Periodic solution and stationary distribution of stochastic S-DI-A epidemic models

Xinhong Zhang; Daqing Jiang; Tasawar Hayat; Ahmed Alsaedi

doi:10.1080/00036811.2016.1257123

Periodic solution and stationary distribution of stochastic S-DI-A epidemic models

Xinhong Zhang
, Daqing Jiang
, Tasawar Hayat
, Ahmed Alsaedi

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

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

8 Scopus citations

Abstract

This paper considers two S-DI-A models in random environments. Firstly, using Has’minskii theory of periodic solution, we show that stochastic periodic S-DI-A model has a nontrivial positive periodic solution if R^s₀ > 1. Then, we construct stochastic Lyapunov functions with regime switching to obtain the existence of ergodic stationary distribution of the solution to S-DI-A model perturbed by white and telephone noises. Finally, examples are introduced to illustrate the results developed.

Original language	English
Pages (from-to)	179-193
Number of pages	15
Journal	Applicable Analysis
Volume	97
Issue number	2
DOIs	https://doi.org/10.1080/00036811.2016.1257123
State	Published - 25 Jan 2018
Externally published	Yes

UN SDGs

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

SDG 3 Good Health and Well-being

Keywords

Markov switching
S-DI-A model
stationary distribution
stochastic periodic solutions

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10.1080/00036811.2016.1257123

Cite this

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title = "Periodic solution and stationary distribution of stochastic S-DI-A epidemic models",

abstract = "This paper considers two S-DI-A models in random environments. Firstly, using Has{\textquoteright}minskii theory of periodic solution, we show that stochastic periodic S-DI-A model has a nontrivial positive periodic solution if Rs0 > 1. Then, we construct stochastic Lyapunov functions with regime switching to obtain the existence of ergodic stationary distribution of the solution to S-DI-A model perturbed by white and telephone noises. Finally, examples are introduced to illustrate the results developed.",

keywords = "Markov switching, S-DI-A model, stationary distribution, stochastic periodic solutions",

author = "Xinhong Zhang and Daqing Jiang and Tasawar Hayat and Ahmed Alsaedi",

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doi = "10.1080/00036811.2016.1257123",

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TY - JOUR

T1 - Periodic solution and stationary distribution of stochastic S-DI-A epidemic models

AU - Zhang, Xinhong

AU - Jiang, Daqing

AU - Hayat, Tasawar

AU - Alsaedi, Ahmed

PY - 2018/1/25

Y1 - 2018/1/25

N2 - This paper considers two S-DI-A models in random environments. Firstly, using Has’minskii theory of periodic solution, we show that stochastic periodic S-DI-A model has a nontrivial positive periodic solution if Rs0 > 1. Then, we construct stochastic Lyapunov functions with regime switching to obtain the existence of ergodic stationary distribution of the solution to S-DI-A model perturbed by white and telephone noises. Finally, examples are introduced to illustrate the results developed.

AB - This paper considers two S-DI-A models in random environments. Firstly, using Has’minskii theory of periodic solution, we show that stochastic periodic S-DI-A model has a nontrivial positive periodic solution if Rs0 > 1. Then, we construct stochastic Lyapunov functions with regime switching to obtain the existence of ergodic stationary distribution of the solution to S-DI-A model perturbed by white and telephone noises. Finally, examples are introduced to illustrate the results developed.

KW - Markov switching

KW - S-DI-A model

KW - stationary distribution

KW - stochastic periodic solutions

UR - https://www.scopus.com/pages/publications/84996482881

U2 - 10.1080/00036811.2016.1257123

DO - 10.1080/00036811.2016.1257123

M3 - Article

AN - SCOPUS:84996482881

SN - 0003-6811

VL - 97

SP - 179

EP - 193

JO - Applicable Analysis

JF - Applicable Analysis

IS - 2

ER -

Periodic solution and stationary distribution of stochastic S-DI-A epidemic models

Abstract

UN SDGs

Keywords

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