitigation strategies on economic activities in the loose patterns is relatively small, the long-term economic costs have been even greater because the epidemic has not been controlled. Some countries attach more importance to maintain the stability of economic activities, and the strict prohibition of economic activities may cause major problems in the loose patterns' countries, leading them to adopt the loose patterns' mitigation strategies. However, in the end, they would suffer more economic costs due to the decision. If the governments in these countries have conducted computational experiments supported by our system model and evaluation model, they may take different strategies and the outcome would be different.
In real society, the mortality rate is related to many factors. Through studying the results of daily new cases, we find that the number of deaths and the number of symptomatic patients are highly correlated, and it seems that the number of patients directly determines the number of deaths. However, in real society, many factors affect the number of deaths, such as hospital capacity, government disposal ability, social population age structure, and so on. Obviously, the larger the hospital capacity is, the lower the mortality rate will be. But if the government does not handle it well, the mortality rate may be high even with a large hospital capacity. For example, ITA and GBR have rich medical resources, but data show that the mortality rates in these two countries are much higher than those in other countries. Moreover, the mortality rate of the elderly is usually higher than the young. If a society has a higher proportion of the elderly, the overall mortality rate of the society will also be higher.
The proposed system model based on the ACP method can realize the evaluation of mitigation strategies, which is a good supplement to the healthy city strategy. This method relies on the parallel evolution of artificial society and real society, injects real society data into artificial society, and continuously simulates the control effects of different strategies, and finally selects suitable strategies for different cities and countries. Therefore, this system model can effectively formulate mitigation strategies for urban pandemic outbreaks in a timely and effective manner.

Conclusions
Based on the ACP method, this paper proposes a system model and constructs an artificial society for the evaluation of mitigation strategies of COVID-19. The artificial society of Wuhan is established through the modeling of five elements: geographical environment, population, contact behavior, disease model, and mitigation strategy. Based on the artificial society, large-scale computational experiments of the mitigation strategies of different countries are quickly carried out. Based on the evaluation model proposed in this paper, the mitigation strategies of the 6 countries are evaluated synthetically in terms of control effects and economic costs.
The contributions of this paper mainly include the following three aspects. First, a system model for the evaluation of mitigation strategies has been established. This system model can effectively respond to COVID-19 outbreaks in cities and help for computational experiments, predictions, evaluations, design, and optimization of mitigation strategies, which has a positive effect on urban healthcare development. Second, a comprehensive evaluation model of mitigation strategies has been established from the aspects of control effects and economic costs. In particular, we focus on the use of environmental data CO 2 as a bridge to establish a mapping relationship between mitigation strategies and GDP loss. The model can effectively evaluate the spread of the epidemic under different mitigation strategies and the impact of different mitigation strategies on urban economic development. Third, experiments are carried out on three strategies in strict patterns (CHN strategy, KOR strategy, and IRN strategy) and three strategies in loose patterns (ITA strategy, GBR strategy, and USA strategy). Based on the simulation results, the different effects of the loose patterns and the strict patterns are analyzed and compared. Our work has a significant application prospect in the development of a healthy city, which helps to prevent and control urban epidemics.
Through the analysis of the mitigation strategies of the 6 countries, we found that the mitigation strategies of the strict patterns are superior to the loose patterns in terms of control effects and economic costs. The difference between the two types of patterns lies in the etiquette culture and the degree of implementation of the mitigation strategies, resulting in the different average number of daily contacts and the probability of infection. For example, strategies such as travel bans can effectively reduce the average number of daily contacts, and wearing a mask can effectively reduce the probability of infection. However, people in some countries conduct a weak implementation of strategies such as wearing masks, leading to an increase in the infection probability. These findings can guide the design of future mitigation strategies that starts from reducing the average number of daily contacts and the average probability of infection.
There are some remaining problems in this work that need further research. To enhance the authenticity of the experimental results, it is necessary to realize the interaction between the real society and the artificial society so that the artificial society can be closer to the real society. Therefore, in future works, the artificial society will be improved with more elaborate modeling, including the activities of individuals and the disease spread. Besides, the evaluation model in this paper only considers the control effects and economic costs, but more elements can be considered to make a more comprehensive evaluation. For example, the cognition of the people and the local culture are also important in judging the pros and cons of mitigation strategies.

