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Backward bifurcation of an epidemic model with infectious force in infected and immune period and treatment. (English) Zbl 1278.92044
In this paper, an epidemic model, with an infectious force in the infected and immune periods and a treatment rate of infectious individuals, is proposed to understand the effect of the capacity for treatment on the disease spread. It is assumed that the treatment rate is proportional to the number of infective individuals below the capacity and is constant when the number of infective individuals is greater than the capacity. It is proved that the existence and stability of equilibria for the model is not only related to the basic reproduction number but also to the capacity for treatment of infective agents. 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
34K18Bifurcation theory of functional differential equations