Quantifying the Temporal and Spatial Spread of COVID-19: Empirical Evidence from Shanghai

Haowen BAO, Zishu CHENG, Yuying SUN, Yongmiao HONG, Shouyang WANG

Journal of Systems Science and Information ›› 2024, Vol. 12 ›› Issue (3) : 309-322.

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Journal of Systems Science and Information ›› 2024, Vol. 12 ›› Issue (3) : 309-322. DOI: 10.21078/JSSI-2023-0028
 

Quantifying the Temporal and Spatial Spread of COVID-19: Empirical Evidence from Shanghai

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Abstract

The worldwide spread of COVID-19 has caused a grave threat to human life, health, and socio-economic development. It is of great significance to study the transmission mechanism of COVID-19 and evaluate the effect of epidemic prevention policies. This paper employs a spatial dynamic panel data (SDPD) model to analyze the temporal and spatial spread of COVID-19, incorporating the time-varying features of epidemic transmission and the impact of geographic interconnections. Empirical studies on the COVID-19 outbreak in Shanghai during early 2022 show that the intra-regional transmission of COVID-19 dominated the cross-regional one. Additionally, strict policies are found to effectively reduce the transmission risk of COVID-19 and curb the spillover effect of the epidemic in Shanghai on other regions. Based on these results, we provide three policy suggestions. Furthermore, this research methodology can be extended to investigate other infectious diseases, thereby providing a scientific framework and theoretical basis for evaluating the spread risk of pandemics and formulating appropriate strategies.

Key words

COVID-19 / spatial econometrics / epidemic prevention policy / dynamic

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Haowen BAO , Zishu CHENG , Yuying SUN , Yongmiao HONG , Shouyang WANG. Quantifying the Temporal and Spatial Spread of COVID-19: Empirical Evidence from Shanghai. Journal of Systems Science and Information, 2024, 12(3): 309-322 https://doi.org/10.21078/JSSI-2023-0028