Declaration of competing interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Modeling of Regular Contact
Generally, the contact behaviors show strong regularity spatially and temporally in the places of work, school, and family. In this paper, the spatiotemporal contact behavior modeling method based on the weighted bimodal network is taken to model the spatial and temporal correlated regular contact relationships. The bimodal network is a network integrated with individual space mobile networks and individual contact networks, the nodes of which include 'agent' nodes and 'spatial' nodes.
An individual schedule is used to describe the spatial movement of agents in an artificial society. Individuals will go to home, workplaces, or schools at different times, and they will have contact behaviors in these places. A contact network can be built based on these contacts.
In the artificial society, individuals (agents) transfer among various locations in the individual space mobile network with the advance of time, and individuals would contact each other when staying in the same region. Note that constrained by the nature of activities and other factors, the number of people that an individual can contact in a place is limited to N C .
Thus, we predefine the probability of an agent contacting another agent s in the same geographic space as p ij . It is assumed that an agent is a i , and the set of agents in the same geographic space is M i , then for anya j ∈ M i , the contact probability for a i to select a i is:

Modeling of Stochastic Contact
Different from regular contacts occurred in places such as family, work, and school, stochastic contacts refer to the behaviors that the schedule cannot accurately summarize and often includes commuting, shopping, leisure, and entertainment. Therefore, it is difficult to collect relevant data due to randomness. But we still can conclude some characteristics of this stochastic contact: (i) the probability of contact increases with the distance between two agents getting closer. For instance, people who live nearby or work together tend to contact at a higher probability; (ii) the contact number of a person obeys power-law distribution. In other words, in a half-day or a day, most people will have contact with very few people, and very few people will have much contact with many people.
Based on these two characteristics, as well as relevant data limitations, the following two assumptions are made: Assumptions 1: Take the subdistrict as the division basis. A network is formed by the stochastic contacts within the subdistrict, which is modeled according to the power-law characteristics. It can be regarded as a community in the contact network of the city.
Assumptions 2: The contact number across subdistricts obeys the 'Gravity -law'. That is, there are more contacts between subdistricts that are closer. And a subdistrict with more population tends to have more contacts with other subdistricts. Therefore, we propose the Scale Distance Degree (SSD) model to generate the stochastic contact network. In the following, we will explain three mechanisms involved in the algorithm:

Community size and distance
On the basis of the Gravity-law, the connections of nodes between different subdistricts are determined by the sizes of the subdistricts, and the distance between them.
That is to say, the larger the scale of the subdistrict is, or the smaller the distance between the subdistricts is, the higher the probability of selecting the subdistrict will be. The subdistrict selection probability P v by a node in subdistrict u is where S v is the size of the subdistrict v; d (u, v) is the distance between subdistrict u and v; α is the impact index of subdistrict size; β is the impact index of distance; C is the set of all the subdistricts.

Preferential attachment
If a new contact happens between two individuals in the same subdistrict or two different subdistricts, the probability that an individual is chosen is proportional to the contact number that the individual already has. The probability of an individual j in subdistrict v is P vj , it can be calculated as: The number of individuals in the artificial society is N = 9785388. Based on the work of Dong et al. (Dong et al., 2019;Edmunds et al., 1997;Mossong et al., 2008), the parameters are set as α = 1.2, β = − 1.5, and the average degree of this network is 13.4. There are 172 subdistricts, and the final contact number in this city is 24,463,470. The result is a network that consists of 9785388 nodes and 24,463,470 edges. As Fig. 1 shows, the degree distribution of this network follows the power-law. The degree distribution can be fitted with a line under the log-log scale as shown in Fig. 1. The coefficient of the line in the figure is -3.61. That is, the power-exponent of the power-law distribution is 3.61. 3 From January 20, information of new cases from each province will be released every day. 2020. 1.21 Policy free refund related to Wuhan was announced 2020. 1. The Department of Disease Control and Prevention of the Republic of Korea raised the alert level of infectious disease disaster crisis from 'concern' to 'attention'. 2. Passengers with temperature over 37.5 • C or symptoms of respiratory diseases will be separately confirmed in their health status and whether they have been in contact with the cases, and quarantined after taking into account epidemiological information such as residence and place of visit. 2020. 1.27 The South Korean government's alert registration for COVID-19 has been raised.

