A geometric analysis of the SIRS epidemiological model on a homogeneous network

We study a fast–slow version of an SIRS epidemiological model on homogeneous graphs, obtained through the application of the moment closure method. We use GSPT to study the model, taking into account that the infection period is much shorter than the average duration of immunity. We show that the dy...

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Autores principales: Jardón-Kojakhmetov, Hildeberto, Kuehn, Christian, Pugliese, Andrea, Sensi, Mattia
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8456690/
https://www.ncbi.nlm.nih.gov/pubmed/34550488
http://dx.doi.org/10.1007/s00285-021-01664-5
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author Jardón-Kojakhmetov, Hildeberto
Kuehn, Christian
Pugliese, Andrea
Sensi, Mattia
author_facet Jardón-Kojakhmetov, Hildeberto
Kuehn, Christian
Pugliese, Andrea
Sensi, Mattia
author_sort Jardón-Kojakhmetov, Hildeberto
collection PubMed
description We study a fast–slow version of an SIRS epidemiological model on homogeneous graphs, obtained through the application of the moment closure method. We use GSPT to study the model, taking into account that the infection period is much shorter than the average duration of immunity. We show that the dynamics occurs through a sequence of fast and slow flows, that can be described through 2-dimensional maps that, under some assumptions, can be approximated as 1-dimensional maps. Using this method, together with numerical bifurcation tools, we show that the model can give rise to periodic solutions, differently from the corresponding model based on homogeneous mixing.
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spelling pubmed-84566902021-09-22 A geometric analysis of the SIRS epidemiological model on a homogeneous network Jardón-Kojakhmetov, Hildeberto Kuehn, Christian Pugliese, Andrea Sensi, Mattia J Math Biol Article We study a fast–slow version of an SIRS epidemiological model on homogeneous graphs, obtained through the application of the moment closure method. We use GSPT to study the model, taking into account that the infection period is much shorter than the average duration of immunity. We show that the dynamics occurs through a sequence of fast and slow flows, that can be described through 2-dimensional maps that, under some assumptions, can be approximated as 1-dimensional maps. Using this method, together with numerical bifurcation tools, we show that the model can give rise to periodic solutions, differently from the corresponding model based on homogeneous mixing. Springer Berlin Heidelberg 2021-09-22 2021 /pmc/articles/PMC8456690/ /pubmed/34550488 http://dx.doi.org/10.1007/s00285-021-01664-5 Text en © The Author(s) 2021 https://creativecommons.org/licenses/by/4.0/Open AccessThis 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 licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence 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 licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Jardón-Kojakhmetov, Hildeberto
Kuehn, Christian
Pugliese, Andrea
Sensi, Mattia
A geometric analysis of the SIRS epidemiological model on a homogeneous network
title A geometric analysis of the SIRS epidemiological model on a homogeneous network
title_full A geometric analysis of the SIRS epidemiological model on a homogeneous network
title_fullStr A geometric analysis of the SIRS epidemiological model on a homogeneous network
title_full_unstemmed A geometric analysis of the SIRS epidemiological model on a homogeneous network
title_short A geometric analysis of the SIRS epidemiological model on a homogeneous network
title_sort geometric analysis of the sirs epidemiological model on a homogeneous network
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8456690/
https://www.ncbi.nlm.nih.gov/pubmed/34550488
http://dx.doi.org/10.1007/s00285-021-01664-5
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