Global analysis of SIS epidemic model with a simple vaccination and multiple endemic equilibria

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 R-0 and R-c (R-c may not exist). There is a unique endemic equilibrium for R-0 > 1 or R-c = R-0; there are two endemic equilibria for R-c < R-0 < 1; and there is no endemic equilibrium for R-0 < R-c < 1. When R-c exists, there is a backward bifurcation from the disease-free equilibrium for R-0 = 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 control the spread of disease.