2020.2.2
It announced that foreigners who have visited or stayed in Hubei province for within 14 days will be denied entry from February 4. 2020.2.4 The 21st Century Hospital in Gwangju, South Korea, has been closed with 121 patients and medical staff locked inside. Inpatients and medical staff on some floors are classified as high risk groups. On that day, 84 people were classified as low-risk and transferred to the dormitory group of Gwangju Fire Fighting School, an isolation facility. 2020. 2.19 Seven hospitals in South Korea have suspended or closed their emergency rooms due to the outbreak, the Ministry said. 2020.2.20 1. Close contact tracing of confirmed patients. 2 The mayor urged Daegu residents to stay at home.

2020.2.21
The Prime Minister has designated Daegu city and Qingbei Ching-tao County, which have seen a large increase in confirmed COVID-19 cases, as key epidemic management areas. Special epidemic prevention measures have been taken to provide hospital beds and human and material support. 2020. 2.22 Speaking to the people, the prime minister urged them to suspend religious activities held indoors or outdoors in crowded areas, and urged them to cooperate with the government's epidemic prevention efforts 2020.2.23 1. President Moon Jae-in of the Republic of Korea presided over the Novel Coronavirus epidemic response meeting in the Office building in Seoul, indicating that the government decided to elevate the epidemic alert to the highest level and strengthen the response measures 2. The Ministry of Education of the Republic of Korea has announced that all schools nationwide will be postponed until March 9.
(continued on next page) South Korean Prime Minister Hyeon-seok announced that the city of Gyeongsan would be designated as a special infectious disease control zone, banning the export of masks and restricting the purchase of masks from Monday. 2020.3.6 1. South Korea announced that it would end the visa-free system for Japanese people during their short-term stay, stop issuing visas, and raise the travel alert to Japan. 2020. 3.15 Moon jae-in declared Daegu and Gyeongshan, North Gyeongsang Province, Qingdao county and Fenghua County, which have been hit hard by the epidemic, as special disaster areas 2020.3.19 1. The scope of South Korea's immigration control is extended to all countries and regions in the world. 2. Moon promised 50 trillion won in emergency economic measures for small businesses. 2020. 4.4 The South Korean government decided to extend the "social distance restriction period" by two weeks until the 19th Policy in Iran. The Iranian government has announced a ban on Chinese citizens entering Iran 2020.2.28 1. Iran's Health minister Saeed Namaki has announced that all schools in the country will be closed for three days 2. The Iranian Football Association has decided to continue all football matches 2020.2.29 1. A team of five volunteers from the Red Cross Society of China arrived in Tehran, the capital, to provide assistance to Iran, and took with them some medical supplies provided by The Chinese side 2020.3.3 1. To prevent novel Coronavirus from spreading through the prison, the Iranian government temporarily released more than 54,000 prisoners 2. The First deputy speaker of Iran's Islamic Parliament, Massoud Pezeshkian, claimed that the health ministry had provided false case data 2020. 3.7 Iran's Minister of Information and Communications Technology, Mohammad Javad Azari Jahromi, said on Twitter that everyone would be given 100 GB of free Internet traffic to encourage them to stay at home 2020.3.13 1. The General Staff of the Army of the Islamic Republic of Iran has announced that the army will take to the streets in the next 24 h to ensure the closure of all commercial centers, streets and markets throughout the country 2. Iran will close most of its petrol stations from The 14th to prevent people from driving out 3. All entrances and exits from Tehran to the field are equipped with checkpoints End of March in 2020 1. Iran announced a "social distancing" program until April 8, after which some people will be allowed to return to work and some academic, cultural and religious sites will be opened Policy in Italy. Ministry of Health and must be quarantined at home or in hotels 2. People who have been in contact with a confirmed patient will be placed under mandatory quarantine for 14 days 3. Italian Prime Minister Giuseppe Conte announced that all access to the affected areas would be closed, and that work and sports would be suspended 4. Health Minister Roberto Speranza said the local health ministry would follow a trustee home quarantine system to monitor quarantines closely and would apply the same measures to those in difficult conditions 5. The Italian army and law enforcement are responsible for enforcing the blockade 6. Schools in ten cities in Lombardy, in Veneto and in Emilia Romagna were closed 7. All public events will be canceled, and commercial activities will be suspended or terminated before 6 o'clock 8. Train services were suspended in the worst-affected areas, with no stops at Codonio, Maleo and Casal Pustelengo stations 9.Patients with symptoms are advised to dial emergency number 112 instead of going directly to hospital to reduce the spread of the disease 10.The Italian Ministry of Health has set up a website and a hotline of 1500 to provide the public with the latest information on the outbreak and reports of suspected cases 11.The Italian Cabinet announced new measures to control the spread of the disease, including quarantine for more than 50,000 people in 11 northern cities 12.Public gatherings were banned, all sports and religious activities were cancelled, and schools, bars and other places were closed. 13.Food, medicine and other essential supplies will be distributed to residential areas to reduce people's travel 2020.

