A modelling framework for the analysis of the transmission of SARS-CoV2
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Action plans against the current SARS-CoV-2 pandemic have been implemented around the globe in order to reduce transmission. The reproduction number has been found to respond to public health interventions changing throughout the pandemic waves. However, the actual global 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 transmission dynamics generating the total number of underlying infections can be described by a continuous time transmission model expressed through a system of non-linear ordinary differential equations, where the transmission rate and consequently the reproduction number are stochastic. We model the transmission rate as a diffusion process, with distinct volatility phases for each pandemic wave, 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's No-U-Turn sampler variant of Hamiltonian Monte Carlo. As we estimate the true number of infections through deaths, 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 to the inferred quantities.
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