Global stability analysis of DS-I-R model

摘要

This paper investigates an SIR model with differential susceptibles.We derive an explicit formula for the basic reproductive number of infection for the investigated model by investigating the local stability of the infection-free equilibrium. We further prove that the infection-free equilibrium of this model is globally asymp- totically stable by qualitative analysis. By using an appropriate Liapunov function, we show that if the basic reproductive number is greater than one, there exists a unique endemic equilibrium for the system, and it is globally asymptotically stable