Global Stability of Vector-Host Disease with Variable Population Size

Abstract EN

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.