On a Discrete-Time Networked Epidemic Model With Time-Varying Heterogeneous Delays

Abstract

Delays caused by the incubation period of an infectious disease are inevitable in modeling the spreading of a real epidemic. With this in mind, our note proposes a novel discrete-time networked susceptible-infected-susceptible (SIS) epidemic model with delays. In this model, the independent edge-based time delay in the network is time-varying and heterogeneous. To prove the asymptotic stability of the model, a super-stochastic matrix based method is proposed to analyze the convergence of an infinite product. By using this method, a sufficient algebraic condition for the convergence of the model to the disease-free equilibrium point is established. The theoretical results obtained are verified by numerical simulations.