A stochastic differential equation SIS epidemic model with regime switching

Siyang Cai; Yongmei Cai; Xuerong Mao

doi:10.3934/dcdsb.2020317

A stochastic differential equation SIS epidemic model with regime switching

Siyang Cai, Yongmei Cai, Xuerong Mao

Research output: Journal Publication › Article › peer-review

12 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	4887-4905
Number of pages	19
Journal	Discrete and Continuous Dynamical Systems - Series B
Volume	26
Issue number	9
DOIs	https://doi.org/10.3934/dcdsb.2020317
Publication status	Published - Sept 2021

Keywords

Extinction
M-matrix
Markovian switching
SIS model
Stationary distribution

ASJC Scopus subject areas

Discrete Mathematics and Combinatorics
Applied Mathematics

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10.3934/dcdsb.2020317

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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 [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.",

keywords = "Extinction, M-matrix, Markovian switching, SIS model, Stationary distribution",

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

note = "Funding Information: The authors would like to thank the reviewers and the editors for their very professional comments and suggestions. SC would like to thank the University of Strathclyde for awarding the PhD studentship. YC acknowledges support from the New Researchers Grant, Faculty of Science and Engineering, University of Nottingham Ningbo China. Funding Information: Acknowledgments. The authors would like to thank the reviewers and the editors for their very professional comments and suggestions. SC would like to thank the University of Strathclyde for awarding the PhD studentship. YC acknowledges support from the New Researchers Grant, Faculty of Science and Engineering, University of Nottingham Ningbo China. Publisher Copyright: {\textcopyright} 2021 American Institute of Mathematical Sciences. All rights reserved.",

year = "2021",

month = sep,

doi = "10.3934/dcdsb.2020317",

language = "English",

volume = "26",

pages = "4887--4905",

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

issn = "1531-3492",

publisher = "Southwest Missouri State University",

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

AU - Cai, Siyang

AU - Cai, Yongmei

AU - Mao, Xuerong

N1 - Funding Information: The authors would like to thank the reviewers and the editors for their very professional comments and suggestions. SC would like to thank the University of Strathclyde for awarding the PhD studentship. YC acknowledges support from the New Researchers Grant, Faculty of Science and Engineering, University of Nottingham Ningbo China. Funding Information: Acknowledgments. The authors would like to thank the reviewers and the editors for their very professional comments and suggestions. SC would like to thank the University of Strathclyde for awarding the PhD studentship. YC acknowledges support from the New Researchers Grant, Faculty of Science and Engineering, University of Nottingham Ningbo China. Publisher Copyright: © 2021 American Institute of Mathematical Sciences. All rights reserved.

PY - 2021/9

Y1 - 2021/9

N2 - 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.

AB - 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.

KW - Extinction

KW - M-matrix

KW - Markovian switching

KW - SIS model

KW - Stationary distribution

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DO - 10.3934/dcdsb.2020317

M3 - Article

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SN - 1531-3492

VL - 26

SP - 4887

EP - 4905

JO - Discrete and Continuous Dynamical Systems - Series B

JF - Discrete and Continuous Dynamical Systems - Series B

IS - 9

ER -

A stochastic differential equation SIS epidemic model with regime switching

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Keywords

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