A modelling framework for the analysis of the transmission of SARS-CoV2

Despite the progress in medical data collection the actual burden of SARS-CoV-2 remains unknown due to severe under-ascertainment of cases. The use of reported deaths has been pointed out as a more reliable source of information, likely less prone to under-reporting. Given that daily deaths occur from past infections weighted by their probability of death, one may infer the true number of infections accounting for their age distribution, using the data on reported deaths. We adopt this framework and assume that the dynamics generating the total number of infections can be described by a continuous time transmission model expressed through a system of non-linear ordinary differential equations where the transmission rate is modelled as a diffusion process allowing to reveal both the effect of control strategies and the changes in individuals behavior. We study the case of 6 European countries and estimate the time-varying reproduction number($R_t$) as well as the true cumulative number of infected individuals using Stan. As we estimate the true number of infections we offer a more accurate estimate of $R_t$. We also provide an estimate of the daily reporting ratio and discuss the effects of changes in mobility and testing on the inferred quantities.