Asymptotic behavior of stochastic multi-group epidemic models with distributed delays

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

doi:10.1016/j.physa.2016.10.034

Asymptotic behavior of stochastic multi-group epidemic models with distributed delays

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

13 Scopus citations

Abstract

In this paper, we introduce stochasticity into multi-group epidemic models with distributed delays and general kernel functions. The stochasticity in the model is a standard technique in stochastic population modeling. When the perturbations are small, by using the method of stochastic Lyapunov functions, we carry out a detailed analysis on the asymptotic behavior of the stochastic model regarding of the basic reproduction number R₀. If R₀≤1, the solution of the stochastic system oscillates around the disease-free equilibrium E₀, while if R₀>1, the solution of the stochastic model fluctuates around the endemic equilibrium E^∗. Moreover, we also establish sufficient conditions of these results.

Original language	English
Pages (from-to)	527-541
Number of pages	15
Journal	Physica A: Statistical Mechanics and its Applications
Volume	467
DOIs	https://doi.org/10.1016/j.physa.2016.10.034
State	Published - 1 Feb 2017
Externally published	Yes

UN SDGs

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

SDG 3 Good Health and Well-being

Keywords

Disease-free equilibrium
Distributed delay
Endemic equilibrium
Lyapunov functional
Stochastic multi-group epidemic model

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10.1016/j.physa.2016.10.034

Cite this

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title = "Asymptotic behavior of stochastic multi-group epidemic models with distributed delays",

abstract = "In this paper, we introduce stochasticity into multi-group epidemic models with distributed delays and general kernel functions. The stochasticity in the model is a standard technique in stochastic population modeling. When the perturbations are small, by using the method of stochastic Lyapunov functions, we carry out a detailed analysis on the asymptotic behavior of the stochastic model regarding of the basic reproduction number R0. If R0≤1, the solution of the stochastic system oscillates around the disease-free equilibrium E0, while if R0>1, the solution of the stochastic model fluctuates around the endemic equilibrium E∗. Moreover, we also establish sufficient conditions of these results.",

keywords = "Disease-free equilibrium, Distributed delay, Endemic equilibrium, Lyapunov functional, Stochastic multi-group epidemic model",

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

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T1 - Asymptotic behavior of stochastic multi-group epidemic models with distributed delays

AU - Liu, Qun

AU - Jiang, Daqing

AU - Shi, Ningzhong

AU - Hayat, Tasawar

AU - Alsaedi, Ahmed

PY - 2017/2/1

Y1 - 2017/2/1

N2 - In this paper, we introduce stochasticity into multi-group epidemic models with distributed delays and general kernel functions. The stochasticity in the model is a standard technique in stochastic population modeling. When the perturbations are small, by using the method of stochastic Lyapunov functions, we carry out a detailed analysis on the asymptotic behavior of the stochastic model regarding of the basic reproduction number R0. If R0≤1, the solution of the stochastic system oscillates around the disease-free equilibrium E0, while if R0>1, the solution of the stochastic model fluctuates around the endemic equilibrium E∗. Moreover, we also establish sufficient conditions of these results.

AB - In this paper, we introduce stochasticity into multi-group epidemic models with distributed delays and general kernel functions. The stochasticity in the model is a standard technique in stochastic population modeling. When the perturbations are small, by using the method of stochastic Lyapunov functions, we carry out a detailed analysis on the asymptotic behavior of the stochastic model regarding of the basic reproduction number R0. If R0≤1, the solution of the stochastic system oscillates around the disease-free equilibrium E0, while if R0>1, the solution of the stochastic model fluctuates around the endemic equilibrium E∗. Moreover, we also establish sufficient conditions of these results.

KW - Disease-free equilibrium

KW - Distributed delay

KW - Endemic equilibrium

KW - Lyapunov functional

KW - Stochastic multi-group epidemic model

UR - https://www.scopus.com/pages/publications/84994275194

U2 - 10.1016/j.physa.2016.10.034

DO - 10.1016/j.physa.2016.10.034

M3 - Article

AN - SCOPUS:84994275194

SN - 0378-4371

VL - 467

SP - 527

EP - 541

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

ER -

Asymptotic behavior of stochastic multi-group epidemic models with distributed delays

Abstract

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Keywords

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