Dynamical behavior of a stochastic SVIR epidemic model with vaccination

Xinhong Zhang; Daqing Jiang; Tasawar Hayat; Bashir Ahmad

doi:10.1016/j.physa.2017.04.173

Dynamical behavior of a stochastic SVIR epidemic model with vaccination

Xinhong Zhang
, Daqing Jiang
, Tasawar Hayat
, Bashir Ahmad

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

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

60 Scopus citations

Abstract

In this paper, we investigate the dynamical behavior of SVIR models in random environments. Firstly, we show that if R₀^s<1, the disease of stochastic autonomous SVIR model will die out exponentially; if R̃₀^s>1, the disease will be prevail. Moreover, this system admits a unique stationary distribution and it is ergodic when R̃₀^s>1. Results show that environmental white noise is helpful for disease control. Secondly, we give sufficient conditions for the existence of nontrivial periodic solutions to stochastic SVIR model with periodic parameters. Finally, numerical simulations validate the analytical results.

Original language	English
Pages (from-to)	94-108
Number of pages	15
Journal	Physica A: Statistical Mechanics and its Applications
Volume	483
DOIs	https://doi.org/10.1016/j.physa.2017.04.173
State	Published - 1 Oct 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

Extinction
SVIR epidemic model
Stationary distribution
Stochastic periodic solutions

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10.1016/j.physa.2017.04.173

Cite this

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title = "Dynamical behavior of a stochastic SVIR epidemic model with vaccination",

abstract = "In this paper, we investigate the dynamical behavior of SVIR models in random environments. Firstly, we show that if R0s<1, the disease of stochastic autonomous SVIR model will die out exponentially; if {\~R}0s>1, the disease will be prevail. Moreover, this system admits a unique stationary distribution and it is ergodic when {\~R}0s>1. Results show that environmental white noise is helpful for disease control. Secondly, we give sufficient conditions for the existence of nontrivial periodic solutions to stochastic SVIR model with periodic parameters. Finally, numerical simulations validate the analytical results.",

keywords = "Extinction, SVIR epidemic model, Stationary distribution, Stochastic periodic solutions",

author = "Xinhong Zhang and Daqing Jiang and Tasawar Hayat and Bashir Ahmad",

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doi = "10.1016/j.physa.2017.04.173",

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T1 - Dynamical behavior of a stochastic SVIR epidemic model with vaccination

AU - Zhang, Xinhong

AU - Jiang, Daqing

AU - Hayat, Tasawar

AU - Ahmad, Bashir

PY - 2017/10/1

Y1 - 2017/10/1

N2 - In this paper, we investigate the dynamical behavior of SVIR models in random environments. Firstly, we show that if R0s<1, the disease of stochastic autonomous SVIR model will die out exponentially; if R̃0s>1, the disease will be prevail. Moreover, this system admits a unique stationary distribution and it is ergodic when R̃0s>1. Results show that environmental white noise is helpful for disease control. Secondly, we give sufficient conditions for the existence of nontrivial periodic solutions to stochastic SVIR model with periodic parameters. Finally, numerical simulations validate the analytical results.

AB - In this paper, we investigate the dynamical behavior of SVIR models in random environments. Firstly, we show that if R0s<1, the disease of stochastic autonomous SVIR model will die out exponentially; if R̃0s>1, the disease will be prevail. Moreover, this system admits a unique stationary distribution and it is ergodic when R̃0s>1. Results show that environmental white noise is helpful for disease control. Secondly, we give sufficient conditions for the existence of nontrivial periodic solutions to stochastic SVIR model with periodic parameters. Finally, numerical simulations validate the analytical results.

KW - Extinction

KW - SVIR epidemic model

KW - Stationary distribution

KW - Stochastic periodic solutions

UR - https://www.scopus.com/pages/publications/85019117489

U2 - 10.1016/j.physa.2017.04.173

DO - 10.1016/j.physa.2017.04.173

M3 - Article

AN - SCOPUS:85019117489

SN - 0378-4371

VL - 483

SP - 94

EP - 108

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

ER -

Dynamical behavior of a stochastic SVIR epidemic model with vaccination

Abstract

UN SDGs

Keywords

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