Bifurcation and stability of a delayed SIS epidemic model with saturated incidence and treatment rates in heterogeneous networks

In this paper, to characterize the limited availability of medical resources, we incorporate a saturated treatment rate into a network-based susceptible-infected-susceptible (SIS) epidemic model with time delay and nonlinear incidence rate. Analytical study shows the boundedness of solutions, the basic reproduction number R-0 and equilibrium points of the proposed system. For any infection delay, we perform both local and global stability analyses for the disease-free equilibrium point by analyzing the characteristic equation and using Lyapunov functional. Furthermore, this system exhibits bifurcation behavior at R-0 = 1 due to the introduction of saturated treatment. More precisely, a backward bifurcation takes place from the disease-free equilibrium point when the saturation constant beta is sufficiently large. Under the given conditions, the unique disease-spreading equilibrium point is also proved to be locally asymptotically stable. In addition, we analyze an optimal control problem with consideration of two time-dependent control measures. Several numerical simulations are presented to validate the obtained theoretical results. (C) 2021 Elsevier Inc. All rights reserved.