Transmissibility of COVID-19 and its association with temperature and humidity

Background: The new coronavirus disease COVID-19 outbroke in Wuhan, Hubei Province, China in December 2019, and has spread by human-to-human transmission to other areas. This study evaluated the transmissibility of the infectious disease and analyzed its association with temperature and humidity, in order to put forward suggestions on how to suppress the transmission. Methods: In this study, we revised the reported data in Wuhan to estimate the actual number of conﬁrmed cases. Then we used the equation derived from the Susceptible–Exposed–Infectious–Recovered (SEIR) model to calculate R 0 from January 24, 2020 to February 13, 2020 in 11 major cities in China for comparison. With the calculation results, we conducted correlation analysis and regression analysis between R 0 and temperature and humidity to see the impact of weather on the transmissibility of COVID-19. Results: It was estimated that the cumulative number of conﬁrmed cases had exceeded 45,000 by February 13, 2020 in Wuhan. The average R 0 in Wuhan was 2.7011, signiﬁcantly higher than those in other cities ranging from 1.7762 to 2.3700. The inﬂection points in the cities outside Hubei Province were between January 30, 2020 and February 3, 2020, while there had not been an obvious downward trend of R 0 in Wuhan. R 0 negatively correlated with both temperature and humidity, which was signiﬁcant at the 0.01 level. Conclusions: The transmissibility of COVID-19 was strong and importance should be attached to the intervention of its transmission especially in Wuhan. According to the correlation between R 0 and weather, the spread of disease will be suppressed as the weather warms.

spread by human-to-human transmission to other Chinese cities as well as areas outside mainland China [1].
As was reported by the National Health Commission of the People's Republic of China, the number of con- 23 [2,3].
The basic reproduction number (R 0 ) refers to the expected number of cases generated from a single case when all people are susceptible to infection [4]. It is widely used to evaluate the transmission ability of an emerging infectious disease and determine what degree of control measures should be taken to eradicate the disease [5][6][7][8]. When R 0 > 1, the disease starts to spread; and when R 0 < 1, the disease is effectively controlled [9]. R 0 is influenced by many other factors except for the characteristics of the disease itself, such as conditions of the environment, policies of the government, people's awareness of infectious diseases and social behavior. Therefore, we can use R 0 to measure the transmissibility of COVID-19 and analyze its influencing factors, which provides data support for suggestion-proposing and decision-making.
Research on transmissible diseases like influenza [10], SARS (Severe Acute Respiratory Syndrome) [11] and MERS (Middle East Respiratory Syndrome) [12] has found that disease transmission is associated with temperature and humidity of the environment [13][14][15][16][17][18]. In terms of biological methods, influenza virus spread was found to be promoted by cold temperature and low rel-ative humidity with the guinea pig as a model host [19]; besides, an experiment on the SARS coronavirus indicated that high temperature and high humidity suppressed the spread of the virus [20]; similarly, MERS coronavirus was more stable when temperature or humidity was lower [21]. In terms of statistical methods, case studies of SARS in four major cities in China suggested that the transmissibility had close relationship with temperature and its variation [22]; and a regres- 1) The first case appeared on December 8, 2019 in Wuhan and transmission started from that day on [26].
2) The cumulative number of cases Y (t) by day t since the first single case followed the exponential function Y (t) = e λt in early development [27].
3) The cumulative number of cases on January 18, 2020 was 4,000, that was, Y (41) = 4000 [25]. 3) According to assumption 4, the number of new additions on February 13, 2020 is 2,997, which is consistent with the officially reported number.
4) According to assumption 2, the daily number of new additions y(t) can be calculated by Thus So the relationship between ln[y(t)] and t is linear.
Replace ln(1−e −λ ) with a and λ with b in Equation

Calculation of the basic reproduction number
The basic reproduction number indicates the average number of people infected by a patient during the infectious period in the absence of control interventions [4]. It is also denoted R 0 , which measures transmissibility of infectious diseases. There are several ways to estimate R 0 , including formula derivation [28,29] and model fitting [30][31][32].
We describe the transmission pattern of COVID-19 with the Susceptible-Exposed-Infectious-Recovered (SEIR) model. In the exposed stage, an individual infection is not able to infect others. The duration of the exposed stage T E is also called the latent period.
The serial interval T g is the sum of T E and T I . Let f = T E /T g be the ratio of the latent period to the serial interval, and then the basic reproduction number can be expressed as [27] The exponential growth rate is t is the number of days required to generate the cumulative number of Y (t) cases from the first case.
According to the research on the first 425 patients with confirmed COVID-19, the mean latent period T E = 5.2 (days) and the mean serial interval T g = 7.5 (days) [34]. Adopting these values, we can calculate the ratio of the latent period to the serial interval by Correlation and regression analysis between R 0 and weather Correlation analysis measures the strength of the linear correlation between two variables and expresses it with appropriate statistical indicators [35]. It is a commonly used statistical method to study the relationship between variables [36]. Regression analysis determines the quantitative relationship between two variables in statistics [37]. Among all kinds of regression methods, linear regression establishes the relationship between the dependent variable Y and the independent variable X with a linear equation Y = a + bX with R 0 as the dependent variable Y and temperature or humidity as the independent variable X.

