A stochastic differential equation SIS epidemic model with regime switching

Cai, Siyang and Cai, Yongmei and Mao, Xuerong (2021) A stochastic differential equation SIS epidemic model with regime switching. Discrete and Continuous Dynamical Systems - Series B, 26 (9). pp. 4887-4905. ISSN 1531-3492 (https://doi.org/10.3934/dcdsb.2020317)

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Abstract

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.

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