Appendix 3
The strategy of the six countries are denoted as M 1 (China), M 2 (South Korea), M 3 (Iran), M 4 (Italy), M 5 (Britain), M 6 (America). Each strategy includes several m t and m t is consisted of 8 different elements, as shown in Equation (4).
In the normal condition, N t and P t are set as 13.4 and 0.05 according to the work of Mossong et al. (Edmunds et al., 1997;Mossong et al., 2008). N t is the average number of contacted persons during the day, which is corresponded to the actual measure. Let N t ′ be the actual number of social contacts of an individual. N t ′ is assumed to be a discrete variable and obeys Normal distribution, with a mean value of N t . The method of box-Muller (Banks et al., 2007) is used to generate N t ′ , as shown in Equation (5): In which N t is the mean value, σ is the standard deviation, r 1 and r 2 are uniformly distributed random numbers between [0,1]. According to the work of Edmunds et al. (1997), σ is estimated as 8.5. C t quantifies the capability of throat swab testing. It is limited by the technical capacity, financial support, and quarantine policy of each country. For the population of the artificial society is about 10 million, we mainly focused on the maximum test number per 10 million people until April 30. Therefore, according to the statistical data from the work ofRichied et al. (Ritchie et al., 2020), the test capability per 10 million people on April 30 for each country were estimated in Table 1. When the disease began to spread, the testing capacity gradually increased over time to meet the demand. Among them, the testing capability of Iran improved a lot after April 30. However, before that time, the number of tests (C t ) is clearly at a relatively low level. So C t from Iran was the lowest among all countries in the period considered in this paper (from the end of December 2019 to the end of April 2020).
As for C t , according to the data disclosed by the countries, it could be assumed that the daily testing capacity increased over this period of observation. In this paper, we assume that C t increased linearly during this period: Let t 0 be the time when the first case is diagnosed. T E is the duration from t 0 to the end of observation, T is the duration from t 0 to t, C t denotes the test capability on time t. C TE represents the test capability at the end of observation. C TE is set according to Table 1. Maximum of the test capability per 10 million people of six countries.
Q t quantifies the measure states that the persons who have contacts with a diagnosed person would be quarantined. B t quantifies the measure of area blockade that the spreading across subdistricts is invalid. By adopting such a measure, it is possible to effectively stop the spread of large areas in the early stage.
R t means random sampling tests for areas with severe epidemics. The measure was implemented by South Korea initially. Here we only consider the implementation of this measure two from South Korea.
S t quantifies the measure of throat swab testing for suspects. The measure is entirely determined by the government's policy and medical resources. It is also influenced by the limitation of test capability.
T is the time delay from the occurrence of the first patient to the implementation of the current measure.
As time goes on, the mitigation strategies of different countries would change according to the specific domestic situation. Assuming that the strategy changes at times t 0 , t 1 , t 2 and so on, and the mitigation strategy of a country for a long period of time can be denoted as: In which m t i indicates quantified strategy for a period of time. The project of Oxford COVID-19 Government Response Tracker initiated by Hale et al., (2020) has collected the government response to COVID-19 from 180 countries. We analyzed the measures from the end of December 2019 to the end of April 2020 taken by six countries (China, South Korea, Iran, the United Kingdom, Italy, and the United States), and extracted one strategy for each country. The six countries are selected for their typical and different strategies.
The measures of strategies from six countries were introduced and quantified based on the statistics of governments' responses (Lewnard et al., 2020). M 0 represents the quantified result of no strategy and it is shown in Table 2. The details of the quantified strategies are explained in the following.

