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Stability and bifurcation of an SIR epidemic model with nonlinear incidence and treatment. (English) Zbl 1159.92036

Summary: The dynamical behavior of an SIR epidemic model with nonlinear incidence and treatment is investigated. It is assumed that the treatment rate is proportional to the number of infectives below the capacity and is a constant when the number of infectives is greater than the capacity. It is found that a backward bifurcation occurs if the capacity is small. It is also found that there exist bistable endemic equilibria if the capacity is low. Theoretical and numerical results suggest that decreasing the basic reproduction number below one is insufficient for disease eradication.

MSC:

92D30 Epidemiology
34D23 Global stability of solutions to ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
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