Pulsating waves in a multidimensional reaction-diffusion system of epidemic type

  • Liangliang Deng

    Lanzhou University, Lanzhou, P. R. China
  • Arnaud Ducrot

    Université du Havre, Le Havre, France
Pulsating waves in a multidimensional reaction-diffusion system of epidemic type cover

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Abstract

In this work we investigate the existence of front propagation for a two-component reaction -diffusion system of epidemic type posed in a multi-dimensional periodic medium. This system is a spatially heterogeneous version of the well-known Kermack–McKendrick epidemic model with Fickian diffusion. We derive sufficient conditions for the existence of pulsating travelling waves propagating in an arbitrarily given unit direction. Specifically, we prove that the set of admissible wave speeds contains a semi-infinite interval. Then, for each direction of propagation and each admissible speed, there exists a pulsating travelling wave solution of the system which is globally bounded.

Cite this article

Liangliang Deng, Arnaud Ducrot, Pulsating waves in a multidimensional reaction-diffusion system of epidemic type. J. Eur. Math. Soc. (2024), published online first

DOI 10.4171/JEMS/1511