Transmissibility of COVID-19 in 11 major cities in China and its association with temperature and humidity in Beijing, Shanghai, Guangzhou, and Chengdu | Infectious Diseases of Poverty

Comparisons of transmission among different cities

The comparison between officially reported data and revised data in Wuhan is presented in Fig. 1 with important points marked on it. The estimated number of cumulative cases was higher than the official number every day, and it had reached 46 933 by February 13, 2020, which was 1.3 times that of the official number 35 991. The unusual high peak of new cases on February 12, 2020 was smoothed by revision.

Comparisons between reported and revised data in Wuhan

The calculation results of the basic reproduction number R₀ from January 24, 2020 to February 13, 2020 in 11 Chinese major cities are shown in Fig. 2. 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 R₀, and the one of “Wuhan (revised)” reflects the value size of R₀. 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.

Calculation results of the basic reproduction number

As can be seen from Fig. 2, R₀ in Wuhan is significantly higher than those in cities outside Hubei Province. Besides, R₀ in cities outside Hubei Province has begun to decrease, while R₀ 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 R₀ from high to low. The inflection point refers to the day after which R₀ shows a downward trend.

It can be seen from Table 1 that the average R₀ in Wuhan far exceeds those in other cities, which is 0.3 higher than that in Chongqing, the city which ranks second. It should be noted that the average R₀ in Wuhan is calculated with the revised data to better fit the real value. In fact, the average basic reproduction number calculated with the officially reported data is also much higher than those in other cities, which is 2.4.

The inflection points of cities outside Hubei Province range from January 30 to February 3, while the inflection point of Wuhan had not appeared because the number of confirmed cases had kept increasing rapidly by February 13, 2020. Although R₀ in Wuhan reaches a peak on February 12, it cannot be determined that February 12 is the inflection point. Because since that day, Hubei Province has included the number of clinically diagnosed cases into the number of confirmed cases. The modification of the diagnostic criteria leads to a sudden increase of newly confirmed patients, which explains why R₀ is particularly high on February 12.

Correlation between R₀ and temperature

The Pearson correlation coefficients and significance between R₀ and temperature are shown in Table 2. The row of “Summary” suggests that calculated as a whole, the correlation between R₀ and temperature is statistically significant at the 0.01 level. The correlation coefficient is -0.459, so R₀ and temperature have a negative correlation, which means that R₀ decreases as the temperature increases. The higher the temperature, the lower the transmission capability. As for the analysis of each city, R₀ negatively correlates with temperature in Shanghai and Chengdu, correlation significant at the 0.01 level. Correlation is not significant in Beijing and Guangzhou. Over the study period, the average R₀ in Beijing, Shanghai, Guangzhou, and Chengdu are 2.3, 2.2, 2.2, and 2.0 respectively and the average temperatures are -1.0 ^∘C, 7.9 ^∘C, 14.9 ^∘C, and 9.9 ^∘C respectively. There is not a significant relationship between the average R₀ in a city versus its average temperature (r=−0.486, P>0.5).

Linear regression was performed on the data for all cities combined 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 R₀=a+bT (where T is temperature) with the corresponding actual values in Table 3, and correlation between R₀ and temperature can be expressed more precisely. For example, the linear regression equation of Shanghai is written as R₀=2.424−0.026T. It can be inferred from b<0 that R₀ negatively correlates with temperature in Shanghai, which is consistent with the correlation analysis result above.

We plotted every pair of temperature and R₀ 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.

Scatter plot of temperature and basic reproduction number

Correlation between R₀ and relative humidity

The Pearson correlation coefficients and significance between R₀ and relative humidity are presented in Table 4. According to the first row, the correlation between R₀ and relative humidity is statistically significant at the 0.01 level in general. The correlation coefficient is -0.391, indicating that R₀ decreases as the relative humidity increases. As for the analysis of each city, R₀ negatively correlates with relative humidity in Beijing and Shanghai, which is significant at the 0.01 level. While the correlation is significantly positive in Chengdu at the 0.01 level, which implies that the transmission ability and relative humidity have consistent trends there. Correlation is not significant in Guangzhou.

The correlation was significant in Beijing, Shanghai, and Chengdu, and thus we conducted linear regression on the data of the three cities as well as the summary of all cities. The linear regression results are presented in Table 5. Replace a and b in the equation R₀=a+bRH (where RH is relative humidity) with the corresponding actual values in Table 5, and the correlation between R₀ and relative humidity can be expressed with a quantitative method.

The scatterplots and corresponding regression lines of relative humidity and R₀ summarized across all cities and by individual cities are presented in Fig. 4.

Correlation between R₀ and absolute humidity

The Pearson correlation coefficients and significance between R₀ and absolute humidity are presented in Table 6. The negative correlation between R₀ and absolute humidity is significant in general as well as in Beijing, Shanghai and Guangzhou and the absolute values of the Pearson correlation coefficients for absolute humidity are larger than those for relative humidity, indicating that the relationship is stronger for absolute humidity than relative humidity. The correlation is not significant in Chengdu.

Scatter plot of relative humidity and basic reproduction number

We conducted linear regression on the data of Beijing, Shanghai, Guangzhou as well as the summary of all cities. The linear regression results are presented in Table 7. Replace a and b in the equation R₀=a+bAH (where AH is absolute humidity) with the corresponding actual values in Table 7, and the correlation between R₀ and absolute humidity can be expressed with a quantitative method.

The scatterplots and corresponding regression lines of absolute humidity and R₀ summarized across all cities and by individual cities are presented in Fig. 5.

Scatter plot of absolute humidity and basic reproduction number

Sensitivity of R₀ to parameters

Substitute the variables in Eqs. (4–7) with λ=0.1372 (which is the average λ from January 24 to February 13 in Beijing), T_g=7.5 and f=0.69, and the specific values can be calculated:

When the variables fluctuate within a small range around the given value, R₀ increases as λ or T_g increases and decreases as f increases. λ, T_g and f range at the scales of 10⁻², 10⁰ and 10⁻¹ respectively. And the scales of their partial derivatives are 10¹, 10⁻¹ and 10⁻¹. Thus the fluctuation scales of R₀ are 10⁻¹, 10⁻¹ and 10⁻² corresponding to λ, T_g and f, which implies that R₀ is more sensitive to λ and T_g than f. The accuracy of parameters or variables is important for the estimation of the basic reproduction number. As the research on COVID-19 progresses, we can get more precise data and better describe the transmission pattern of the new coronavirus. But the calculation in this paper still makes sense, considering that we focus on relative values instead of absolute values of R₀ in comparison and correlation analysis. Results are reasonable as long as we use the consistent equation and parameters to calculate R₀. By comparison, we can see that the control of COVID-19 is especially urgent in Wuhan and people in other cities should also attach importance to inhibiting the spread of the disease. The vigilance cannot languish until R₀ drops below 1.