Lyapunov Functions and Global Properties of SEIR Epidemic Model

Abstract

The aim of this paper is to analyze an SEIR epidemic model in which prophylactic for the exposed individuals is included. We are interested in finding the basic reproductive number of the model which determines whether the disease dies out or persist in the population. The global attractivity of the disease-free periodic solution is obtained when the basic reproductive number is less than unity and the disease persist in the population whenever the basic reproductive number is greater than unity, i.e. the epidemic will turn out to endemic. The linear and non–linear Lyapunov function of Goh–Volterra type was used to establish the sufficient condition for the global stability of the model.