Modeling the COVID-19 outbreaks and the effectiveness of the containment measures adopted across countries

Edward De Brouwer; Daniele Raimondi; Yves Moreau

later of the Lodi province. The further spreading of the cases led to the lockdown of the most affected regions in northern Italy (Lombardia, Veneto, and Emilia-Romagna) and eventually of the entire country on March 10, 2020. The growth of cases in Spain started with a delay with respect to Italy, but the worrying trend prompted the government to lock down first Madrid and then the entire country. Similar incremental actions have been adopted in Belgium, on the March 13, 2020 and on March 18, 2020. In this study, we collected the publicly available data regarding cases, recovered and deaths related to the COVID-19 epidemics in China, Italy, Belgium and Spain and we trained a Bayesian SEIR model to perform a parametric regression on these time series. This approach allowed us to model the outbreak progression in those countries inferring the change of basic reproduction ratio R 0 due to the introduction of government-issued containment measures aimed at slowing the outbreak. To do so we used a Markov Chain Monte Carlo (MCMC) approach to fit the SEIR model on the cumulative cases time series by inferring a β i value corresponding to each containment measure adopted, thus estimating their effectiveness in reducing the transmission or SARS-CoV-2. This approach could help governments nowcasting the behavior of the outbreaks and detecting flaws in the containment measures in place and thus act as rapidly as possible, ensuring a proper containment of the disease. We show that the parameters learned by the SEIR model suggest an gradual effectiveness of the containment, with the most drastic effect observed in Spain, with a 71% reduction of R 0 after the measures introduced on March 3, 2020. We also provide an estimation of the actual number of COVID-19 cases in Italy for March 12, 2020, suggesting that this number have been at that time around 3 times higher than the official cases count. Finally, despite our model's limitations, we argue that the idea of "flattening the curve" (i.e., reducing the R 0 of the epidemic to a level that would allow the gradual build up of natural immunity in the population) is likely to be unfeasible. Indeed, reaching herd immunity at a manageable pace is probably not possible in a reasonable time scale.