1 Introduction

Corona Virus Disease 2019 (COVID-19) has caused multiple epidemic waves to many countries since its initial outbreak in December 2019. The World Health Organization (WHO) designated the COVID-19 outbreak as a global pandemic on March 11, 2020. COVID-19 has not only posed a grave threat to human life and health in various countries and regions around the world, but also hindered the normal operation of world economic activities[13]. As of December 6, 2022, there have been approximately 350, 000 confirmed cases of COVID-19 in China, resulting in a cumulative death toll of 5, 235. Globally, the number of confirmed cases has exceeded 640 million, with over 6.63 million deaths1. COVID-19 has become the most widespread global pandemic in almost a century. Therefore, it is of great practical significance to study the transmission risk of COVID-19 and the impact of epidemic prevention policies on its spread.
1Data source: Wind database.
The COVID-19 pandemic has had a huge impact on economic activities, social production and people's lives, drawing the attention of scholars and policymakers worldwide. There are a large number of relevant studies, the main research areas include: Forecast of COVID-19[410], the economic impact of the epidemic[1114], the impact of the pandemic on financial markets[1517], politics and the pandemic[1820], and the management of the epidemic[2124]. Many studies have also focused on the transmission mechanism and risk of COVID-19. For example, Kraemer, et al.[25] studied the spillover risk of the epidemic in Wuhan and found that local prevention and control measures such as strict social isolation played an important role in controlling the spread of the epidemic. Jia, et al.[26] used population flow data to develop a spatio-temporal "risk source" model for epidemic transmission, which can predict the distribution of confirmed cases and can also be used to evaluate the change of epidemic transmission risk in different locations over time. So, et al.[27] studied the transmission risk of COVID-19 by the network analysis method. Compared with the method that only relies on confirmed case data, the network analysis method can make full use of the connectivity of the epidemic transmission network graph, thus providing a more powerful and direct visualization of the COVID-19 pandemic risk.
The COVID-19 pandemic has highlighted the importance of epidemic prevention policies in hindering the spread of the virus. Compared to other infectious diseases, COVID-19 has a more complex transmission mechanism, spreads faster, and carries a higher risk. Therefore, when studying the impact of epidemic prevention policies on the spread of the virus, it is essential to consider various factors such as virus transmission, human mobility, spatio-temporal characteristics, policy scenarios, and social development. Several studies have examined the impact of epidemic prevention policies on the spread of COVID-19. For instance, Block, et al.[28] applied the social network model to the study of epidemic transmission and evaluated the impact of three different strategies based on social distancing on epidemic prevention and control. The results show that reducing contacts at the social network level can greatly improve the effectiveness of epidemic prevention policies and reduce the risk of epidemic transmission. Fanelli and Piazza[29] analyzed the temporal dynamics of COVID-19 in China, Italy and France, and established a simulation experiment to study the impact of Italy's strict control measures on the epidemic. This study shows that strict prevention and control measures can reduce the infection rate of the virus, which in turn causes a quench of the epidemic peak and the decline of the death rate. Qian, et al.[30] introduced a new implied social distance index (ISD index) based on an extended varying coefficient SIR (vSIR) infectious disease model, to each country or region, which can quantify the effects of national quarantine policies effectively. These studies provide important theoretical support for formulating epidemic prevention policies and controlling the spread of the epidemic. However, none of them simultaneously considered the time-varying characteristics of epidemic transmission, the influence of geography, social environment and other factors. To solve these problems, Han, et al.[31] used the spatial dynamic panel data (SDPD) model and conducted a multiscale geographic analysis of the spread of COVID-19 in a policy-influenced dynamic network to quantify COVID-19 importation risk under different policy scenarios using evidence from China.
With the development of the COVID-19 pandemic, the virus has undergone several rounds of mutation, resulting in significant changes to its transmission characteristics and mechanism. Omicron, for example, is more transmissible and causes less severe disease compared to other variants. Note that China's epidemic prevention policies are constantly being optimized and adjusted, and the risk of virus transmission may vary greatly under different epidemic prevention and control policies. Therefore, it is of positive practical significance to study the transmission mechanism of COVID-19 at the present stage and the impact of China's epidemic prevention policy adjustment on the spread of epidemic. As far as we know, there is no literature studying the temporal and spatial spread of COVID-19 in Shanghai, 2022, and its spillover effect. In this paper, we use the SDPD model proposed by Han, et al.[31] to study the transmission mechanism of COVID-19 during the pandemic in Shanghai in 2022 and evaluate the spread risk of the epidemic under different policy scenarios. In our model, a geographical network composed of 31 provinces in China (excluding Hong Kong, Macao and Taiwan) is constructed to study the COVID-19 spread between different regions. Compared with traditional econometric models, SDPD model adopts time-varying spatial weight matrix and parameter settings, so it can capture the characteristics of epidemic transmission in terms of time and space simultaneously. Furthermore, our model comprehensively consider the factors that may affect the transmission risk of COVID-19, such as the frequent mobility of people, the uneven population density, and the unbalanced distribution of medical resources among different provinces and cities in China. In addition, we also study the spillover effect of the epidemic outbreak and epidemic prevention policies in Shanghai on other regions through human mobility and geographical links.
The main contribution of this paper are as follows: First, our method constructs a quantitative research framework for studying the transmission mechanism of COVID-19 from the perspective of spatial econometrics. This framework contains the temporal and spatial characteristics of COVID-19 spread and other factors that affects the spread of the virus. More importantly, our method is not only applicable to the transmission of COVID-19, but also can be extended to other infectious diseases, offering a scientific research methodology for addressing potential public health emergencies in the future.
Second, the empirical study shows that the transmission risk of COVID-19 within a region is greater than that across regions. Therefore, differentiated epidemic prevention policies should be adopted for different regions, rather than "one size fits all", which provides scientific basis and theoretical support for formulating appropriate and precise epidemic prevention measures. For example, policymakers should focus on the control of the epidemic spread within the region (province, city, district, etc.), while adopting relatively loose ones cross the regions.
Furthermore, our method can evaluate the implementation effect of epidemic prevention policies. The empirical results show that the risk of intra-regional and cross-regional transmission of the epidemic and the spillover effect have been effectively reduced in a short period of time after the implementation of rigorous epidemic prevention and control measures such as lockdown and quarantine in Shanghai.
The remainder of this paper is organized as follows. Section 2 introduces the spatial dynamic panel data model. Section 3 analyzes some statistical data about COVID-19 and sorts out of the time line of its outbreak in Shanghai. Section 4 is the empirical analysis and provides three policy suggestions. Section 5 concludes the paper.

