Do Weather Conditions Affect COVID-19 Epidemic? Evidence Based on Panel Data of Prefecture-level Administrative Regions in China

21 Background: Similar to other infectious diseases, weather conditions may affect the COVID-19 22 epidemic through changes to transmission dynamics, host susceptibility, and virus survival in the 23 environment. It’s critical to explore the relationship between weather variables and the spread of 24 the COVID-19 for understanding seasonality and the possibility of future outbreaks, developing 25 early warning systems, infection control methods, and public health measures. However, the 26 influence of weather change on COVID-19 edidemic is still an emerging research field, and there 27 is still relatively limited literature available. 28 Objectives: Our study aims to explore the causal relationship between weather conditions and 29 COVID-19 epidemic, the regional heterogeneity of the influence of weathner conditions in east30 middle-west and coastal-inland, the moderating effect of diurnal temperature difference, public 31 health measures, and public opinion on the influence of weather conditions on the epidemic to 32 investigate the effects of these factors on the intensity of weather conditions. 33 Methods: First, we theoretically explain the influence mechanism of weather conditions on the 34 epidemic based on the epidemiological triangle model. Then, we collect COVID-19-related 35 prefecture-daily panel data in mainland China from January 1, 2020, to February 19, apply two36 way fixed effect model of multiple linear regression, and also take into account other influencing 37 factors such as population movement, public health interventions of the local government, 38 economic and social conditions, to explore the causal relationship between weather conditions and 39 the COVID-19 epidemic. 40 Results: It is found that first, there is a conditional negative linear relationship between the weather 41 conditions and the epidemic. When the average temperature is greater than -7°C , there is a 42 significant negative causal relationship between the average temperature and the growth rate of 43 the confirmed cases. Similarly, when the relative humidity is greater than 46%, the increase in the 44 relative humidity significantly contain the epidemic. However, when the average temperature is 45 less than -7°C or the relative humidity is less than 46%, the effect of weather conditions is not 46 significant. Further, from the perspective of weather conditions, prefecture-level administrative 47 regions such as Chifeng, Zhangjiakou, and Ulanqab are more conducive to the outbreak of the 48 epidemic in winter. Then, weather conditions have a greater influence in the east than in the middle 49 and western regions, and it is better in coastal region than in the inland. Finally, increasing diurnal 50 temperature differences will improve the impact of weather conditions on the confirmed cases. In 51 dry and cold regions, higher diurnal temperature differences will increase the risk of spread of the 52 disease; Strict public health measures and good public opinion can mitigate the adverse effects of 53 cold and dry weather on the spread of the epidemic. 54 Discussion: In future research, it can adopt more detailed investigation methods. Under the legal 55 framework of privacy protection, questionnaire surveys can be carried out with patients' consent 56 to draw more accurate conclusions. At the same time, in terms of the mechanism of the role of 57 weather variables, more in-depth interdisciplinary cooperation with epidemiologists is needed to 58 study the specific impact of weather conditions on the survivability of the COVID-19 virus and 59 the immunity of susceptible populations to obtain a clearer picture and compelling conclusions. 60


Introduction
The main contributions of this article are as follows. First, in this article, daily confirmed COVID-107 19 cases reported by prefecture-level administrative regions 2 of mainland China are used as the 108 research sample, which helps to reach a more accurate conclusion. Regarding the influence of in this paper, we carry out multiple linear regression using panel data which is more conducive to 117 identifying the causal relationship between variables (Angrist & Pischke, 2008). In addition, we 118 compare and analyze whether the relationship between weather variables and the COVID-19 119 epidemic is a nonlinear or conditional linear relationship, and further explore the regional 120 heterogeneity and the moderating effects of diurnal temperature variation, public health measures, 121 and social public opinion. 122 Third, different from the existing literature, we also consider the diurnal temperature difference The relationship between climate, weather, and infectious disease epidemics has attracted people's 164 attention since 2500 years ago when Hippocrates and his followers described the relationship 165 between seasonal changes and the spread of infectious diseases (Fisman, 2007;Lloyd et al., 1983). 166 Hippocratic treatise, Airs, Waters, Places describe the influence of the environment and seasons 167 on the constitution and instructed physicians to observe the health of a community concerning sun 168 exposure, soil, elevation, climate, and geography (Miller, 1962). During the 16th and 18th 169 centuries, interest in the effects of climate on health arose from the ability to measure and weather is related to these changes since weather changes are conducive to increasing 194 transmission or leading to increased morbidity and mortality (Liu & Zhang et al., 2020). When a 195 cold winter is followed by a mild winter, with the weather changes, the weather changes more and   are not yet mature (Polgreen & Polgreen, 2018). First, the limitations of these methods are apparent.

