Stability analysis of SIR holing type II infectious epidemic model with treatment failure rate

Abstract

In this paper a mathematical model of  SIR epidemics diseases holing type II with a treatment failure rate on a population of individuals had been introduced and studied so, its dynamical behavior such as stability  derived ,first we prove the existence of  equilibrium points via Discartes rule of signs ,then local  stability demonstrate for the above equilibrium points  using Roth Hurwitz criteria , finally the global stability established with assistance of  Lyapunov theorem  to the equilibrium points above  and the results was encouraging and satisfy.

Key words stability , Holling type II , epidemic SIR model .