2 Methodology

One of our aims in this paper is to quantify the transmission risk of COVID-19 within and across provinces in China. However, due to the differences in geographical location, population density, human mobility and other aspects in different regions, the traditional linear regression model cannot meet the modeling needs. This inspires us to use spatial econometric models, which can capture the spatial correlation and spatial heterogeneity of the data. Spatial econometrics is defined as a range of methods for studying various properties caused by space in the statistical analysis of regional scientific models[32]. In addition, the spread of COVID-19 in different regions is closely related to the local epidemic prevention policies, which are dynamically adjusted in China. And the transmission characteristics of the virus will change with the variation of the virus strain, the temperature, and the population immunity. Therefore, it is necessary to consider time-varying coefficients and spatial weight matrices in spatial econometric models to capture these dynamic characteristics.
In this paper, we introduce the spatial dynamic panel data (SDPD) model to study the transmission mechanism of COVID-19 and apply it to study the outbreak of COVID-19 in Shanghai in 2022. The SDPD model can be expressed as
Yt=λ(t)WtYt+γ(t)Mtyt+ρ(t)Yt1+ξtϕ(t)+Xtβ1+Cβ2+lnαt+Ut,
(1)
where Yt denotes the spread degree of COVID-19 in different regions at time t. For example, we could set Yt as the daily number of newly confirmed cases of COVID-19 outside Shanghai. Shanghai as the epicenter is modeled separately as a regressor with its daily newly confirmed cases of yt. Wt is the time-varying spatial weight matrix, which describes the spatial heterogeneity and correlation of each region. In this paper, Wt is the population flow matrix among 30 provinces from Baidu Mobility, representing the spatial spillover effect by human mobility. And the data from Baidu Mobility has been widely used in the literature about COVID-19, such as [3335]. Wt can also be defined as a constant matrix, such as the matrix based on the distance between provincial capitals or the matrix based on the concept of proximity. λ(t) is the estimated time-varying coefficient, which can be used to characterize the risk of cross-regional transmission of COVID-19. γ(t)Mtyt represents the spillover effect of COVID-19 in Shanghai, where γ(t) is the time-varying coefficient to measure the spillover risk of the epidemic and Mt characterizes the spatial relationships between epicenter and other regions. Specifically, Mt is set as the vector of population flows between Shanghai and other provinces. Yt1 is the first-order lag of Yt and denotes the spread degree of COVID-19 at time t1. And ρ(t) denotes the impact of Yt1 on Yt, which measures the risk of epidemic transmission within the regions.
Besides, ξtϕ(t) represents the scale effect of tourism inflow in these regions, and ξt is set to be the number of tourist arrivals of each region. Xt denotes the time-varying exogenous variables that affect the spread of COVID-19, such as the temperature which affects the viral activity. And C is a constant variable related to the spread of the epidemic, such as medical resources and population density of each province. These variables do not change over time in a short period of time. lnαt is the time effect and Ut denotes the disturbances.
Remark 1   Model (1) can not only be applied to studying the system containing the provinces in China, but also to studying the spread of the epidemic within a province or a city. In these cases, we should consider the cities in the province or the districts in the city. In addition, when the imported cases from abroad have a great impact on the spread of COVID-19 in China, the external input risk term including imported cases, inbound flights and other variables can also be added to our model. In this paper, considering that China's epidemic prevention policy has strict restrictions on inbound travelers and transnational packages, the risk of external importation is relatively small, so it is not included in model (1).
Remark 2   If the purpose of our study does not concentrate on the spillover effect of COVID-19 outbreak in epicenter on other regions, or there are no regions with serious epidemic outbreaks in the sample period of the study, model (1) can be simplified as follows: Yt=λ(t)WtYt+ρ(t)Yt1+ξtϕ(t)+Xtβ1+Cβ2+lnαt+Ut, which deletes the spillover effect term γ(t)Mtyt. In this case, Yt represents the spread of COVID-19 in all areas. For example, to study the spread of COVID-19 in the United States, note that the spread of COVID-19 was similar across states. Therefore, there is no region in the U.S. like Shanghai that has a great impact on other regions. In this case, Yt can be set as the vector containing the daily numbers of newly confirmed cases of COVID-19 in 51 states.