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For example, the time series regression model is built on the premise that the data satisfy linearity 287 and staticity, and relies on a large amount of uninterrupted time series data. However, the COVID-288 19 case data is not necessarily linear, and the data is difficult to satisfy the requirements of   Outside of the optimal ranges, the viability of the virus is limited, but it is sufficient to spread since 319 people lack an adaptive immune response to the previously unknown coronavirus . China is the first country to be attacked, and cases occurred in all provincial-level administrative 337 regions and most prefecture-level administrative regions (as of the end of February, there were 19 338 prefecture-level administrative regions without outbreaks). China's territory spans the tropical, 339 temperate, and frigid zones from south to north, where the Qinling-Huaihe line as a geographic 340 boundary is the 0 ℃ isotherm in January. The average temperature in January is above 0 in the 341 south of the Qinling and below 0 in the north. There is a big difference in temperature between the 342 northern and southern prefecture-level administrative regions. In January 2020, the average high 343 temperature in the northern city of Heihe is -13℃, and the average low temperature is -25℃, while 344 in the southern city of Sanya is 25℃ and 16℃, respectively, with a difference of 38℃ and 41℃.

345
In February 2020, the average high temperature in Heihe is -9℃, and the average low temperature is -21℃, while in Sanya is 27℃ and 19℃, respectively, with a difference of 36℃ and 40℃. In 347 China, January is usually the coldest month, but the temperature starts to rise in February and rises 348 sharply in March when spring begins when most of the country's temperature is above 0, and the 349 temperature difference between regions is greatly reduced. In March 2020, the highest temperature 350 in Sanya reaches 30℃, and that in Heihe is 14℃. 6 The regional temperature difference between  Based on the above analysis,we proposes the research hypotheses as follows.

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Based on the theoretical analysis above, we apply econometrics approach and empirically test the influence 373 of weather condition on the epidemic using panal data of mainland China. Econometric approach is 374 commonly used to measure the effects of a factor on economic growth. Similar to early COVID-19 375 infections, economic output generally increases exponentially with a variable rate that can be affected by 376 policies and other conditions (Hsiang et al., 2020). Therefore, it is appropriate to apply econometrics 377 techniques to analyze the influence of weather condition on the outbreak of the epidemic. As mentioned 378  conditions, therefore, there are significant differences between regions. In this paper, we conduct   Celsius). Figure 4 shows the distribution of the mean of the relative humidity from January 1 to 464 February 19, 2020. It can be seen that the relative humidity in the southeast coastal area is higher, 465 and it shows a decreasing trend in the northwest direction.   Table 5 reports the results of the baseline regression. The explanatory variable is the growth rate 527 of cumulative cases, and the explanatory variables are average temperature and relative humidity.

528
Column (1) only introduces the explanatory variables, and column (2) -column (5) adds the control 529 variables in sequence based on column (1). The results show that the average temperature 530 coefficient is significantly negative, which indicates that there is a significant negative casual 531 relationship between temperature and the growth rate of the confirmed cases. In cities with higher 532 temperatures, the transmission rate of the epidemic is slow, and the growth rate of confirmed cases 533 is lower; on the contrary, the virus transmission ability is stronger in cold conditions. Similarly, 534 the coefficient of relative humidity is significantly negative, which indicates that there is a 535 significant negative casual relationship between the relative humidity and the growth rate of 536 confirmed cases. In cities with higher humidity, the growth rate of confirmed cases is lower, while 537 in cities with low humidity, the epidemic spread rate is faster, and the growth rate of confirmed 538 cases is higher.
539 We also analyze control variables. It is concluded that the coefficient of public health measures is   553 We have preliminarily verified that the average temperature and relative humidity negatively 554 affects the epidemic, however, we're also concerned that whether this negative relationship only 555 holds up over a certain interval, or whether there is the possibility of a nonlinear relationship.

556
Therefore, we try to introduce the quadratic terms of the average temperature and relative humidity 557 respectively, to further explore the influence of weather conditions on the epidemic. Standard errors in parentheses, *** p<0.01, ** p<0.05, * p<0.1 560 Table 6 reports the regression results of the nonlinear model and figure 7 shows the nonlinear 561 relationship between the average temperature, relative humidity and the epidemic. We find that  Table 7 reports the results of the sub-sample regression. It can be seen that when the average 571 temperature is more than -7 ℃, it has a negative correlation with the growth rate of the cases; when 572 it is lower than -7 ℃, then there is no significant correlation between the average temperature and 573 the epidemic; Similarly, when the relative humidity is higher than 46%, there is a negative 574 correlation between it and the cumulative case growth rate, but when it is lower than 46, the 575 decrease of relative humidity will not affect the epidemic. Therefore, there is a conditional linear 576 relationship between weather conditions and the COVID-19 epidemic.   Table 8. It can be seen that the sign and significance of the coefficients are consistent 594 with the baseline regression, indicating that the conclusion is still robust after changing the sample 595 selection basic assumptions.

