Estimativa de parâmetros aplicados em modelos epidemiológicos

Abstract

In this study, the Bayesian Monte Carlo technique via Markov Chain (MCMC) was selected to estimate the parameters of the differential equations of the SQUIDER3 and SEIR4 compartmental models, seeking to reflect the propagation of Covid-19 in the state of Pará. An algorithm was developed in Matlab, reproducing the MCMC technique that uses stochastic processes and simulates a random selection of values of each parameter. When sampling proportionally to the probability of the values, a probability distribution was reached in order to be able to both adjust the model parameters and converge to the stationary distribution of interest. The parameters estimated in this paper for the SQUIDER and SEIR compartmental models were compared to real data using the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) metrics. Both of these were applied for a better definition of the model that best represents the Covid-19 propagation phenomenon in the state of Pará. As a result, histograms were obtained that indicate a convergence of parameters in the SQUIDER model, which did not happen in the SEIR model. By applying the AIC and BIC, it was demonstrated that the SQUIDER model was the best model to represent the phenomena (i.e. the propagation of Covid-19 in the state of Pará), and has the potential to be used as a predictive model.