# American Institute of Mathematical Sciences

## A stochastic differential equation SIS epidemic model with regime switching

 1 Department of Mathematics and Statistics, University of Strathclyde, Glasgow G1 1XH, UK 2 School of Mathematical Sciences, University of Nottingham Ningbo China, Ningbo, 315100, China

* Corresponding author: yongmei.cai@nottingham.edu.cn

Received  February 2020 Revised  September 2020 Published  November 2020

In this paper, we combined the previous model in [2] with Gray et al.'s work in 2012 [8] 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 [20] 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 [2, 3], our threshold value are given based on the overall behaviour of the solution but not separately specified in every state of the Markov chain.

Citation: Siyang Cai, Yongmei Cai, Xuerong Mao. A stochastic differential equation SIS epidemic model with regime switching. Discrete & Continuous Dynamical Systems - B, doi: 10.3934/dcdsb.2020317
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##### References:
Extinction with $I(0) = 90$
Extinction with $I(0) = 10$
Persistence Case 1 with $I(0) = 90$
Persistence Case 1 with $I(0) = 10$
Persistence Case 2 with $I(0) = 90$
Persistence Case 2 with $I(0) = 10$
Stationary Distribution Case 1 with $I(0) = 90$
Stationary Distribution Case 1 with $I(0) = 10$
Stationary Distribution Case 2 with $I(0) = 90$
Stationary Distribution Case 2 with $I(0) = 10$
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