An SIS epidemic model with time delay and stochastic perturbation on heterogeneous networks

An SIS epidemic model with time delay and stochastic perturbation on scale-free networks is established in this paper. And we derive sufficient conditions guaranteeing extinction and persistence of epidemics, respectively, which are related to the basic reproduction number $ R_0 $ of the correspondi...

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Main Authors:	Meici Sun, Qiming Liu
Format:	article
Language:	EN
Published:	AIMS Press 2021
Subjects:	stochastic sis model time delay a.s. exponentially stable extinction persistence Biotechnology TP248.13-248.65 Mathematics QA1-939
Online Access:	https://doaj.org/article/ddd7ed9c636243eb9f0f0dc7c33d6480
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spelling	oai:doaj.org-article:ddd7ed9c636243eb9f0f0dc7c33d64802021-11-12T02:22:55ZAn SIS epidemic model with time delay and stochastic perturbation on heterogeneous networks10.3934/mbe.20213371551-0018https://doaj.org/article/ddd7ed9c636243eb9f0f0dc7c33d64802021-08-01T00:00:00Zhttps://www.aimspress.com/article/doi/10.3934/mbe.2021337?viewType=HTMLhttps://doaj.org/toc/1551-0018An SIS epidemic model with time delay and stochastic perturbation on scale-free networks is established in this paper. And we derive sufficient conditions guaranteeing extinction and persistence of epidemics, respectively, which are related to the basic reproduction number $ R_0 $ of the corresponding deterministic model. When $ R_0 < 1 $, almost surely exponential extinction and $ p $-th moment exponential extinction of epidemics are proved by Razumikhin-Mao Theorem. Whereas, when $ R_0 > 1 $, the system is persistent in the mean under sufficiently weak noise intensities, which indicates that the disease will prevail. Finally, the main results are demonstrated by numerical simulations.Meici SunQiming Liu AIMS Pressarticlestochastic sis modeltime delaya.s. exponentially stableextinctionpersistenceBiotechnologyTP248.13-248.65MathematicsQA1-939ENMathematical Biosciences and Engineering, Vol 18, Iss 5, Pp 6790-6805 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	stochastic sis model time delay a.s. exponentially stable extinction persistence Biotechnology TP248.13-248.65 Mathematics QA1-939
spellingShingle	stochastic sis model time delay a.s. exponentially stable extinction persistence Biotechnology TP248.13-248.65 Mathematics QA1-939 Meici Sun Qiming Liu An SIS epidemic model with time delay and stochastic perturbation on heterogeneous networks
description	An SIS epidemic model with time delay and stochastic perturbation on scale-free networks is established in this paper. And we derive sufficient conditions guaranteeing extinction and persistence of epidemics, respectively, which are related to the basic reproduction number $ R_0 $ of the corresponding deterministic model. When $ R_0 < 1 $, almost surely exponential extinction and $ p $-th moment exponential extinction of epidemics are proved by Razumikhin-Mao Theorem. Whereas, when $ R_0 > 1 $, the system is persistent in the mean under sufficiently weak noise intensities, which indicates that the disease will prevail. Finally, the main results are demonstrated by numerical simulations.
format	article
author	Meici Sun Qiming Liu
author_facet	Meici Sun Qiming Liu
author_sort	Meici Sun
title	An SIS epidemic model with time delay and stochastic perturbation on heterogeneous networks
title_short	An SIS epidemic model with time delay and stochastic perturbation on heterogeneous networks
title_full	An SIS epidemic model with time delay and stochastic perturbation on heterogeneous networks
title_fullStr	An SIS epidemic model with time delay and stochastic perturbation on heterogeneous networks
title_full_unstemmed	An SIS epidemic model with time delay and stochastic perturbation on heterogeneous networks
title_sort	sis epidemic model with time delay and stochastic perturbation on heterogeneous networks
publisher	AIMS Press
publishDate	2021
url	https://doaj.org/article/ddd7ed9c636243eb9f0f0dc7c33d6480
work_keys_str_mv	AT meicisun ansisepidemicmodelwithtimedelayandstochasticperturbationonheterogeneousnetworks AT qimingliu ansisepidemicmodelwithtimedelayandstochasticperturbationonheterogeneousnetworks AT meicisun sisepidemicmodelwithtimedelayandstochasticperturbationonheterogeneousnetworks AT qimingliu sisepidemicmodelwithtimedelayandstochasticperturbationonheterogeneousnetworks
_version_	1718431321186893824

An SIS epidemic model with time delay and stochastic perturbation on heterogeneous networks

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