A stochastic threshold to predict extinction and persistence of an epidemic SIRS system with a general incidence rate

A. Settati; A. Lahrouz; M. Zahri; A. Tridane; M. El Fatini; H. El Mahjour; M. Seaid

doi:10.1016/j.chaos.2021.110690

A stochastic threshold to predict extinction and persistence of an epidemic SIRS system with a general incidence rate

A. Settati
, A. Lahrouz
, M. Zahri
, A. Tridane
, M. El Fatini
, H. El Mahjour
, M. Seaid

Department of Mathematical Sciences

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

24 Citations (Scopus)

Abstract

This work aims to give a detailed analysis of a stochastic epidemic model with a general incidence rate g(S)I. We introduce the generalized stochastic threshold R_s(g) that will be used as a threshold condition of extinction, persistence and existence of an ergodic stationary distribution. We also investigate the critical case when R_s(g)=1. Numerical illustrations of the findings are given via different types of function g.

Original language	English
Article number	110690
Journal	Chaos, Solitons and Fractals
Volume	144
DOIs	https://doi.org/10.1016/j.chaos.2021.110690
Publication status	Published - Mar 2021

Keywords

Persistence
Stationary distribution
Stochastic epidemic model
Stochastic stability

ASJC Scopus subject areas

Statistical and Nonlinear Physics
General Mathematics
General Physics and Astronomy
Applied Mathematics

Access to Document

10.1016/j.chaos.2021.110690

Cite this

@article{b38fb9c2f16d4c2ba910f831419947ec,

title = "A stochastic threshold to predict extinction and persistence of an epidemic SIRS system with a general incidence rate",

abstract = "This work aims to give a detailed analysis of a stochastic epidemic model with a general incidence rate g(S)I. We introduce the generalized stochastic threshold Rs(g) that will be used as a threshold condition of extinction, persistence and existence of an ergodic stationary distribution. We also investigate the critical case when Rs(g)=1. Numerical illustrations of the findings are given via different types of function g.",

keywords = "Persistence, Stationary distribution, Stochastic epidemic model, Stochastic stability",

author = "A. Settati and A. Lahrouz and M. Zahri and A. Tridane and \{El Fatini\}, M. and \{El Mahjour\}, H. and M. Seaid",

note = "Publisher Copyright: {\textcopyright} 2021 Elsevier Ltd",

year = "2021",

month = mar,

doi = "10.1016/j.chaos.2021.110690",

language = "English",

volume = "144",

journal = "Chaos, Solitons and Fractals",

issn = "0960-0779",

publisher = "Elsevier Ltd",

}

TY - JOUR

T1 - A stochastic threshold to predict extinction and persistence of an epidemic SIRS system with a general incidence rate

AU - Settati, A.

AU - Lahrouz, A.

AU - Zahri, M.

AU - Tridane, A.

AU - El Fatini, M.

AU - El Mahjour, H.

AU - Seaid, M.

PY - 2021/3

Y1 - 2021/3

N2 - This work aims to give a detailed analysis of a stochastic epidemic model with a general incidence rate g(S)I. We introduce the generalized stochastic threshold Rs(g) that will be used as a threshold condition of extinction, persistence and existence of an ergodic stationary distribution. We also investigate the critical case when Rs(g)=1. Numerical illustrations of the findings are given via different types of function g.

AB - This work aims to give a detailed analysis of a stochastic epidemic model with a general incidence rate g(S)I. We introduce the generalized stochastic threshold Rs(g) that will be used as a threshold condition of extinction, persistence and existence of an ergodic stationary distribution. We also investigate the critical case when Rs(g)=1. Numerical illustrations of the findings are given via different types of function g.

KW - Persistence

KW - Stationary distribution

KW - Stochastic epidemic model

KW - Stochastic stability

UR - https://www.scopus.com/pages/publications/85100378317

UR - https://www.scopus.com/pages/publications/85100378317#tab=citedBy

U2 - 10.1016/j.chaos.2021.110690

DO - 10.1016/j.chaos.2021.110690

M3 - Article

AN - SCOPUS:85100378317

SN - 0960-0779

VL - 144

JO - Chaos, Solitons and Fractals

JF - Chaos, Solitons and Fractals

M1 - 110690

ER -

A stochastic threshold to predict extinction and persistence of an epidemic SIRS system with a general incidence rate

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this