Equações Diferenciais Ordinárias aplicadas a modelos epidemiológicos: uma análise da propagação da COVID-19 no estado da Bahia

Abstract

This work aims to analyze the epidemiological models based on Differential Equations ap plied to epidemic diseases, in order to understand their implications in predicting, control ling and preventing outbreaks and pandemics, seeking to verify the improvement of public health strategies and the welfare of the population through mathematical models. The SIS (Susceptible-Infected-Susceptible), SIR (Susceptible-Infected-Recovered) and SEIHR (Susceptible-Exposed-Infected-Hospitalized-Recovered) models are presented, considering a constant total population. The SIR model was applied to project the evolution levels of COVID-19 epidemic infection in the state of Bahia in the first 15 weeks of 2021. For this end, I specify throughout this work, part of the Differential Equations historicity, their analytical solution methods and the Runge-Kutta method, used as a solution parameter for the model for the application of COVID-19 in Bahia. According to the results ob tained, the model achieves significant approximations to the infected population in the analyzed period.