Abstract:

An SIS epidemic model with a simple vaccination is investigated in this article. The efficiency of vaccine, the disease-related death rate and population dynamics are also considered in this model. The authors find two threshold R₀ and R_c (R_c may not exist). There is a unique endemic equilibrium for R₀>1 or R_c=R₀; there are two endemic equilibria for R_c<R₀<1; and there is no endemic equilibrium for R₀<R_c<1. When R_c exists, there is a backward
bifurcation from the disease-free equilibrium for R₀=1. They analyze the stability of equilibria and obtain the globally dynamic behaviors of the model. The results acquired in this article show that an accurate estimation of the efficiency of vaccine is necessary to prevent and controll the spread of disease.

Key words: Epidemic model, equilibrium, backwards bifurcation, vaccination, stability