Existence of the backward bifurcation of a non-markovian SIS-network model with saturation treatment function

Facing an emerging infectious disease, the occurrence of the medical runs has an inevitable effect on curtailing the disease prevalence. The heterogeneity of individuals' contacts significantly affects the patterns of the disease transmission. In this paper, we propose a SIS mean-field model coupling a non-markovian recovery process and a delay factor caused by the limitation of medical resources. The positivity and boundedness of the solution to the model have been established by the Volterra integral equation theory. Furthermore, if the lag effect of the treatment is terrible, the system exhibits a bistable phenomenon, whose stability of every feasible equilibrium is established by the Lyapunov-Schmidt approach and bifurcation analysis. Finally, numerical simulations have shown that the system may bifurcate multiple endemic steady states.& COPY; 2023 Elsevier Ltd. All rights reserved.