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An SIRS model with nonmonotone incidence and saturated treatment in a changing environment

Nonmonotone incidence and saturated treatment are incorporated into an SIRS model under constant and changing environments. The nonmonotone incidence rate describes the psychological or inhibitory effect: when the number of the infected individuals exceeds a certain level, the infection function dec...

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Autores principales: Pan, Qin, Huang, Jicai, Wang, Hao
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2022
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9392446/
https://www.ncbi.nlm.nih.gov/pubmed/35986794
http://dx.doi.org/10.1007/s00285-022-01787-3
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author Pan, Qin
Huang, Jicai
Wang, Hao
author_facet Pan, Qin
Huang, Jicai
Wang, Hao
author_sort Pan, Qin
collection PubMed
description Nonmonotone incidence and saturated treatment are incorporated into an SIRS model under constant and changing environments. The nonmonotone incidence rate describes the psychological or inhibitory effect: when the number of the infected individuals exceeds a certain level, the infection function decreases. The saturated treatment function describes the effect of infected individuals being delayed for treatment due to the limitation of medical resources. In a constant environment, the model undergoes a sequence of bifurcations including backward bifurcation, degenerate Bogdanov-Takens bifurcation of codimension 3, degenerate Hopf bifurcation as the parameters vary, and the model exhibits rich dynamics such as bistability, tristability, multiple periodic orbits, and homoclinic orbits. Moreover, we provide some sufficient conditions to guarantee the global asymptotical stability of the disease-free equilibrium or the unique positive equilibrium. Our results indicate that there exist three critical values [Formula: see text] and [Formula: see text] for the treatment rate r: (i) when [Formula: see text] , the disease will disappear; (ii) when [Formula: see text] , the disease will persist. In a changing environment, the infective population starts along the stable disease-free state (or an endemic state) and surprisingly continues tracking the unstable disease-free state (or a limit cycle) when the system crosses a bifurcation point, and eventually tends to the stable endemic state (or the stable disease-free state). This transient tracking of the unstable disease-free state when [Formula: see text] predicts regime shifts that cause the delayed disease outbreak in a changing environment. Furthermore, the disease can disappear in advance (or belatedly) if the rate of environmental change is negative and large (or small). The transient dynamics of an infectious disease heavily depend on the initial infection number and rate or the speed of environmental change. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s00285-022-01787-3.
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spelling pubmed-93924462022-08-22 An SIRS model with nonmonotone incidence and saturated treatment in a changing environment Pan, Qin Huang, Jicai Wang, Hao J Math Biol Article Nonmonotone incidence and saturated treatment are incorporated into an SIRS model under constant and changing environments. The nonmonotone incidence rate describes the psychological or inhibitory effect: when the number of the infected individuals exceeds a certain level, the infection function decreases. The saturated treatment function describes the effect of infected individuals being delayed for treatment due to the limitation of medical resources. In a constant environment, the model undergoes a sequence of bifurcations including backward bifurcation, degenerate Bogdanov-Takens bifurcation of codimension 3, degenerate Hopf bifurcation as the parameters vary, and the model exhibits rich dynamics such as bistability, tristability, multiple periodic orbits, and homoclinic orbits. Moreover, we provide some sufficient conditions to guarantee the global asymptotical stability of the disease-free equilibrium or the unique positive equilibrium. Our results indicate that there exist three critical values [Formula: see text] and [Formula: see text] for the treatment rate r: (i) when [Formula: see text] , the disease will disappear; (ii) when [Formula: see text] , the disease will persist. In a changing environment, the infective population starts along the stable disease-free state (or an endemic state) and surprisingly continues tracking the unstable disease-free state (or a limit cycle) when the system crosses a bifurcation point, and eventually tends to the stable endemic state (or the stable disease-free state). This transient tracking of the unstable disease-free state when [Formula: see text] predicts regime shifts that cause the delayed disease outbreak in a changing environment. Furthermore, the disease can disappear in advance (or belatedly) if the rate of environmental change is negative and large (or small). The transient dynamics of an infectious disease heavily depend on the initial infection number and rate or the speed of environmental change. SUPPLEMENTARY INFORMATION: The online version contains supplementary material available at 10.1007/s00285-022-01787-3. Springer Berlin Heidelberg 2022-08-20 2022 /pmc/articles/PMC9392446/ /pubmed/35986794 http://dx.doi.org/10.1007/s00285-022-01787-3 Text en © The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023, corrected publication 2023Springer 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
Pan, Qin
Huang, Jicai
Wang, Hao
An SIRS model with nonmonotone incidence and saturated treatment in a changing environment
title An SIRS model with nonmonotone incidence and saturated treatment in a changing environment
title_full An SIRS model with nonmonotone incidence and saturated treatment in a changing environment
title_fullStr An SIRS model with nonmonotone incidence and saturated treatment in a changing environment
title_full_unstemmed An SIRS model with nonmonotone incidence and saturated treatment in a changing environment
title_short An SIRS model with nonmonotone incidence and saturated treatment in a changing environment
title_sort sirs model with nonmonotone incidence and saturated treatment in a changing environment
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9392446/
https://www.ncbi.nlm.nih.gov/pubmed/35986794
http://dx.doi.org/10.1007/s00285-022-01787-3
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