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Global analysis of SIS epidemic model with a simple vaccination and multiple endemic equilibria. (English) Zbl 1092.92041
Summary: An SIS epidemic model with simple vaccination is investigated. The efficiency of vaccine, the disease-related death rate and population dynamics are also considered in this model. The authors find two thresholds $$R_0$$ 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 behavior 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.

MSC:
 92D30 Epidemiology 34D23 Global stability of solutions to ordinary differential equations 34C60 Qualitative investigation and simulation of ordinary differential equation models 37N25 Dynamical systems in biology
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