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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.

34D23Global stability of ODE
34C60Qualitative investigation and simulation of models (ODE)
Full Text: DOI
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