3 Data Description

In this section, we analyze the data on the epidemic transmission and population flow during the COVID-19 outbreak in Shanghai. In 2022, the COVID-19 epidemic in China continues to fluctuate, with regional outbreaks occurring. For example, the epidemic in Shanghai, which began at the end of February, 2022, resulted in over 600, 000 infections2. Note that infections include asymptomatic COVID-19 patients who do not show any symptoms, such as fever and cough, but their tests for the novel coronavirus are positive. in three months. Most of China's provinces and cities have reported cases related to Shanghai's patients. The COVID-19 outbreak in Shanghai is also the most severe epidemic in China since the outbreak in Wuhan in early 2020, which poses great challenges to epidemic prevention and control in China and provides valuable reference for the subsequent adjustments of the policies. Therefore, we intend to study the COVID-19 spread in China during its outbreak in Shanghai.
2The infections means people who have been infected with the COVID-19.
Table 1 summarizes the important events after the COVID-19 outbreak in Shanghai in chronological order. Although the first local confirmed case in Shanghai was detected on March 1, considering the incubation period and transmission process of COVID-19, the epidemic outbreak in Shanghai should have started to spread silently in late February or even earlier. As a result of this, the starting time of the sample is set to be February 1. It can be observed from Table 1 that since the implementation of strict epidemic prevention polices in Shanghai on March 28, the number of infections on April 22 showed a trend of continuous decline, which means that the growth trend of the epidemic in Shanghai has been effectively contained in less than a month. And Shanghai cut off all COVID-19 transmission chains in communities on May 17, which indicates that the epidemic in Shanghai was coming to an end after nearly two months of "life on pause".
Table 1 Key events during the COVID-19 outbreak in Shanghai
Time Event
March 1 The first confirmed case of local transmission with no clear source of infection appeared in Shanghai
March 24 29 newly confirmed cases and 1, 580 asymptomatic cases, with more than 1, 000 new virus carriers in one day for the first time
March 28 The phased lockdown of Pudong and Puxi
March 29 326 newly confirmed cases and 565 asymptomatic cases, with more than 5, 000 new virus carriers in one day for the first time
March 30 Shanghai adopted a strategy of "citywide static management and COVID-19 test"
April 4 268 newly confirmed cases and 13086 asymptomatic cases, with more than 10, 000 new virus carriers in one day for the first time
April 13 The COVID-19 outbreak in Shanghai has reached the peak, with 2, 573 new confirmed cases and 25, 146 asymptomatic cases
April 22 The number of infections in Shanghai has continued to decline
April 27 Limited opening of areas which hit zero-COVID status at the community level
May 15 Shanghai announced a phased resumption of commerce and market
May 17 The 16 districts in Shanghai have hit zero-COVID status at the community level
May 31 Social production and people's daily lives returned to normal
Note: The first column of this table refers to the time line of COVID-19 in Shanghai from March 1 to May 31. Only some important events are listed in the table.
Table 2 shows the descriptive statistics of the daily confirmed cases in Shanghai and China. To compare the difference of COVID-19 in China and other countries, we also report the confirmed cases in the U.S., the U.K., Germany and Japan in this table. Several observations can be obtained from Table 2. First, the maximum of confirmed cases in Shanghai and China are close, which indicates that Shanghai was the epicenter of COVID-19 during a period of time. Second, the gap between mean and median of the confirmed cases is large in Shanghai and China, but small in other countries. This implies that the COVID-19 in China is sometimes well controlled, and sometimes there is an outbreak. And spreads of COVID-19 in other countries were always severe. Third, all these descriptive statistics show that, compared with other countries, China's epidemic prevention and control has achieved remarkable results.
Table 2 The descriptive statistics of data
SHH CHN US UK GER JPN
min 4 27 8941 4988 6453 0
max 5489 5659 576521 109288 307901 106609
mean 494 983 77203 40607 136684 50995
median 56 354 48326 37561 135744 47212
std 947 1092 80553 29041 83980 22281
Note: The sample starts from February 1 to May 31. And the results are rounded to an integer.
Figure 1(a) shows the daily number of newly confirmed cases and the cumulative number of confirmed cases in Shanghai from February 1 to May 31, 2022. It can be seen from Figure 1(a) that during the COVID-19 outbreak in Shanghai, the spread speed of the epidemic was relatively slow in the early stage, but later entered a period of rapid growth. With the gradual effectiveness of epidemic prevention and control measures, the spread of the epidemic was effectively contained, leading to a gradual decrease of the confirmed cases. Figure 1(b) shows the daily number of new confirmed cases and the cumulative number of confirmed cases in China (excluding Hong Kong, Macao and Taiwan) during the same period. Figure 1(b) implies
Figure 1 Daily number of newly confirmed cases and cumulative number of confirmed cases
Note: The solid blue lines in the figure refer to the newly confirmed cases, and the dashed orange lines refer to the cumulative confirmed cases.

