A regime-switching SIR epidemic model with a ratio-dependent incidence rate and degenerate diffusion

In this paper, we present a regime-switching SIR epidemic model with a ratio-dependent incidence rate and degenerate diffusion. We utilize the Markov semigroup theory to obtain the existence of a unique stable stationary distribution. We prove that the densities of the distributions of the solutions...

Descripción completa

Detalles Bibliográficos
Autores principales: Cao, Zhongwei, Liu, Xu, Wen, Xiangdan, Liu, Liya, Zu, Li
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Nature Publishing Group UK 2019
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6650464/
https://www.ncbi.nlm.nih.gov/pubmed/31337826
http://dx.doi.org/10.1038/s41598-019-47131-6
_version_ 1783438133221654528
author Cao, Zhongwei
Liu, Xu
Wen, Xiangdan
Liu, Liya
Zu, Li
author_facet Cao, Zhongwei
Liu, Xu
Wen, Xiangdan
Liu, Liya
Zu, Li
author_sort Cao, Zhongwei
collection PubMed
description In this paper, we present a regime-switching SIR epidemic model with a ratio-dependent incidence rate and degenerate diffusion. We utilize the Markov semigroup theory to obtain the existence of a unique stable stationary distribution. We prove that the densities of the distributions of the solutions can converge in L(1) to an invariant density under certain condition. Moreover, the sufficient conditions for the extinction of the disease, which means the disease will die out with probability one, are given in two cases. Meanwhile, we obtain a threshold parameter which can be utilized in identifying the stochastic extinction and persistence of the disease. Some numerical simulations are given to illustrate the analytical results.
format Online
Article
Text
id pubmed-6650464
institution National Center for Biotechnology Information
language English
publishDate 2019
publisher Nature Publishing Group UK
record_format MEDLINE/PubMed
spelling pubmed-66504642019-07-29 A regime-switching SIR epidemic model with a ratio-dependent incidence rate and degenerate diffusion Cao, Zhongwei Liu, Xu Wen, Xiangdan Liu, Liya Zu, Li Sci Rep Article In this paper, we present a regime-switching SIR epidemic model with a ratio-dependent incidence rate and degenerate diffusion. We utilize the Markov semigroup theory to obtain the existence of a unique stable stationary distribution. We prove that the densities of the distributions of the solutions can converge in L(1) to an invariant density under certain condition. Moreover, the sufficient conditions for the extinction of the disease, which means the disease will die out with probability one, are given in two cases. Meanwhile, we obtain a threshold parameter which can be utilized in identifying the stochastic extinction and persistence of the disease. Some numerical simulations are given to illustrate the analytical results. Nature Publishing Group UK 2019-07-23 /pmc/articles/PMC6650464/ /pubmed/31337826 http://dx.doi.org/10.1038/s41598-019-47131-6 Text en © The Author(s) 2019 Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/.
spellingShingle Article
Cao, Zhongwei
Liu, Xu
Wen, Xiangdan
Liu, Liya
Zu, Li
A regime-switching SIR epidemic model with a ratio-dependent incidence rate and degenerate diffusion
title A regime-switching SIR epidemic model with a ratio-dependent incidence rate and degenerate diffusion
title_full A regime-switching SIR epidemic model with a ratio-dependent incidence rate and degenerate diffusion
title_fullStr A regime-switching SIR epidemic model with a ratio-dependent incidence rate and degenerate diffusion
title_full_unstemmed A regime-switching SIR epidemic model with a ratio-dependent incidence rate and degenerate diffusion
title_short A regime-switching SIR epidemic model with a ratio-dependent incidence rate and degenerate diffusion
title_sort regime-switching sir epidemic model with a ratio-dependent incidence rate and degenerate diffusion
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6650464/
https://www.ncbi.nlm.nih.gov/pubmed/31337826
http://dx.doi.org/10.1038/s41598-019-47131-6
work_keys_str_mv AT caozhongwei aregimeswitchingsirepidemicmodelwitharatiodependentincidencerateanddegeneratediffusion
AT liuxu aregimeswitchingsirepidemicmodelwitharatiodependentincidencerateanddegeneratediffusion
AT wenxiangdan aregimeswitchingsirepidemicmodelwitharatiodependentincidencerateanddegeneratediffusion
AT liuliya aregimeswitchingsirepidemicmodelwitharatiodependentincidencerateanddegeneratediffusion
AT zuli aregimeswitchingsirepidemicmodelwitharatiodependentincidencerateanddegeneratediffusion
AT caozhongwei regimeswitchingsirepidemicmodelwitharatiodependentincidencerateanddegeneratediffusion
AT liuxu regimeswitchingsirepidemicmodelwitharatiodependentincidencerateanddegeneratediffusion
AT wenxiangdan regimeswitchingsirepidemicmodelwitharatiodependentincidencerateanddegeneratediffusion
AT liuliya regimeswitchingsirepidemicmodelwitharatiodependentincidencerateanddegeneratediffusion
AT zuli regimeswitchingsirepidemicmodelwitharatiodependentincidencerateanddegeneratediffusion

Ejemplares similares