A stochastic differential equation SIS epidemic model with regime switching

Siyang Cai, Yongmei Cai, Xuerong Mao

Research output: Contribution to journalArticle

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
JournalDiscrete and Continuous Dynamical Systems - Series B
Publication statusAccepted/In press - 12 Sep 2020

Keywords

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

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