Strategy China (M 1 )
Wuhan is the first city in China to suffer from the epidemic and the strategies in Wuhan is representative. Fig. 2 shows the strategy of Wuhan. On January 20, the Chinese Health Commission released the information that the disease could be transmitted by human beings. Then the strict measure of city lockdown was carried out, which attracted great attention from the public, resulting in the rapid decrease of the average number of contacts and infection probability. So starting on January 20,N t and P t decreased rapidly. The minimum of N t after the closure of the city on January 24 is estimated to be about 4 according to the average household population in the statistical data and daily purchase of necessities per person. From January 20 to January 24, N t was considered as the average number of contacts under normal conditions and closed city results. The minimum of P t is set as the minimum value in Eastern strategies, which is estimated as 0.0005. P t is set to drop linearly from January 20 to February 2, considering that the information about the pandemic would need some days to spread to all the public. The quantitative results of all measures of China's epidemic mitigation strategy from December 30 to April 30 are shown in Table 3.

Strategy South Korea (M 2 )
The strategy of Souch Korea is shown in Fig. 3. On January 20, South Korea raised its alert level and introduced timely and rigorous testing, quarantine, and patient isolation measures, which attracted great attention from the public, resulting in the rapid decrease of the average number of contacts and infection probability. So starting on January 20, N t and P t decreased rapidly.
On January 27, the alert level was raised again, so N t and P t decreased again. By February 23, the most stringent quarantine measures were in place, and the measure of random testing to the public was carried out.
The alert level was upgraded on February 23, and the most stringent lockdown measures were adopted on February 25. The minimum N t after the closure of the city was estimated as 4 according to the average household population in the statistical data and daily purchase of necessities. From January 9 to February 25, it was considered as a linear decline process.
It was considered that P t reached the minimum value on February 23, which was set as 0.0005 according to the estimated minimum value of Eastern strategies. The public would have a few days to respond to the information, the P t was set to decline from January 9 to 23 gradually. Table 4 shows the quantified results of all measures of strategy South Korea from January 9 to April 30.

Strategy Iran (M 3 )
Strategy of Iran is shown in Fig. 4. N t and P t were reduced due to the outbreak in Iran on February 19, which attracted public attention. International traffic control began around February 27, and all schools were closed, so N t and P t were reduced again. By March 13, when the most stringent quarantine measures were in place, N t and P t reached the lowest.
The minimum N t after the closure of the city was estimated as 4 according to the average household population in the statistical data and daily purchase of necessities.
Note that P t reached its minimum value on March 13, which was set as 0.0005 according to the estimated minimum value of Eastern strategy. The general public needs a few days to respond to the information, so the P t was set to decrease from February 19 to March 13 gradually.

Strategy Italy (M 4 )
Strategy of Italy is shown in Fig. 5. N t and P t started to reduce slightly for the outbreak in Italy on January 31. Many measures about quarantines and blockages began around February 22, so N t and P t rapidly decreased starting from February 22. By March 7, when the most stringent lockdown measures were in place, N t and P t reached their lowest levels. The minimum of N t after the closure was calculated as 6 according to the average household population in the statistical data and daily purchase of necessities.
It was considered that the P t reached the minimum on March 7, which was set as 0.001 according to the estimated minimum value of western strategy. Set P t gradually decreased from January 31 to March 7. Table 6 shows the quantified results of all measures of the strategy Italy from January 31 to April 30.

