Global analysis of an SAIS model

Abstract

This paper is concerned with global analysis of an SAIS epidemiological model in a population of varying size introduced by Busenberg and van den Driessche. In this model the population is divided into three subgroups of susceptible, asymptomatic and infective individuals. It has been shown that this system has no periodic solutions and all its trajectories tend to the equilibria of the system. We use the Poincaré Index theorem to determine the number of the equilibria and their stability properties. We have shown that bistability occurs for suitable values of parameters and found a set of examples of all possible dynamics of the system.

Global Dynamics and Sensitivity Analysis of a Vector-Host-Reservoir Model

“…Quite a good number of studies have been carried out to observe the disease dynamics with different settings and assumptions (for example, see [11,12,13]). As far our knowledge goes, no research has been done to describe the dynamics of a general vector-host-reservoir model.…”