Periodic solution for a stochastic nonautonomous SIR epidemic model with logistic growth

Qun Liu; Daqing Jiang; Ningzhong Shi; Tasawar Hayat; Ahmed Alsaedi

doi:10.1016/j.physa.2016.06.052

Periodic solution for a stochastic nonautonomous SIR epidemic model with logistic growth

Qun Liu
, Daqing Jiang
, Ningzhong Shi
, Tasawar Hayat
, Ahmed Alsaedi

Northeast Normal University
Yulin 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

22 Scopus citations

Abstract

In this paper, we analyze the dynamics of a stochastic nonautonomous SIR epidemic model, in which population growth is subject to logistic growth in absence of disease. For the periodic system, we present sufficient conditions for persistence of the epidemic and in the case of persistence, by constructing some suitable Lyapunov functions, we show that there is at least one nontrivial positive periodic solution. One of the most important findings is that random perturbations may be beneficial to formate the periodic solution to the stochastic nonautonomous SIR epidemic model.

Original language	English
Pages (from-to)	816-826
Number of pages	11
Journal	Physica A: Statistical Mechanics and its Applications
Volume	462
DOIs	https://doi.org/10.1016/j.physa.2016.06.052
State	Published - 15 Nov 2016
Externally published	Yes

UN SDGs

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

SDG 3 Good Health and Well-being

Keywords

Lyapunov function
Periodic solution
Persistence
Stochastic SIR epidemic model

Access to Document

10.1016/j.physa.2016.06.052

Cite this

@article{40e28944c91b4299af14f3665a68e546,

title = "Periodic solution for a stochastic nonautonomous SIR epidemic model with logistic growth",

abstract = "In this paper, we analyze the dynamics of a stochastic nonautonomous SIR epidemic model, in which population growth is subject to logistic growth in absence of disease. For the periodic system, we present sufficient conditions for persistence of the epidemic and in the case of persistence, by constructing some suitable Lyapunov functions, we show that there is at least one nontrivial positive periodic solution. One of the most important findings is that random perturbations may be beneficial to formate the periodic solution to the stochastic nonautonomous SIR epidemic model.",

keywords = "Lyapunov function, Periodic solution, Persistence, Stochastic SIR epidemic model",

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

note = "Publisher Copyright: {\textcopyright} 2016 Elsevier B.V.",

year = "2016",

month = nov,

day = "15",

doi = "10.1016/j.physa.2016.06.052",

language = "English",

volume = "462",

pages = "816--826",

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

issn = "0378-4371",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - Periodic solution for a stochastic nonautonomous SIR epidemic model with logistic growth

AU - Liu, Qun

AU - Jiang, Daqing

AU - Shi, Ningzhong

AU - Hayat, Tasawar

AU - Alsaedi, Ahmed

PY - 2016/11/15

Y1 - 2016/11/15

N2 - In this paper, we analyze the dynamics of a stochastic nonautonomous SIR epidemic model, in which population growth is subject to logistic growth in absence of disease. For the periodic system, we present sufficient conditions for persistence of the epidemic and in the case of persistence, by constructing some suitable Lyapunov functions, we show that there is at least one nontrivial positive periodic solution. One of the most important findings is that random perturbations may be beneficial to formate the periodic solution to the stochastic nonautonomous SIR epidemic model.

AB - In this paper, we analyze the dynamics of a stochastic nonautonomous SIR epidemic model, in which population growth is subject to logistic growth in absence of disease. For the periodic system, we present sufficient conditions for persistence of the epidemic and in the case of persistence, by constructing some suitable Lyapunov functions, we show that there is at least one nontrivial positive periodic solution. One of the most important findings is that random perturbations may be beneficial to formate the periodic solution to the stochastic nonautonomous SIR epidemic model.

KW - Lyapunov function

KW - Periodic solution

KW - Persistence

KW - Stochastic SIR epidemic model

UR - https://www.scopus.com/pages/publications/84978906073

U2 - 10.1016/j.physa.2016.06.052

DO - 10.1016/j.physa.2016.06.052

M3 - Article

AN - SCOPUS:84978906073

SN - 0378-4371

VL - 462

SP - 816

EP - 826

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

ER -

Periodic solution for a stochastic nonautonomous SIR epidemic model with logistic growth

Abstract

UN SDGs

Keywords

Access to Document

Other files and links

Fingerprint

Cite this