Modelos matemáticos em epidemiologia.

Abstract

The present work has as main objective to present and qualitatively analyze three models of nonlinear differential equations applied to epidemiology, they are: SI, SIS and SIR. For the analysis of such models, initially, we present the basic theory about linear systems and the classification of the equilibrium points according to their eigenvalues.Then, we work with the theory of nonlinear autonomous systems and how to linearize them close to their equilibrium points. The initial analysis of the SI, SIS and SIR models was made based on their respective dimensionless models, hence the R0, which is the basic reproductive rate of an infectious disease.Due to their importance, the models were simulated numerically for different values of R0 which is the parameter that really determines the occurrence or not of an epidemic. The results for each model are presented graphically and analyzed in their biological context. Due to the pandemic caused by the new coronavirus (COVID 19), models in epidemiology have gained a lot of prominence. Thus, to finalize the work, we present an application of the SIR model to COVID-19.