A stochastic differential equation SIS epidemic model with regime switching

In this paper, we combined the previous model in [1] with Gray et al.’s work in 2012 [2] to add telegraph noise by using Markovian switching to generate a stochastic SIS epidemic model with regime switching. Similarly, threshold value for extinction and persistence are then given and proved, followed by explanation on the stationary distribution, where the M-matrix theory elaborated in [3] is fully applied. Computer simulations are clearly illustrated with different sets of parameters, which support our theoretical results. Compared to our previous work in 2019 [1, 4], our threshold value are given based on the overall behaviour of the solution but not separately specified in every state of the Markov chain.