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

Edward De Brouwer; Daniele Raimondi; Yves Moreau

The parameters of this model are δ, β and γ. Those tune the dynamics of the epidemics. δ −1 can be interpreted as the average incubation period (i.e., the average time spent in pool E before becoming infectious I). β corresponds to the average number of infections an infectious individual will cause per unit of time and γ −1 corresponds to the average time necessary to recover from the disease (i.e., going from I to R). The average number of new infections arising from a single infectious person is then R 0 = β/γ. In this study we set δ −1 = 5.2 days (12) and we used β and γ as trainable parameters. We inferred a single γ for each country, therefore keeping both γ and δ constant over time, before and after the introduction of containment measures. The effect of these measures is then modelled by a change in β. Importantly, in this work, we considered that the measures enforcement resulted in a adaptive change in β. This is motivated by the fact that people are only gradually adopting the enforced measures, as suggested by seismic data (18) and mobile data (see Discussion for more details). We assumed that the beta was then exponentially adapting to a new target. Let β 0 be the β right before lockdown enforcement. We posit that the β after lockdown is decaying towards its target β ∞ as: