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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...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer International Publishing
2023
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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. |
format | Online Article Text |
id | pubmed-10117279 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2023 |
publisher | Springer International Publishing |
record_format | MEDLINE/PubMed |
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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