A stochastic differential equation SIS model on network under Markovian switching

We study a stochastic SIS (susceptible-infected-susceptible) epidemic dynamics on network, under the effect of Markovian regime-switching. first prove existence unique global positive solution, and find invariant set for system. Then, we sufficient conditions a.s. extinction permanence, showing also their relation with stationary probability distribution Markov chain that governs switching network topology. provide an asymptotic lower bound time average sample-path solution ensuring permanence. From this bound, are able to measure if condition permanence holds. Under different condition, recurrence ergodicity regime-switching diffusion.