A bifurcation study on epidemic models with density-dependent treatments

Numerically studies have shown that the bi-stability and backward bifurcation are not automatically connected in epidemic models. In fact, when a backward bifurcation occurs, the disease-free equilibrium may be globally stable or it may support to a stable limit cycle. In this paper, a continuous epidemic model that incorporates density-dependent treatments is analyzed. It is shown that it supports new types of backward bifurcations. We proceed to find bifurcation curves in a subset of entire parameter space. Finally, we analyze an analog discrete-time epidemic model.