N-intertwined SIS epidemic model with Markovian switching

Epidemic dynamics is often subject to environmental noise and uncertainty. In this paper, we investigate the effect of color noise on the spread of epidemic in complex networks, which is modeled by stochastic switched differential equations based on the N-intertwined SIS model using a continuous time finite-state Markov chain. Applying Lyapunov functions, we prove that the model has a unique global positive solution and establish sufficient conditions for stochastic extinction and permanence of the epidemic. We also show that the solution is stochastically ultimately bounded and the variance of the solution is bounded too. Furthermore, we discuss the limit of the time average of the solution. Finally, numerical simulations are carried out to illustrate our theoretical results.