Strategy Britain (M 5 )
Strategy of Britain is shown in Fig. 6. N t and P t started to reduce as a result of the outbreak in the United Kingdom on January 31. They dropped rapidly after the school closures and public closures began around March 18. By March 23, when the most stringent lockdown measures were in place, N t and P t reached their lowest levels.
The strictest isolation measures were taken on March 23. The minimum of N t after the closure of the city was calculated as 6 people according to the average household population in the statistical data and daily purchase of necessities. From January 31 to March 23, N t was considered to linearly decreased.
Note that P t reached its minimum value on March 23, which was set as 0.0001 according to the estimated minimum value of western strategies. P t was set to decrease from January 31 to March 23 gradually. Table 7 shows the quantified results of all measures of the UK vaccination strategy from January 31 to April 30.

Strategy America (M 6 )
Strategy of America is shown in Fig. 7. N t and P t were reduced slightly for the emergence of the epidemic in the United States on January 21. By March 4, when the CDC began to advertise people to avoid gathering contacts, N t and P t were further reduced. On March 30, when the most stringent lockdown measures were carried out, N t and P t , reached the lowest levels.
The minimum daily contact number after the closure of the city was estimated to be 6 according to the average household population in the statistical data and daily purchase of necessities. From January 21 to March 30, N t decreased linearly.
It was considered that P t reached the minimum on March 30, which is set as 0.001 according to the estimated minimum value of western strategy. P t was set to gradually decrease from January 31 to March 7. Table 8 shows the quantified results of all measures of the strategy America from January 31 to April 30.

Appendix 4
The elementary effects (EE) method proposed by Morris are used in our sensitivity analysis. It focuses on identifying a few significant input parameters from numerous input parameters in a model using very few calculations. For a given value x of X, the EE of the ith input parameter can be defined as Equation (8).
where x is one sample of input parameter vector X and g(x) is the corresponding model output, e i denotes a vector of zeros while its ith component is equal to 1, Δ i is a step length of x i moving along the X i axis, x + e i Δ i is another sample by changing the ith input parameter fromx i to x i + e i Δ i and g(x +e i Δ i ) is the corresponding model output. Two sensitivity measures, μ * i and σ i (Canpolongo and Saltelli, 1997), are used to assessing sensitivity and they are defined in Equations (9) and (10).
μ * i and σ i are the mean of the |EE i | distribution and the standard deviation of the EE i distribution respectively. Since EE i measures the influence of X i on the model output at a local point, the mean μ * i can be employed to measure the overall influence of the X i on the model output. The standard deviation σ i measures the ensemble of the input parameter's effects including nonlinear effect or interactions with other input parameters.
We choose five input parameters, including P t , α, β, T E , and T IR , and three output indicators, including R 0 , T gen andĊ in the sensitivity analysis. By consulting the literature, we obtain the range of these input parameters (Lewnard et al., 2020;Nishiura et al., 2020;Yang et al., 2020) as shown in Table 9. The distribution of the parameters is shown in Fig. 8 (d).

Table 9
The results of sensitivity analysis  Table 9 summarises the results of the global sensitivity analysis using the Morris method, with r = 20 repeats and k = 5 input parameters, resulting in 120 parameter combinations i.e., r (k+1). When estimating R 0 and T gen for each parameter combination, we run simulations n = 12,000 times. For another output indicator Ċ , we run simulations n = 500 times for each parameter conmibation, averaging the results over these runs before the computations of the sensitivity effects.
The results in Table 9 are visualized in Fig. 8. The small values of σ i and μ * i indicate the low sensitivity of the parameters. From Fig. 8, we know that R 0 and T gen are most sensitive to the changes in the incubation period (T E ), but these two parameters still stay within the expected ranges (e.g., R 0 varies between 1.921 and 4.054, and T gen varies between 8.283 and 11.902). Ċ shows the small gloabal sensitivity to all input parameters. In summary, the analysis shows that the model is robust to the changes in the input parameters, with the highest sensitivity detected in R 0 and T gen , in response to the incubation period (T E ). Even for the most affected variables, the resulting variations are limited within their expected ranges.