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Analysis of Stochastic SIRC Model with Cross Immunity Based on Ornstein–Uhlenbeck Process

In this paper, we analyze a stochastic SIRC model with Ornstein–Uhlenbeck process. Firstly, we give the existence and uniqueness of global solution of stochastic SIRC model and prove it. In addition, the existence of ergodic stationary distributions for stochastic SIRC system is proved by constructi...

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Detalles Bibliográficos
Autores principales: Ni, Zhiming, Jiang, Daqing, Cao, Zhongwei, Mu, Xiaojie
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2023
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10117279/
https://www.ncbi.nlm.nih.gov/pubmed/37124841
http://dx.doi.org/10.1007/s12346-023-00782-3
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author Ni, Zhiming
Jiang, Daqing
Cao, Zhongwei
Mu, Xiaojie
author_facet Ni, Zhiming
Jiang, Daqing
Cao, Zhongwei
Mu, Xiaojie
author_sort Ni, Zhiming
collection PubMed
description In this paper, we analyze a stochastic SIRC model with Ornstein–Uhlenbeck process. Firstly, we give the existence and uniqueness of global solution of stochastic SIRC model and prove it. In addition, the existence of ergodic stationary distributions for stochastic SIRC system is proved by constructing a suitable series of Lyapunov functions. A quasi-endemic equilibrium related to endemic equilibrium of deterministic systems is defined by considering randomness. And we obtain the probability density function of the linearized system near the equilibrium point. After the proof of probability density function, the sufficient condition of disease extinction is given and proved. We prove the theoretical results in the paper by numerical simulation at the end of the paper.
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spelling pubmed-101172792023-04-25 Analysis of Stochastic SIRC Model with Cross Immunity Based on Ornstein–Uhlenbeck Process Ni, Zhiming Jiang, Daqing Cao, Zhongwei Mu, Xiaojie Qual Theory Dyn Syst Article In this paper, we analyze a stochastic SIRC model with Ornstein–Uhlenbeck process. Firstly, we give the existence and uniqueness of global solution of stochastic SIRC model and prove it. In addition, the existence of ergodic stationary distributions for stochastic SIRC system is proved by constructing a suitable series of Lyapunov functions. A quasi-endemic equilibrium related to endemic equilibrium of deterministic systems is defined by considering randomness. And we obtain the probability density function of the linearized system near the equilibrium point. After the proof of probability density function, the sufficient condition of disease extinction is given and proved. We prove the theoretical results in the paper by numerical simulation at the end of the paper. Springer International Publishing 2023-04-20 2023 /pmc/articles/PMC10117279/ /pubmed/37124841 http://dx.doi.org/10.1007/s12346-023-00782-3 Text en © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2023, Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. This article is made available via the PMC Open Access Subset for unrestricted research re-use and secondary analysis in any form or by any means with acknowledgement of the original source. These permissions are granted for the duration of the World Health Organization (WHO) declaration of COVID-19 as a global pandemic.
spellingShingle Article
Ni, Zhiming
Jiang, Daqing
Cao, Zhongwei
Mu, Xiaojie
Analysis of Stochastic SIRC Model with Cross Immunity Based on Ornstein–Uhlenbeck Process
title Analysis of Stochastic SIRC Model with Cross Immunity Based on Ornstein–Uhlenbeck Process
title_full Analysis of Stochastic SIRC Model with Cross Immunity Based on Ornstein–Uhlenbeck Process
title_fullStr Analysis of Stochastic SIRC Model with Cross Immunity Based on Ornstein–Uhlenbeck Process
title_full_unstemmed Analysis of Stochastic SIRC Model with Cross Immunity Based on Ornstein–Uhlenbeck Process
title_short Analysis of Stochastic SIRC Model with Cross Immunity Based on Ornstein–Uhlenbeck Process
title_sort analysis of stochastic sirc model with cross immunity based on ornstein–uhlenbeck process
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10117279/
https://www.ncbi.nlm.nih.gov/pubmed/37124841
http://dx.doi.org/10.1007/s12346-023-00782-3
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