Estudo de modelos compartimentais via teoria da estabilidade de EDO’s

Abstract

This monograph deals with some concepts of ordinary differential equations (ODE’s) stability theory. The core concept of this theory is understanding how the solution paths of an ODE system behave in the vicinity of an equilibrium point. This qualitative analisys is useful to study the behavior of a physical or biological fenomenon modeled by an ODE system without having to obtain your analytical solution, that may not even be possible. Based on this, the monograph first addresses some basic concepts and definitions of differential equations theory. Secondly it studies the concepts derived from linear ODE’s system stability via eingenvalues study. After that, it presents an extension of linear ODE’s system stability to non-linear ODE’s via Jacobian matrix eingenvalues study applied to the equilibrium point and the presentation of Lyapunov functions which can also be used for stability analysis. Finally the monograph presents the aplication of stability theory in some epidemiological models known as compartimental models.