title: 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 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.
authors.affiliation: Department of Mathematics, Abdul Wali Khan University, Mardan, Khyber Pakhtunkhwa, Pakistan. altafdir@gmail.com
authors.forename: Muhammad Altaf
authors.initials: MA
authors.lastname: Khan
authors.forename: Saeed
authors.initials: S
authors.lastname: Islam
authors.forename: Sher Afzal
authors.initials: SA
authors.lastname: Khan
authors.forename: Gul
authors.initials: G
authors.lastname: Zaman
mesh_terms: D000818:Animals; D004196:Disease Outbreaks; D004199:Disease Vectors; D019353:Endemic Diseases; D054884:Host-Pathogen Interactions / Q000235:genetics*; D006801:Humans; D008962:Models, Theoretical; D011156:Population Density