A stochastic differential equation SIS epidemic model with regime switching

Siyang Cai; Yongmei Cai; Xuerong Mao

A stochastic differential equation SIS epidemic model with regime switching

Siyang Cai, Yongmei Cai, Xuerong Mao

Mathematics And Statistics

Research output: Contribution to journal › Article › peer-review

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 language	English
Journal	Discrete and Continuous Dynamical Systems - Series B
Publication status	Accepted/In press - 12 Sep 2020

Keywords

SIS model
independent Brownian motions
Markovian switching
extinction
persistence
stationary distribution

Embargoed Document

Cai-etal-DCDS-2020-A-stochastic-differential-equation-SIS-epidemic-model-with-regime-switching
Accepted author manuscript, 494 KB
Licence: Unspecified
Embargo ends: 12/09/21

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title = "A stochastic differential equation SIS epidemic model with regime switching",

abstract = "In this paper, we combined the previous model in [1] with Gray et al.{\textquoteright}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.",

keywords = "SIS model, independent Brownian motions, Markovian switching, extinction, persistence, stationary distribution",

author = "Siyang Cai and Yongmei Cai and Xuerong Mao",

year = "2020",

month = sep,

day = "12",

language = "English",

journal = "Discrete and Continuous Dynamical Systems - Series B",

issn = "1531-3492",

publisher = "American Institute of Mathematical Sciences",

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TY - JOUR

T1 - A stochastic differential equation SIS epidemic model with regime switching

AU - Cai, Siyang

AU - Cai, Yongmei

AU - Mao, Xuerong

PY - 2020/9/12

Y1 - 2020/9/12

N2 - 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.

AB - 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.

KW - SIS model

KW - independent Brownian motions

KW - Markovian switching

KW - extinction

KW - persistence

KW - stationary distribution

M3 - Article

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

SN - 1531-3492

ER -