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that the growth rate of confirmed cases in China was relatively slow in early March, and then grew rapidly, which is similar to that in Shanghai. As the spread of COVID-19 in Shanghai was brought under control, the epidemic in China was also contained.
Figure 2 displays the outflow index of people from Shanghai during the period from February 1 to May 31, sourced from Baidu Mobility Data. Two main observations can be found from Figure 2. First, the outflow of people from Shanghai declined rapidly after the COVID-19 outbreak in Shanghai. Specifically, the outflow index fell below 1 after the phased lockdown of Shanghai on March 28. And the average index in April was just 0.439, down 91.27% from February's average of 5.033. It was not until mid-May, i.e., Shanghai announced a phased resumption of commerce and market on May 15, that the index began to rise. Second, compared with Figure 1(a), we observe that there is a negative correlation between the cross-regional movement of people and the spread of the epidemic. This inspires us to employ the daily flow of people among different provinces to construct a geographical network to capture the spatial transmission characteristics of COVID-19. In addition, the exogenous variables contained in our model also include the daily average temperature of provincial capitals, the number of grade A tertiary hospitals in each province, and the population density, etc. All these data can be downloaded from the Wind database.
Figure 2 Outflow index from Shanghai
Note: The outflow index is download from Baidu Mobility, which reflects the size of the population moving out.

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In this paper, we follow the spirit of Han, et al.[31] to obtain the spatial weight, which captures the spatial correlation of different regions3.
3Han, et al.[31] used travel inflow distributions from Baidu Mobility to construct the spatial weight, which represented the domestic travel network of all cities.
To visually show the spatial correlation of COVID-19 in Shanghai and other regions, Figure 3 provides the average percentage of people moving into Shanghai from other provinces during February 1 to May 31. From this figure, we obtained that Jiangsu, Zhejiang and Anhui have more closer contacts with Shanghai than other regions. A possible explanation for this is that these three provinces are located near Shanghai. Another interesting observation about Figure 3 is that the migration from Xizang, Qinghai and Ningxia to Shanghai is almost zero. In fact, there is almost no travel between Xizang and other regions in China, which makes it virtually free of confirmed COVID-19 cases. Furthermore, as mentioned above, the migration of people between different regions is the main reason for the spread of COVID-19. Therefore, the spatial matrix based on the flow of people can reflect the spatial correlation between different regions.
Figure 3 Percentage of people moving into Shanghai
Note: The data in the figure are obtained by averaging the daily percentage from February 1 to May 31. And the percentage of people moving into Shanghai from other provinces are downloaded from Baidu Mobility.

