Identificação de um modelo SIR variante no tempo para Covid-19

Abstract

Throughout human history, epidemics have been a constant presence. Understanding their dynamics is essential to predict scenarios and make substantiated decisions. Mathematical models are powerful tools to describe an epidemic behavior. Among the most used, the compartmental ones stand out, dividing population into classes with well-defined characteristics. In this work, it is proposed a SIR model with time-varying transmission rate parameter with a method to estimate this parameter based on an optimization problem, which minimizes the sum of the squares of the errors between the model and historical data. Epidemic data released by the government of the State of Rio Grande do Sul in Brazil was used to evaluate the models, where the models shown a very good fit with data.