Asymptotic behavior of a stochastic delayed HIV-1 infection model with nonlinear incidence

Qun Liu; Daqing Jiang; Tasawar Hayat; Bashir Ahmad

doi:10.1016/j.physa.2017.05.069

Asymptotic behavior of a stochastic delayed HIV-1 infection model with nonlinear incidence

Qun Liu
, Daqing Jiang
, Tasawar Hayat
, Bashir Ahmad

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

23 Scopus citations

Abstract

In this paper, a stochastic delayed HIV-1 infection model with nonlinear incidence is proposed and investigated. First of all, we prove that there is a unique global positive solution as desired in any population dynamics. Then by constructing some suitable Lyapunov functions, we show that if the basic reproduction number R₀≤1, then the solution of the stochastic system oscillates around the infection-free equilibrium E₀, while if R₀>1, then the solution of the stochastic system fluctuates around the infective equilibrium E^∗. Sufficient conditions of these results are established. Finally, we give some examples and a series of numerical simulations to illustrate the analytical results.

Original language	English
Pages (from-to)	867-882
Number of pages	16
Journal	Physica A: Statistical Mechanics and its Applications
Volume	486
DOIs	https://doi.org/10.1016/j.physa.2017.05.069
State	Published - 15 Nov 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

Lyapunov functional
Nonlinear incidence
Stochastic HIV-1 infection model
Time delay

Access to Document

10.1016/j.physa.2017.05.069

Cite this

@article{324d3c3d132e4280818c8cbddf30664b,

title = "Asymptotic behavior of a stochastic delayed HIV-1 infection model with nonlinear incidence",

abstract = "In this paper, a stochastic delayed HIV-1 infection model with nonlinear incidence is proposed and investigated. First of all, we prove that there is a unique global positive solution as desired in any population dynamics. Then by constructing some suitable Lyapunov functions, we show that if the basic reproduction number R0≤1, then the solution of the stochastic system oscillates around the infection-free equilibrium E0, while if R0>1, then the solution of the stochastic system fluctuates around the infective equilibrium E∗. Sufficient conditions of these results are established. Finally, we give some examples and a series of numerical simulations to illustrate the analytical results.",

keywords = "Lyapunov functional, Nonlinear incidence, Stochastic HIV-1 infection model, Time delay",

author = "Qun Liu and Daqing Jiang and Tasawar Hayat and Bashir Ahmad",

note = "Publisher Copyright: {\textcopyright} 2017 Elsevier B.V.",

year = "2017",

month = nov,

day = "15",

doi = "10.1016/j.physa.2017.05.069",

language = "English",

volume = "486",

pages = "867--882",

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

issn = "0378-4371",

publisher = "Elsevier B.V.",

}

TY - JOUR

T1 - Asymptotic behavior of a stochastic delayed HIV-1 infection model with nonlinear incidence

AU - Liu, Qun

AU - Jiang, Daqing

AU - Hayat, Tasawar

AU - Ahmad, Bashir

PY - 2017/11/15

Y1 - 2017/11/15

N2 - In this paper, a stochastic delayed HIV-1 infection model with nonlinear incidence is proposed and investigated. First of all, we prove that there is a unique global positive solution as desired in any population dynamics. Then by constructing some suitable Lyapunov functions, we show that if the basic reproduction number R0≤1, then the solution of the stochastic system oscillates around the infection-free equilibrium E0, while if R0>1, then the solution of the stochastic system fluctuates around the infective equilibrium E∗. Sufficient conditions of these results are established. Finally, we give some examples and a series of numerical simulations to illustrate the analytical results.

AB - In this paper, a stochastic delayed HIV-1 infection model with nonlinear incidence is proposed and investigated. First of all, we prove that there is a unique global positive solution as desired in any population dynamics. Then by constructing some suitable Lyapunov functions, we show that if the basic reproduction number R0≤1, then the solution of the stochastic system oscillates around the infection-free equilibrium E0, while if R0>1, then the solution of the stochastic system fluctuates around the infective equilibrium E∗. Sufficient conditions of these results are established. Finally, we give some examples and a series of numerical simulations to illustrate the analytical results.

KW - Lyapunov functional

KW - Nonlinear incidence

KW - Stochastic HIV-1 infection model

KW - Time delay

UR - https://www.scopus.com/pages/publications/85021174336

U2 - 10.1016/j.physa.2017.05.069

DO - 10.1016/j.physa.2017.05.069

M3 - Article

AN - SCOPUS:85021174336

SN - 0378-4371

VL - 486

SP - 867

EP - 882

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

ER -

Asymptotic behavior of a stochastic delayed HIV-1 infection model with nonlinear incidence

Abstract

UN SDGs

Keywords

Access to Document

Other files and links

Fingerprint

Cite this