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Propagation of Epidemics Along Lines with Fast Diffusion
It has long been known that epidemics can travel along communication lines, such as roads. In the current COVID-19 epidemic, it has been observed that major roads have enhanced its propagation in Italy. We propose a new simple model of propagation of epidemics which exhibits this effect and allows f...
Autores principales: | , , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
Springer US
2020
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7734393/ https://www.ncbi.nlm.nih.gov/pubmed/33315147 http://dx.doi.org/10.1007/s11538-020-00826-8 |
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author | Berestycki, Henri Roquejoffre, Jean-Michel Rossi, Luca |
author_facet | Berestycki, Henri Roquejoffre, Jean-Michel Rossi, Luca |
author_sort | Berestycki, Henri |
collection | PubMed |
description | It has long been known that epidemics can travel along communication lines, such as roads. In the current COVID-19 epidemic, it has been observed that major roads have enhanced its propagation in Italy. We propose a new simple model of propagation of epidemics which exhibits this effect and allows for a quantitative analysis. The model consists of a classical SIR model with diffusion, to which an additional compartment is added, formed by the infected individuals travelling on a line of fast diffusion. The line and the domain interact by constant exchanges of populations. A classical transformation allows us to reduce the proposed model to a system analogous to one we had previously introduced Berestycki et al. (J Math Biol 66:743–766, 2013) to describe the enhancement of biological invasions by lines of fast diffusion. We establish the existence of a minimal spreading speed, and we show that it may be quite large, even when the basic reproduction number [Formula: see text] is close to 1. We also prove here further qualitative features of the final state, showing the influence of the line. |
format | Online Article Text |
id | pubmed-7734393 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2020 |
publisher | Springer US |
record_format | MEDLINE/PubMed |
spelling | pubmed-77343932020-12-14 Propagation of Epidemics Along Lines with Fast Diffusion Berestycki, Henri Roquejoffre, Jean-Michel Rossi, Luca Bull Math Biol Original Article It has long been known that epidemics can travel along communication lines, such as roads. In the current COVID-19 epidemic, it has been observed that major roads have enhanced its propagation in Italy. We propose a new simple model of propagation of epidemics which exhibits this effect and allows for a quantitative analysis. The model consists of a classical SIR model with diffusion, to which an additional compartment is added, formed by the infected individuals travelling on a line of fast diffusion. The line and the domain interact by constant exchanges of populations. A classical transformation allows us to reduce the proposed model to a system analogous to one we had previously introduced Berestycki et al. (J Math Biol 66:743–766, 2013) to describe the enhancement of biological invasions by lines of fast diffusion. We establish the existence of a minimal spreading speed, and we show that it may be quite large, even when the basic reproduction number [Formula: see text] is close to 1. We also prove here further qualitative features of the final state, showing the influence of the line. Springer US 2020-12-14 2021 /pmc/articles/PMC7734393/ /pubmed/33315147 http://dx.doi.org/10.1007/s11538-020-00826-8 Text en © Society for Mathematical Biology 2020 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 Article Berestycki, Henri Roquejoffre, Jean-Michel Rossi, Luca Propagation of Epidemics Along Lines with Fast Diffusion |
title | Propagation of Epidemics Along Lines with Fast Diffusion |
title_full | Propagation of Epidemics Along Lines with Fast Diffusion |
title_fullStr | Propagation of Epidemics Along Lines with Fast Diffusion |
title_full_unstemmed | Propagation of Epidemics Along Lines with Fast Diffusion |
title_short | Propagation of Epidemics Along Lines with Fast Diffusion |
title_sort | propagation of epidemics along lines with fast diffusion |
topic | Original Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7734393/ https://www.ncbi.nlm.nih.gov/pubmed/33315147 http://dx.doi.org/10.1007/s11538-020-00826-8 |
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