Backward bifurcation and stability analysis of a network-based SIS epidemic model with saturated treatment function

Abstract

In this paper, we present a study on a network-based SIS epidemic model with a saturated treatment function to characterize the saturation phenomenon of limited medical resources. In this model, we first obtain a threshold value R0, which is the threshold condition for the stability of the disease-free equilibrium. We show that a backward bifurcation occurs under certain conditions. More precisely, the saturated treatment function leads to a such bifurcation. In this case, R0<1 is not sufficient to eradicate the disease from the population. Furthermore, we also study the stability of the endemic equilibrium and the corresponding stability condition is given. Numerical experiments are conducted and their results validate the theoretical results.