A modeling framework for the analysis of the SARS‐CoV2 transmission dynamics

Despite the progress in medical data collection the actual burden of SARS-CoV-2 remains unknown due to under-ascertainment of cases. This was apparent in the acute phase of the pandemic and the use of reported deaths has been pointed out as a more reliable source of information, likely less prone to under-reporting. Since daily deaths occur from past infections weighted by their probability of death, one may infer the total 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 nonlinear ordinary differential equations where the transmission rate is modeled as a diffusion process allowing to reveal both the effect of control strategies and the changes in individuals behavior. We develop this flexible Bayesian tool in Stan and study 3 pairs of European countries, estimating the time-varying reproduction number ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow> <mml:mrow><mml:mi>t</mml:mi></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {R}_t $$</mml:annotation></mml:semantics> </mml:math> ) as well as the true cumulative number of infected individuals. As we estimate the true number of infections we offer a more accurate estimate of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:semantics> <mml:mrow> <mml:msub><mml:mrow><mml:mi>R</mml:mi></mml:mrow> <mml:mrow><mml:mi>t</mml:mi></mml:mrow> </mml:msub> </mml:mrow> <mml:annotation>$$ {R}_t $$</mml:annotation></mml:semantics> </mml:math> . We also provide an estimate of the daily reporting ratio and discuss the effects of changes in mobility and testing on the inferred quantities.