Stochastically asymptotically stability of the multi-group SEIR and SIR models with random perturbation

Chengjun Yuan; Daqing Jiang; Donal O'Regan; Ravi P. Agarwal

doi:10.1016/j.cnsns.2011.07.025

Stochastically asymptotically stability of the multi-group SEIR and SIR models with random perturbation

Chengjun Yuan
, Daqing Jiang
, Donal O'Regan
, Ravi P. Agarwal

Mathematics

Northeast Normal University
Harbin University
Department of Mathematical Sciences
King Fahd University of Petroleum and Minerals

Research output: Contribution to a Journal (Peer & Non Peer) › Article › peer-review

52 Citations (Scopus)

Abstract

In this paper, we discuss the multi-group SEIR and SIR model with random perturbation, allowing random fluctuation around the endemic equilibrium of deterministic SEIR and SIR models. We prove that the endemic equilibriums of the two models are both stochastic asymptotically stable. In addition, the stability condition is obtained by the construction of the Lyapunov function and graph theory. Finally, numerical simulations are presented to illustrate our mathematical findings.

Original language	English
Pages (from-to)	2501-2516
Number of pages	16
Journal	Communications in Nonlinear Science and Numerical Simulation
Volume	17
Issue number	6
DOIs	https://doi.org/10.1016/j.cnsns.2011.07.025
Publication status	Published - Jun 2012

UN SDGs

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

SDG 3 Good Health and Well-being

Keywords

Brownian motion
Itô's formula
Kirchhoff's Matrix-Tree Theorem
Lyapunov function
Stochastic asymptotically stable
Stochastic multi-group SEIR and SIR model

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10.1016/j.cnsns.2011.07.025

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abstract = "In this paper, we discuss the multi-group SEIR and SIR model with random perturbation, allowing random fluctuation around the endemic equilibrium of deterministic SEIR and SIR models. We prove that the endemic equilibriums of the two models are both stochastic asymptotically stable. In addition, the stability condition is obtained by the construction of the Lyapunov function and graph theory. Finally, numerical simulations are presented to illustrate our mathematical findings.",

keywords = "Brownian motion, It{\^o}'s formula, Kirchhoff's Matrix-Tree Theorem, Lyapunov function, Stochastic asymptotically stable, Stochastic multi-group SEIR and SIR model",

author = "Chengjun Yuan and Daqing Jiang and Donal O'Regan and Agarwal, \{Ravi P.\}",

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T1 - Stochastically asymptotically stability of the multi-group SEIR and SIR models with random perturbation

AU - Yuan, Chengjun

AU - Jiang, Daqing

AU - O'Regan, Donal

AU - Agarwal, Ravi P.

PY - 2012/6

Y1 - 2012/6

N2 - In this paper, we discuss the multi-group SEIR and SIR model with random perturbation, allowing random fluctuation around the endemic equilibrium of deterministic SEIR and SIR models. We prove that the endemic equilibriums of the two models are both stochastic asymptotically stable. In addition, the stability condition is obtained by the construction of the Lyapunov function and graph theory. Finally, numerical simulations are presented to illustrate our mathematical findings.

AB - In this paper, we discuss the multi-group SEIR and SIR model with random perturbation, allowing random fluctuation around the endemic equilibrium of deterministic SEIR and SIR models. We prove that the endemic equilibriums of the two models are both stochastic asymptotically stable. In addition, the stability condition is obtained by the construction of the Lyapunov function and graph theory. Finally, numerical simulations are presented to illustrate our mathematical findings.

KW - Brownian motion

KW - Itô's formula

KW - Kirchhoff's Matrix-Tree Theorem

KW - Lyapunov function

KW - Stochastic asymptotically stable

KW - Stochastic multi-group SEIR and SIR model

UR - https://www.scopus.com/pages/publications/84855233210

U2 - 10.1016/j.cnsns.2011.07.025

DO - 10.1016/j.cnsns.2011.07.025

M3 - Article

SN - 1007-5704

VL - 17

SP - 2501

EP - 2516

JO - Communications in Nonlinear Science and Numerical Simulation

JF - Communications in Nonlinear Science and Numerical Simulation

IS - 6

ER -

Stochastically asymptotically stability of the multi-group SEIR and SIR models with random perturbation

Abstract

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Keywords

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