Threshold dynamics of a stochastic SIS epidemic model with nonlinear incidence rate

Qun Liu; Daqing Jiang; Tasawar Hayat; Ahmed Alsaedi

doi:10.1016/j.physa.2019.04.182

Threshold dynamics of a stochastic SIS epidemic model with nonlinear incidence rate

Qun Liu
, Daqing Jiang
, Tasawar Hayat
, Ahmed Alsaedi

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

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

7 Scopus citations

Abstract

In this paper, we study a stochastic SIS epidemic model with nonlinear incidence rate. By employing the Markov semigroups theory, we verify that the reproduction number R₀−[Formula presented] can be used to govern the threshold dynamics of the studied system. If R₀−[Formula presented]>1, we show that there is a unique stable stationary distribution and the densities of the distributions of the solutions can converge in L¹ to an invariant density. If R₀−[Formula presented]<1, under mild extra conditions, we establish sufficient conditions for extinction of the epidemic. Our results show that larger white noise can lead to the extinction of the epidemic while smaller white noise can ensure the existence of a stable stationary distribution which leads to the stochastic persistence of the epidemic.

Original language	English
Article number	120946
Journal	Physica A: Statistical Mechanics and its Applications
Volume	526
DOIs	https://doi.org/10.1016/j.physa.2019.04.182
State	Published - 15 Jul 2019
Externally published	Yes

UN SDGs

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

SDG 3 Good Health and Well-being

Keywords

Extinction
Markov semigroups
Nonlinear incidence rate
Stationary distribution
Stochastic SIS epidemic model
Threshold

Access to Document

10.1016/j.physa.2019.04.182

Cite this

@article{0c8da55587ee43c88c9a083d860445aa,

title = "Threshold dynamics of a stochastic SIS epidemic model with nonlinear incidence rate",

abstract = "In this paper, we study a stochastic SIS epidemic model with nonlinear incidence rate. By employing the Markov semigroups theory, we verify that the reproduction number R0−[Formula presented] can be used to govern the threshold dynamics of the studied system. If R0−[Formula presented]>1, we show that there is a unique stable stationary distribution and the densities of the distributions of the solutions can converge in L1 to an invariant density. If R0−[Formula presented]<1, under mild extra conditions, we establish sufficient conditions for extinction of the epidemic. Our results show that larger white noise can lead to the extinction of the epidemic while smaller white noise can ensure the existence of a stable stationary distribution which leads to the stochastic persistence of the epidemic.",

keywords = "Extinction, Markov semigroups, Nonlinear incidence rate, Stationary distribution, Stochastic SIS epidemic model, Threshold",

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

note = "Publisher Copyright: {\textcopyright} 2019 Elsevier B.V.",

year = "2019",

month = jul,

day = "15",

doi = "10.1016/j.physa.2019.04.182",

language = "English",

volume = "526",

journal = "Physica A: Statistical Mechanics and its Applications",

issn = "0378-4371",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - Threshold dynamics of a stochastic SIS epidemic model with nonlinear incidence rate

AU - Liu, Qun

AU - Jiang, Daqing

AU - Hayat, Tasawar

AU - Alsaedi, Ahmed

PY - 2019/7/15

Y1 - 2019/7/15

N2 - In this paper, we study a stochastic SIS epidemic model with nonlinear incidence rate. By employing the Markov semigroups theory, we verify that the reproduction number R0−[Formula presented] can be used to govern the threshold dynamics of the studied system. If R0−[Formula presented]>1, we show that there is a unique stable stationary distribution and the densities of the distributions of the solutions can converge in L1 to an invariant density. If R0−[Formula presented]<1, under mild extra conditions, we establish sufficient conditions for extinction of the epidemic. Our results show that larger white noise can lead to the extinction of the epidemic while smaller white noise can ensure the existence of a stable stationary distribution which leads to the stochastic persistence of the epidemic.

AB - In this paper, we study a stochastic SIS epidemic model with nonlinear incidence rate. By employing the Markov semigroups theory, we verify that the reproduction number R0−[Formula presented] can be used to govern the threshold dynamics of the studied system. If R0−[Formula presented]>1, we show that there is a unique stable stationary distribution and the densities of the distributions of the solutions can converge in L1 to an invariant density. If R0−[Formula presented]<1, under mild extra conditions, we establish sufficient conditions for extinction of the epidemic. Our results show that larger white noise can lead to the extinction of the epidemic while smaller white noise can ensure the existence of a stable stationary distribution which leads to the stochastic persistence of the epidemic.

KW - Extinction

KW - Markov semigroups

KW - Nonlinear incidence rate

KW - Stationary distribution

KW - Stochastic SIS epidemic model

KW - Threshold

UR - https://www.scopus.com/pages/publications/85064381487

U2 - 10.1016/j.physa.2019.04.182

DO - 10.1016/j.physa.2019.04.182

M3 - Article

AN - SCOPUS:85064381487

SN - 0378-4371

VL - 526

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

M1 - 120946

ER -

Threshold dynamics of a stochastic SIS epidemic model with nonlinear incidence rate

Abstract

UN SDGs

Keywords

Access to Document

Other files and links

Fingerprint

Cite this