Threshold of a regime-switching SIRS epidemic model with a ratio-dependent incidence rate

Qun Liu; Daqing Jiang; Tasawar Hayat; Ahmed Alsaedi

doi:10.1016/j.physa.2019.01.115

Threshold of a regime-switching SIRS epidemic model with a ratio-dependent incidence rate

Qun Liu
, Daqing Jiang
, Tasawar Hayat
, Ahmed Alsaedi

Northeast Normal University
King Abdulaziz University
China University of Petroleum (East China)
Quaid-I-Azam University

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

4 Scopus citations

Abstract

In this paper, we study the dynamical behavior of a regime-switching SIRS epidemic model with a ratio-dependent incidence rate. We propose a stochastic reproduction number R₀ ^S which can be regarded as a threshold to use in identifying the stochastic extinction and persistence: if R₀ ^S<1, the disease dies out exponentially with probability one; while if R₀ ^S>1, there exists a unique ergodic stationary distribution of the positive solutions to the system which implies the stochastic persistence of the infectious disease.

Original language	English
Pages (from-to)	614-625
Number of pages	12
Journal	Physica A: Statistical Mechanics and its Applications
Volume	521
DOIs	https://doi.org/10.1016/j.physa.2019.01.115
State	Published - 1 May 2019
Externally published	Yes

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This output contributes to the following UN Sustainable Development Goals (SDGs)

SDG 3 Good Health and Well-being

Keywords

Extinction
Markov switching
Ratio-dependent incidence rate
Stationary distribution and ergodicity
Threshold

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10.1016/j.physa.2019.01.115

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title = "Threshold of a regime-switching SIRS epidemic model with a ratio-dependent incidence rate",

abstract = "In this paper, we study the dynamical behavior of a regime-switching SIRS epidemic model with a ratio-dependent incidence rate. We propose a stochastic reproduction number R0 S which can be regarded as a threshold to use in identifying the stochastic extinction and persistence: if R0 S<1, the disease dies out exponentially with probability one; while if R0 S>1, there exists a unique ergodic stationary distribution of the positive solutions to the system which implies the stochastic persistence of the infectious disease.",

keywords = "Extinction, Markov switching, Ratio-dependent incidence rate, Stationary distribution and ergodicity, Threshold",

author = "Qun Liu and Daqing Jiang and Tasawar Hayat and Ahmed Alsaedi",

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AU - Liu, Qun

AU - Jiang, Daqing

AU - Hayat, Tasawar

AU - Alsaedi, Ahmed

PY - 2019/5/1

Y1 - 2019/5/1

N2 - In this paper, we study the dynamical behavior of a regime-switching SIRS epidemic model with a ratio-dependent incidence rate. We propose a stochastic reproduction number R0 S which can be regarded as a threshold to use in identifying the stochastic extinction and persistence: if R0 S<1, the disease dies out exponentially with probability one; while if R0 S>1, there exists a unique ergodic stationary distribution of the positive solutions to the system which implies the stochastic persistence of the infectious disease.

AB - In this paper, we study the dynamical behavior of a regime-switching SIRS epidemic model with a ratio-dependent incidence rate. We propose a stochastic reproduction number R0 S which can be regarded as a threshold to use in identifying the stochastic extinction and persistence: if R0 S<1, the disease dies out exponentially with probability one; while if R0 S>1, there exists a unique ergodic stationary distribution of the positive solutions to the system which implies the stochastic persistence of the infectious disease.

KW - Extinction

KW - Markov switching

KW - Ratio-dependent incidence rate

KW - Stationary distribution and ergodicity

KW - Threshold

UR - https://www.scopus.com/pages/publications/85061190403

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JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

ER -

Threshold of a regime-switching SIRS epidemic model with a ratio-dependent incidence rate

Abstract

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Keywords

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