Analysis and forecast of COVID-19 spreading in China, Italy and France

Abstract

In this note we analyze the temporal dynamics of the coronavirus disease 2019 outbreak in China, Italy and France in the time window $22/01-15/03/2020$ . A first analysis of simple day-lag maps points to some universality in the epidemic spreading, suggesting that simple mean-field models can be meaningfully used to gather a quantitative picture of the epidemic spreading, and notably the height and time of the peak of confirmed infected individuals. The analysis of the same data within a simple susceptible-infected-recovered-deaths model indicates that the kinetic parameter that describes the rate of recovery seems to be the same, irrespective of the country, while the infection and death rates appear to be more variable. The model places the peak in Italy around March 21^st 2020, with a peak number of infected individuals of about 26000 (not including recovered and dead) and a number of deaths at the end of the epidemics of about 18,000. Since the confirmed cases are believed to be between 10 and 20% of the real number of individuals who eventually get infected, the apparent mortality rate of COVID-19 falls between 4% and 8% in Italy, while it appears substantially lower, between 1% and 3% in China. Based on our calculations, we estimate that 2500 ventilation units should represent a fair figure for the peak requirement to be considered by health authorities in Italy for their strategic planning. Finally, a simulation of the effects of drastic containment measures on the outbreak in Italy indicates that a reduction of the infection rate indeed causes a quench of the epidemic peak. However, it is also seen that the infection rate needs to be cut down drastically and quickly to observe an appreciable decrease of the epidemic peak and mortality rate. This appears only possible through a concerted and disciplined, albeit painful, effort of the population as a whole.

Keywords: Covid-19; epidemic spreading; non linear fitting; population model.

Fig. 1

Recurrence plots for the three populations for which data ara publicly available (symbols) for the outbreaks in China, Italy and France and best fit with a power law of the kind (1) (solid lines). All data appear to follow the exact same trend on average (see text).

Fig. 2

Predicted evolution of the COVID-19 outbreak in Italy (top) and China (bottom). Symbols represent the official data retrieved from the CSSE repository . Solid lines are the predicted trends based on the fits of the SIRD model, Eqs (4), to the data. The black circle in the top graph marks the predicted number of confirmed infected individuals at the announced end of the imposed lockdown on the Italian territory, April 3^rd 2020.

Fig. 3

Predicted evolution of the total number of confirmed infected people for the COVID-19 outbreak in Italy (solid line). The fitted data are shown as filled circles (see also Table 1). The epidemic peak (population I) and the announced end of the lockdown (black circle) are also shown for comparison.

Fig. 4

Predicted evolution of the COVID-19 outbreak in China obtained by fitting the data up to February 19^th 2020. The fitted data are shown as filled circles (see also Table 1). A very similar prediction is obtained by restricting the fit up to February 15^th 2020, where the peak had not been reached yet (data not shown).

Fig. 5

Predicted effect of the lockdown measures imposed by the Italian government on the whole national territory on March 8^th 2020. The predicted evolution of the confirmed infected population and the number of casualties are plotted for different values of the reduction of the infection rate achieved thanks to the lockdown, see Eq.  (5). The black circle marks the announced end of the imposed lockdown, April 3^rd 2020. Top graph: $\Delta t=7$ days. Bottom graph: $\Delta t=2$ days.