Threshold behaviour of a stochastic epidemic model with two-dimensional noises

M. El Fatini; R. Taki; A. Tridane

doi:10.1016/j.physa.2019.04.224

Threshold behaviour of a stochastic epidemic model with two-dimensional noises

M. El Fatini, R. Taki, A. Tridane

Department of Mathematical Sciences

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

1 Citation (Scopus)

Abstract

The aim of this work is to study a new stochastic SIR epidemic model that includes two types of white noises. These noises perturb two important parameters in the disease dynamic: the disease transmission rate and the recovery rate. By means of the Lyapunov functions, we prove the global existence and positivity of the solution. We also investigate the conditions of the extinction and the persistence of the disease and use a suitable Lyapunov function to study the stability of the model. Numerical simulations of our result are also presented.

Original language	English
Pages (from-to)	776-786
Number of pages	11
Journal	Physica A: Statistical Mechanics and its Applications
Volume	524
DOIs	https://doi.org/10.1016/j.physa.2019.04.224
Publication status	Published - Jun 15 2019

Keywords

Epidemic model
Extinction
Instability stochastic
Lyapunov function
Persistence in mean
Stochastic process

ASJC Scopus subject areas

Statistics and Probability
Condensed Matter Physics

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10.1016/j.physa.2019.04.224

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title = "Threshold behaviour of a stochastic epidemic model with two-dimensional noises",

abstract = "The aim of this work is to study a new stochastic SIR epidemic model that includes two types of white noises. These noises perturb two important parameters in the disease dynamic: the disease transmission rate and the recovery rate. By means of the Lyapunov functions, we prove the global existence and positivity of the solution. We also investigate the conditions of the extinction and the persistence of the disease and use a suitable Lyapunov function to study the stability of the model. Numerical simulations of our result are also presented.",

keywords = "Epidemic model, Extinction, Instability stochastic, Lyapunov function, Persistence in mean, Stochastic process",

author = "{El Fatini}, M. and R. Taki and A. Tridane",

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T1 - Threshold behaviour of a stochastic epidemic model with two-dimensional noises

AU - El Fatini, M.

AU - Taki, R.

AU - Tridane, A.

PY - 2019/6/15

Y1 - 2019/6/15

N2 - The aim of this work is to study a new stochastic SIR epidemic model that includes two types of white noises. These noises perturb two important parameters in the disease dynamic: the disease transmission rate and the recovery rate. By means of the Lyapunov functions, we prove the global existence and positivity of the solution. We also investigate the conditions of the extinction and the persistence of the disease and use a suitable Lyapunov function to study the stability of the model. Numerical simulations of our result are also presented.

AB - The aim of this work is to study a new stochastic SIR epidemic model that includes two types of white noises. These noises perturb two important parameters in the disease dynamic: the disease transmission rate and the recovery rate. By means of the Lyapunov functions, we prove the global existence and positivity of the solution. We also investigate the conditions of the extinction and the persistence of the disease and use a suitable Lyapunov function to study the stability of the model. Numerical simulations of our result are also presented.

KW - Epidemic model

KW - Extinction

KW - Instability stochastic

KW - Lyapunov function

KW - Persistence in mean

KW - Stochastic process

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M3 - Article

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VL - 524

SP - 776

EP - 786

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

ER -

Threshold behaviour of a stochastic epidemic model with two-dimensional noises

Abstract

Keywords

ASJC Scopus subject areas

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