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Backward bifurcation and global dynamics of an SIS epidemic model with general incidence rate and treatment. (English) Zbl 1167.34338

Summary: An SIS epidemic model with treatment is proposed. The incidence rate of the model, which can include the bilinear incidence rate and the standard incidence rate, is a general nonlinear incidence rate. The global dynamics of the model are studied and then we can understand the effect of the capacity for treatment. It is found that a backward bifurcation occurs and there exist bistable endemic equilibria if the capacity is low. Mathematical results suggest that decreasing the basic reproduction number is insufficient for disease eradication and improving the efficiency and capacity of treatment is important for this end.

MSC:

34C23 Bifurcation theory for ordinary differential equations
37N25 Dynamical systems in biology
92D30 Epidemiology
34D23 Global stability of solutions to ordinary differential equations
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