APPLICATION OF THE SIR MODEL TO COVID-19: social distance and (no-)evolution of the pandemic in state of the Tocantins

Abstract

This article is a study about the behavior and spread of the Covid-19 pandemic, in the state of Tocantins, based on data reported from March 18 to June 10. A modification of the mathematical model SIR was used, in which some auxiliary compartments were added. We analyzed epidemic aspects such as the speed of the contagion curve and its impacts on the health system. As the data are made available daily, a discretization of the system of differential equations that make up the model was performed, and based on the availability of known data, we investigated the correlation between the social isolation index and the basic reproduction factor. Through a very simple interpolation, approximate contagion rates were obtained, enabling us to evaluate the behavior of the evolution of contagion curves and those that depend on them, which allows us to anticipate scenarios based on the trend lines of the data generated, thus helping decision making public power.