Global Stability of Vector-Host Disease with Variable Population Size

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 R (0) < 1. We also show that for R (0) < 1, the disease free-equilibrium of the model is both locally as well as globally stable. For R (0) > 1, there exists a unique positive endemic equilibrium. For R (0) > 1, the disease persistence occurs. The endemic equilibrium is locally as well as globally asymptotically stable for R (0) > 1. Numerical results are presented for the justifications of theoratical results.