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596 Table 8 Robustness 597 variables needs to meet two requirements: the first is that there is a significant relationship between 605 the instrumental variables and the endogenous explanatory variables; and the second is that the 606 instrument variable must be exogenous. We take the 1st lag of the explanatory variable as an 607 instrument variable, and in order to ensure the robustness of the results, we respectively 608 use two-stage least squares (2SLS), limited information maximum likelihood (LIML), and 609 generalized method of moments (GMM). Table 9 reports the results of the instrumental variable 610 approach. We can say that there is no obvious change in the sign and significance of the 611 coefficients. The results of the instrumental variables approach are consistent with the baseline 612 regression, indicating that the conclusion is still robust after considering endogeneity.
613 Table 9. IV Results 614  Since we have proved that when the average temperature is more significant than -7°C, the average 618 temperature is negatively correlated with the spread of the epidemic, and when the relative 619 humidity is greater than 46%, the relative humidity is negatively correlated with the epidemic, then 620 it can be inferred that when the temperature is -7°C, the spread of the epidemic is the most serious; 621 when the relative humidity is 46%, the spread of the epidemic is the most serious. So, in China, a 622 county with vast territory and wide difference in climatic conditions, which cities have more 623 favorable climate conditions for the development of the epidemic? 624 We make statistics of the prefecture-level administrative regions which meet the requirements that 625 the average temperature is -7℃ ± one standard deviation (9.0667℃), the relative humidity is 46% 626 ± one standard deviation (17.15%), and both meet the two conditions simultaneously from January 627 1, 2020 to February 19. We construct a dummy variable of whether the city falls into the interval 628 for regression and count the number of days that each city meets the conditions. Table 10 reports 629 the impact of the dangerous weather on the epidemic. It can be seen that the epidemic is indeed 630 more severe in the dangerous weather.       Table 15. Column (1) introduces the interaction between average temperature and 697 high diurnal temperature variation (hightf), and column (2) introduces the interaction between 698 relative humidity and the item; similarly, column (3) and column (4) presents the results of public 699 health measures, and column (3) and column (4) presents the results of social publicopinion.

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It can be seen that, whether it is average temperature or relative humidity, the coefficient of the 701 interaction with high diurnal temperature difference (hightf) is significantly negative, that is, the  First, we analyze the effects of the average temperature on the growth rate of the confirmed cases, 722 and we find that there is a conditional negative linear relationship between the weather conditions 723 and the epidemic. When the average temperature is greater than -7℃, there is a significant negative 724 causal relationship between the average temperature and the growth rate in the confirmed cases, 725 while when the average temperature is less than -7℃, it has no significant effect on the epidemic.

726
Similarly, when relative humidity is greater than 46%, it has a negative impact on the spread of 727 the epidemic, while when relative humidity is less than 46%, the reduction inrelative humidity will 728 no longer affect the epidemic. In robustness checks, we try to remove data of Hubei province from 729 the whole sample, which is most affected by the epidemic in China, and to adjust the assumption 730 of incubation period length in the calculation of actual cumulative case growth rate; considering 731 the possible endogeneity, we take the first-order lag of the main explanatory variables as an instrument variable, and to ensure the robustness of the results, we respectively use two-stage least COVID-19 epidemic, we make statistics of the prefecture-level administrative regions which meet 737 the requirements that the average temperature is -7℃ ± one standard deviation (9.0667℃), the 738 relative humidity is 46% ± one standard deviation (17.15%), and both meet the two conditions 739 simultaneously from January 1, 2020, to February 19. It is concluded that from the perspective of 740 weather conditions, prefecture-level administrative regions such Chifeng, Zhangjiakou, and

741
Ulanqab are more conducive to the outbreak of the epidemic in winter.

742
Third, we explore the heterogeneity of the influence of weather conditions. Based on the 743 geographical characteristics of China, we conduct sample regression according to the eastern, 744 middle, west, and inland , coastal regions, respectively. We find that the coefficient of average 745 temperature is still significantly negative in the eastern and western regions, in which the influence 746 of average temperature in the east is greater than that in the west, but it doesn't work in the middle.

747
The effect of relative humidity is the most significant in the middle, followed by the east and the 748 weakest in the west. The influence of both average temperature and relative humidity is greater in 749 the coastal areas, which indicating that the role of weather conditions is more important in the 750 coastal areas than inland.

751
Finally, by introducing interaction terms, we explore the moderating effect of diurnal temperature 752 difference, public health measures, and public opinion on the influence of weather conditions on 753 the epidemic to investigate the effects of these factors on the intensity of weather conditions. We find that the coefficient of the interaction between weather conditions and the high diurnal 755 temperature difference is significantly negative, suggesting that the increase in diurnal temperature