5)
We split the data by the city label and repeated procedure 3 and 4 for each city separately.    The calculation results of the basic reproduction number R 0 from January 24, 2020 to February 13, 2020 in 11 Chinese major cities are shown in Fig. 2.

Comparisons of transmission among different cities
The values with the label "Wuhan" were calculated using the officially reported number of cases, while those with "Wuhan (revised)" were calculated using the revised number of cases. In this way, the broken line of "Wuhan" reflects the changing trend of R 0 , and the one of "Wuhan (revised)" reflects the value size of R 0 . It is assumed that the cumulative number of confirmed cases reported officially in cities outside Hubei Province is accurate, so the broken lines of the other 10 cities represent not only trends but also actual values.
As can be seen from Fig. 2, R 0 in Wuhan is significantly higher than those in cities outside Hubei Province. Besides, R 0 in cities outside Hubei Province has begun to decrease, while R 0 in Wuhan does not show a significant downward trend.
For a more detailed analysis, the average basic reproduction number of the 21 days in each city and the date of the inflection point are presented in Table 1.
The cities are listed by the average R 0 from high to low. The inflection point refers to the day after which R 0 shows a downward trend.  Correlation between R 0 and temperature Table 2 shows the Pearson correlation coefficients and significance between R 0 and temperature. The row of "Summary" suggests that calculated as a whole, the correlation between R 0 and temperature is statistically significant at the 0.01 level. The correlation coefficient is -0.459, so R 0 and temperature have a negative correlation, which means that R 0 decreases as the temperature increases. The higher the temperature, the lower the transmission capability. As for the analysis of each city, R 0 negatively correlates with temperature in Shanghai and Chengdu, correlation significant at the 0.01 level. Correlation is not significant in Beijing, and Guangzhou. Linear regression was performed on the whole data as well as the data in Shanghai and Chengdu which showed a significant correlation. Table 3 presents the linear regression results. Replace a and b in the equation Y = a + bX with the corresponding actual values in Table 3, and correlation between R 0 (corre-  We plotted every pair of temperature and R 0 in a city or the whole data on the scatter figure to make correlation more intuitive, which was presented in Fig.   3. The regression lines followed the corresponding linear regression equations.

Correlation between R 0 and humidity
The Pearson correlation coefficients and significance between R 0 and humidity are presented in Table 4.
According to the first row, the correlation between  Table 5. Replace a and b in the equation Y = a+bX with the corresponding actual values in Table 5, and the correlation between R 0 (corresponding to Y ) and humidity (corresponding to X) can be expressed with a quantitative method.

Discussion
Sensitivity analysis of R 0 To analyze the sensitivity of R 0 to the three key parameters in Equation (4): we differentiated R 0 to λ, T g and f respectively: Substitute the variables with λ = 0.1372 (which is the average λ from January 24 to February 13 in Beijing), T g = 7.5 and f = 0.6933, and the specific values can be calculated: Basic reproduction number Temperature (℃) Guangzhou Figure 3 . Scatter plot of temperature and basic reproduction number.
The sensitivity of the basic reproduction number R 0 to the exponential growth rate λ, the serial interval   f , which implies that R 0 is more sensitive to λ and Results are reasonable as long as we use the consistent equation and parameters to calculate R 0 . By comparison, we can see that the control of COVID-19 is es- The joint distribution between weather and potential confounders such as policies, medical condition, and health awareness should be taken into account. Nevertheless, we promote a constructive idea of using R 0 as the measurement of the transmissibility and analyzing the relationship between R 0 and weather with statistical methods, and put forward valuable suggestions on the adjustment of temperature and humidity.

Conclusions
In this paper, we calculated and compared the basic reproduction number of COVID-19 in different cities, and analyzed its association with temperature and humidity. First, we revised the daily number of new cases and cumulative cases in Wuhan and estimated that the real number of cumulative cases was 1.3 times that of the officially reported number on February 13, 2020.
Second, we calculated R 0 from January 24, 2020 to February 13, 2020 in 11 major cities in China, and found out that R 0 in Wuhan was significantly higher than those in other cities. Besides, the inflection point was around February 1, 2020 in cities outside Hubei Province, while the inflection point had not appeared in Wuhan. Third, we conducted correlation analysis and linear regression between R 0 and two weather in-