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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...

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Detalles Bibliográficos
Autores principales: Berestycki, Henri, Roquejoffre, Jean-Michel, Rossi, Luca
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2020
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
Descripción
Sumario: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.