Backward bifurcation of an epidemic model with treatment

An epidemic model with a limited resource for treatment is proposed to understand the effect of the capacity for treatment. It is assumed that 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.