A stochastic differential equation SIS epidemic model with regime switching

Siyang Cai, Yongmei Cai, Xuerong Mao

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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.
Original languageEnglish
Pages (from-to)4887-4905
Number of pages19
JournalDiscrete and Continuous Dynamical Systems - Series B
Volume26
Issue number9
DOIs
Publication statusPublished - 30 Sep 2021

Keywords

  • SIS model
  • independent Brownian motions
  • Markovian switching
  • extinction
  • persistence
  • stationary distribution

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