Global stability of vector-host disease with variable population size

Abstract

The paper presents the vector-host disease with a variability in population. We assume, the disease is fatal and for some cases the infected individuals become susceptible. We first show the local and global stability of the disease-free equilibrium, for the case when R0< 1. We also show that for R0< 1, the disease free-equilibrium of the model is both locally as well as globally stable. For R0> 1, there exists a unique positive endemic equilibrium. For R0> 1, the disease persistence occurs. The endemic equilibrium is locally as well as globally asymptotically stable for R0> 1. Numerical results are presented for the justifications of theoratical results. © 2013 Muhammad Altaf Khan et al.