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Stationary distribution and density function expression for a stochastic SIQRS epidemic model with temporary immunity
Recently, considering the temporary immunity of individuals who have recovered from certain infectious diseases, Liu et al. (Phys A Stat Mech Appl 551:124152, 2020) proposed and studied a stochastic susceptible-infected-recovered-susceptible model with logistic growth. For a more realistic situation...
Autores principales: | , , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer Netherlands
2021
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8186371/ https://www.ncbi.nlm.nih.gov/pubmed/34121810 http://dx.doi.org/10.1007/s11071-020-06151-y |
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author | Zhou, Baoquan Jiang, Daqing Dai, Yucong Hayat, Tasawar |
author_facet | Zhou, Baoquan Jiang, Daqing Dai, Yucong Hayat, Tasawar |
author_sort | Zhou, Baoquan |
collection | PubMed |
description | Recently, considering the temporary immunity of individuals who have recovered from certain infectious diseases, Liu et al. (Phys A Stat Mech Appl 551:124152, 2020) proposed and studied a stochastic susceptible-infected-recovered-susceptible model with logistic growth. For a more realistic situation, the effects of quarantine strategies and stochasticity should be taken into account. Hence, our paper focuses on a stochastic susceptible-infected-quarantined-recovered-susceptible epidemic model with temporary immunity. First, by means of the Khas’minskii theory and Lyapunov function approach, we construct a critical value [Formula: see text] corresponding to the basic reproduction number [Formula: see text] of the deterministic system. Moreover, we prove that there is a unique ergodic stationary distribution if [Formula: see text] . Focusing on the results of Zhou et al. (Chaos Soliton Fractals 137:109865, 2020), we develop some suitable solving theories for the general four-dimensional Fokker–Planck equation. The key aim of the present study is to obtain the explicit density function expression of the stationary distribution under [Formula: see text] . It should be noted that the existence of an ergodic stationary distribution together with the unique exact probability density function can reveal all the dynamical properties of disease persistence in both epidemiological and statistical aspects. Next, some numerical simulations together with parameter analyses are shown to support our theoretical results. Last, through comparison with other articles, results are discussed and the main conclusions are highlighted. |
format | Online Article Text |
id | pubmed-8186371 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | Springer Netherlands |
record_format | MEDLINE/PubMed |
spelling | pubmed-81863712021-06-09 Stationary distribution and density function expression for a stochastic SIQRS epidemic model with temporary immunity Zhou, Baoquan Jiang, Daqing Dai, Yucong Hayat, Tasawar Nonlinear Dyn Original Paper Recently, considering the temporary immunity of individuals who have recovered from certain infectious diseases, Liu et al. (Phys A Stat Mech Appl 551:124152, 2020) proposed and studied a stochastic susceptible-infected-recovered-susceptible model with logistic growth. For a more realistic situation, the effects of quarantine strategies and stochasticity should be taken into account. Hence, our paper focuses on a stochastic susceptible-infected-quarantined-recovered-susceptible epidemic model with temporary immunity. First, by means of the Khas’minskii theory and Lyapunov function approach, we construct a critical value [Formula: see text] corresponding to the basic reproduction number [Formula: see text] of the deterministic system. Moreover, we prove that there is a unique ergodic stationary distribution if [Formula: see text] . Focusing on the results of Zhou et al. (Chaos Soliton Fractals 137:109865, 2020), we develop some suitable solving theories for the general four-dimensional Fokker–Planck equation. The key aim of the present study is to obtain the explicit density function expression of the stationary distribution under [Formula: see text] . It should be noted that the existence of an ergodic stationary distribution together with the unique exact probability density function can reveal all the dynamical properties of disease persistence in both epidemiological and statistical aspects. Next, some numerical simulations together with parameter analyses are shown to support our theoretical results. Last, through comparison with other articles, results are discussed and the main conclusions are highlighted. Springer Netherlands 2021-06-08 2021 /pmc/articles/PMC8186371/ /pubmed/34121810 http://dx.doi.org/10.1007/s11071-020-06151-y Text en © The Author(s), under exclusive licence to Springer Nature B.V. 2021 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 | Original Paper Zhou, Baoquan Jiang, Daqing Dai, Yucong Hayat, Tasawar Stationary distribution and density function expression for a stochastic SIQRS epidemic model with temporary immunity |
title | Stationary distribution and density function expression for a stochastic SIQRS epidemic model with temporary immunity |
title_full | Stationary distribution and density function expression for a stochastic SIQRS epidemic model with temporary immunity |
title_fullStr | Stationary distribution and density function expression for a stochastic SIQRS epidemic model with temporary immunity |
title_full_unstemmed | Stationary distribution and density function expression for a stochastic SIQRS epidemic model with temporary immunity |
title_short | Stationary distribution and density function expression for a stochastic SIQRS epidemic model with temporary immunity |
title_sort | stationary distribution and density function expression for a stochastic siqrs epidemic model with temporary immunity |
topic | Original Paper |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8186371/ https://www.ncbi.nlm.nih.gov/pubmed/34121810 http://dx.doi.org/10.1007/s11071-020-06151-y |
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