Modelling the COVID-19 epidemics in Brasil: Parametric identification and public health measures influence

Renato Machado Cotta; Carolina Palma Naveira-Cotta; pierre magal

Here, the SIR-type model in [2] [3] [4] [5] [6] [7] is implemented for the direct problem formulation of the COVID-19 epidemic evolution, adding a time variable parametrization for the fraction of asymptomatic infectious that become reported symptomatic individuals, a very important parameter in the public health measure associated with massive testing and consequent focused isolation. The same analytical identification procedure is maintained for the required initial conditions, as obtained from the early stages exponential behaviour. However, a Bayesian inference approach is here adopted for parametric estimation, employing the Markov Chain Monte Carlo method with the Metropolis-Hastings sampling algorithm [8] [9] [10] [11] [12] . At first, the goal of the inverse problem analysis was estimating the parameters associated with the transmission rate and the fraction of asymptomatic infectious that become reported symptomatic individuals, which can be quite different in the various regions and countries and also very according to the public health measures. Then, in light of the success in this parametric identification, an extended estimation was also employed which incorporates the average time the asymptomatic infectious are asymptomatic and the average time the infectious stay in the symptomatic condition, due to the relative uncertainty on these parameters in the literature. The proposed approach was then applied to the data from China, first by taking just the first half of these data points in the estimation, while using the second half to validate the model using the estimated parameters with just the first half of the epidemy evolution, and second by employing the whole time series in the MCMC estimation procedure, thus identifying parameters for the whole evolution period. This second estimation was particularly aimed at refining the data for the average times that asymptomatic infectious individuals and that symptomatic individuals remain infectious.