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4 Empirical Analysis

4.1 Experiment Results

In this section, the SDPD model is applied to study the spread of COVID-19 during the epidemic outbreak in Shanghai. We aims to quantify the spread risk of COVID-19 under different epidemic prevention policies and the spillover effect in Shanghai.
According to the analysis results in Section 3, the sample period is set from February 1 to May 14, 2022. And the initial time break point is set at March 28, before which Shanghai adopted a relatively relaxed epidemic prevention policy. Then a series of strict epidemic prevention measures were adopted, including phased lockdowns, COVID-19 test, working remotely, public traffic restrictions, etc. The time-varying coefficients λ(t), ρ(t) and γ(t) can be solved from model (1), which quantify the transmission risk and spillover effects of the epidemic. And we can also get the growth of confirmed cases outside Shanghai under a counterfactual scenario that assumes no adjustment to epidemic prevention policies.
Figure 4 shows the intra-regional transmission risk (ρ), cross-regional transmission risk (λ) and spillover effect (γ) of the epidemic during the COVID-19 outbreak in Shanghai.
Figure 4 Transmission risk and spillover effect of COVID-19
Note: The solid lines indicate the value of λ, ρ and γ. And the dotted lines refer to the lower/upper 95% confidence limit. And the changes in the figure are on March 29 and April 23.

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And the corresponding values of the coefficients and their 95% confidence intervals are listed in Table 3. Three results can be obtained from Figure 4 and Table 3.
Table 3 The estimated coefficients and their confidence interval
λ λ: 95%CI ρ ρ: 95%CI γ γ: 95%CI
period 1 0.3458 0.3285 0.3631 0.5481 0.5152 0.5865 0.7622 0.7470 0.7736
period 2 0.0567 0.0539 0.0595 0.0172 0.0138 0.0206 0.0057 0.0054 0.0060
Note: 95%CI means the confidence interval at 95% level. The period 1 for λ and ρ is Februray 1 to March 28, 2022. And the period 1 for γ is Februray 1 to April 22, 2022.
First, the intra-regional transmission risk of the epidemic (ρ=0.5481) was greater than the cross-regional one (λ=0.3458), which indicates that the spread of the epidemic was mainly within the region at the beginning of the outbreak. Second, the risk of both intra-regional and cross-regional transmission of COVID-19 has been greatly reduced after Shanghai adopted strict epidemic prevention polices. Specifically, λ decreased by 83.6% from 0.3458 (95% CI: [0.3285,0.3617]) to 0.0567 (95% CI: [0.0539,0.0595]), and ρ decreased by 98.0% from 0.5481 (95% CI: [0.5152,0.5865]) to 0.0172 (95% CI: [0.0138,0.0206]). This indicates that strict prevention and control polices can greatly reduce the risk of transmission and hinder the spread of the epidemic. Third, when the epidemic in Shanghai passed its peak, the risk of spillover of COVID-19 also decreased. Namely, γ decreased by 99.3% from 0.7622 (95% CI: [0.7470,0.7736]) to 0.0057 (95% CI: [0.0054,0.0060]) on April 23, 2022.
Figure 5 presents the counterfactual results of the confirmed COVID-19 cases without an adjustment of epidemic prevention policies. It can be observed from the figure that, first, the growth trend of the cumulative number of confirmed cases outside Shanghai slowed down after March 28, on which Shanghai adopted strict epidemic prevention policies. But the cumulative number of confirmed cases will increase according to the dotted line in Figure 5 if there is no strict polices. Second, the dashed and solid lines almost overlapped until March 28, and then diverged considerably, with the dotted line growing much faster than the solid line. A possible explanation for this is that the movement of people between the epicenter and other areas has been greatly restricted due to the strict epidemic prevention policies, which reduces the spillover risk of the epidemic. Specifically, compared to the actual 48, 194 cumulative cases in these 30 provinces and cities (excluding Shanghai) by April 4, 2022 (one week after the adjustment of epidemic prevention policies), the counterfactual cumulative cases would have been 7, 126 (or 14.79%) more. And compared with the actual cumulative confirmed cases of 55, 696 on April 28, 2022, the counterfactual result would have increased by 126, 712 cases, an increase of 2.28 times. In addition, it can also been observed from Figure 5 that the growth rate of cumulative confirmed cases is relatively slow when there is no severe COVID-19 outbreak in China. This implies that the normalized epidemic prevention policy has achieved good results.
Figure 5 Simulated cumulative cases outside of Shanghai
Note: The solid line is the number of the actual confirmed cases. And the dashed line represents the counterfactual confirmed cases under the dummy condition of not adjusting the epidemic prevention policy. The circle line and star line are the 95% upper and lower confidence limits of the counterfactual results.

