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Backward bifurcation of an epidemic model with treatment. (English) Zbl 1093.92054
Summary: An epidemic model with a limited resource for treatment is proposed to understand the effect of the capacity for treatment. 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.
MSC:
92D30Epidemiology
34C60Qualitative investigation and simulation of models (ODE)
34D23Global stability of ODE