Temperature dependence of COVID-19 transmission

Abstract

The recent COVID-19 pandemic follows in its early stages an almost exponential expansion, with the number of cases as a function of time reasonably well fit by N(t) ∝ e^αt, in many countries. We analyze the rate α in different countries, starting in each country from a threshold of 30 total cases and fitting for the following 12 days, capturing thus the early exponential growth in a rather homogeneous way. We look for a link between the rate α and the average temperature T of each country, in the month of the initial epidemic growth. We analyze a base set of 42 countries, which developed the epidemic at an earlier stage, an intermediate set of 88 countries and an extended set of 125 countries, which developed the epidemic more recently. Fitting with a linear behavior α(T), we find increasing evidence in the three datasets for a slower spread at high T, at 99.66% C.L., 99.86% C.L. and 99.99995% C.L. (p-value 5⋅10^-7, or 5σ detection) in the base, intermediate and extended dataset, respectively. The doubling time at 25 °C is 40% ~ 50% longer than at 5 °C. Moreover we analyzed the possible existence of a bias: poor countries, typically located in warm regions, might have less intense testing. By excluding countries below a given GDP per capita from the dataset, we find that this affects our conclusions only slightly and only for the extended dataset. The significance always remains high, with a p-value of about 10^-3 - 10^-4 or less. Our findings give hope that, for northern hemisphere countries, the growth rate should significantly decrease as a result of both warmer weather and lockdown policies. In general, policy measures should be taken to prevent a second wave, such as safe ventilation in public buildings, social distancing, use of masks, testing and tracking policies, before the arrival of the next cold season.

Keywords: COVID-19; Environmental risk factors; Epidemiology.

Graphical abstract

Fig. 1

Countries included in the analysis: the base dataset is in red, the intermediate dataset includes both countries in red and in green, and the extended dataset includes red, green and yellow. (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 2

Exponent α for each country vs. average temperature T, for the relevant period of time, as defined in the text, for the base set of 42 countries. We show the data points and the best-fit for the linear interpolation.

Fig. 3

Exponent α for each country vs. average temperature T, as defined in the text, for the base set of 42 countries. We show here the quadratic best-fit.

Fig. 4

Exponent α for each country vs. average temperature T, for the relevant period of time, as defined in the text, for the intermediate set of 88 countries. We show the data points and the best-fit for the linear interpolation.

Fig. 5

Exponent α for each country vs. average temperature T, for the relevant period of time, as defined in the text, for the extended set of 125 countries. We show the data points and the best-fit for the linear interpolation.

Fig. 6

We show the best estimate and the standard deviation for the parameter β of the linear model, excluding countries with a GDP per capita below a given threshold (in units of thousand dollars) from the extended set of 125 countries.

Fig. 7

We show the significance (p-value) for a nonzero parameter β, excluding countries with a GDP per capita below a given threshold in units of thousand dollars, from the extended set of 125 countries.

Fig. 8

We show here in the vertical axis the mean value over the full sample of 126 countries of the errors, δα, on the exponents α, from the exponential fits. On the horizontal axis: the number of days used in the analysis.

Fig. 9

In the left panel: we show the best estimate for the parameter β of the linear model with the error bar given by its standard error σ_β, as a function of the number of days used in the analysis, after the first day (with a number of cases N_i=30). In the right panel: we show the t-statistic, i.e. β/σ_β, as a function of the number of days used in the analysis.