Sistemas de equações diferenciais ordinárias e o modelo fundamental da Epidemiologia Matemática

Abstract

This course completion work aims to present, through the study of Ordinary Differential Equations (ODE), the fundamental model of mathematical epidemiology, the SIR model (susceptible, infected and recovered). For this, it was necessary an explanation about Ordinary Differential Equations and more precisely about the linear systems that contain them. Within this bibliographic review, the explanation of the methods to solve homogeneous and non-homogeneous linear systems was made. Linked to this, graphs of examples of systems were observed and interpreted, being an essential part to later bring the SIR model as an application and to be able to understand it. Finally, the importance of mathematical modeling in the area of epidemiology and how this is significant for humanity was discussed.