Estabilidade global e aplicações ao modelo epidemiológico SEIRS

Abstract

In this dissertation, we provide necessary conditions for an asymptotically stable equilibrium solution of a nonlinear ordinary differential equation be globally stable. An essential condition is a generalization of the criteria of Bendixson and Dulac for towdimensional differential equations which is used to ensure the absence of periodic orbits, we call this Bendixson criterion. We provide a new Bendixson criterion robust under C1 local perturbations, which together with the Global Stability Principle, ensure the global stability of an asymptotically stable equilibrium. We use this criterion in the study of asymptotic behavior of an epidemiological model called SEIRS