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4.2 Policy Recommendations

Based on the empirical results in the previous section, we put forward the following policy recommendations for dealing with public health emergencies such as COVID-19:
First, since cross-provincial tourism can bring significant economic benefits, appropriate liberalization of cross-provincial tourism restrictions will help stimulate consumption and restore the economy, and also help balance the relationship between epidemic prevention and economic development. It can be seen from the coefficients in the SDPD model that, the intra-regional transmission of the COVID-19 virus dominated in the early stage of the epidemic outbreak. In other words, the transmission risk of the epidemic within provinces was greater than the cross-regional transmission risk between them. This indicates that the risk of epidemic spread caused by movement of people between "low-risk" regions is relatively low.
Second, thorough, rigorous and comprehensive epidemic prevention polices, such as lockdown and quarantine, are effective ways to prevented a wider spread and further development of COVID-19. And policy makers should take timely and effective measures to curb the spread of COVID-19 at the early stage of its spread to avoid greater harm. It can be seen from the changes of time-varying coefficients that strict epidemic prevention measures have significantly reduced the risk of both intra-regional and cross-regional transmission of COVID-19. Moreover, the counterfactual analysis suggests that adopting strict prevention measures during the pandemic can effectively minimize the spread risk of COVID-19 and reduce the number of confirmed cases.
Third, epidemic prevention and control policies should be adjusted in a timely manner according to the development of the epidemic. Although strict epidemic prevention policies can effectively curb the spread of COVID-19, they also cause considerable socio-economic costs, slow economic recovery, and inconvenience in people's daily life. It can be seen that the number of newly confirmed cases in Shanghai dropped rapidly after reaching its peak, eventually maintaining at a low level and gradually approaching zero. Therefore, after the epidemic is under control, it is necessary to carefully consider how to gradually relax epidemic prevention policies.

5 Conclusion

The COVID-19 global pandemic is the most extensive to afflict humanity in a century. This paper uses the SDPD model to study the transmission mechanism of COVID-19 and the impact of epidemic prevention policies on its spread. The prevention of COVID-19 is a complex system that requires a comprehensive consideration of factors such as virus virulence, population density, climate, geography, medical resources, and social ideology. To deal with these problems, a spatial network of human mobility among provinces and cities in China is taken into account. Our method provides a scientific approach to characterizing the spread of the epidemic, including its spillover effects, intra- and cross-regional transmission.
The empirical results show that, first, during the COVID-19 outbreak in Shanghai, the risk of intra-regional transmission of the epidemic was greater than that of cross-regional transmission. Second, timely and effective epidemic prevention polices can reduce the transmission risk and spillover effect of COVID-19, and play an important role in containing the spread of the epidemic. Furthermore, based on these results, we also provide three policy recommendations for epidemic prevention, as well as for future responses to other public health emergencies.
More importantly, this paper provides a research framework for quantifying the transmission risk of pandemic diseases such as COVID-19 and evaluating the effectiveness of different epidemic prevention policies. This framework is not only applicable to the study of epidemic transmission in China, but also can be used for urban epidemic prevention and control management, or extended to the spatial network composed of more countries and regions to study its transmission mechanism around the world. For future research, we suggest employing spatial econometric models to investigate the local and spillover effects of COVID-19 and other public health emergencies on various industries and economic activities. This analysis will be enhanced by integrating supply chain and industrial chain considerations into our approach. Besides, studying the time-varying transborder spillover effects of poverty on crime with SDPD model is also an interesting problem. Furthermore, it is meaningful to explore how to combine the distributed computing technology with spatial regression model.

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Funding

National Key R&D Program of China(2021ZD0111204)
National Natural Science Foundation of China(72073126)
National Natural Science Foundation of China(72091212)
National Natural Science Foundation of China(71973116)
National Natural Science Foundation of China(71988101)
Young Elite Scientists Sponsorship Program by CAST(YESS20200072)
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