Bi-stable dynamics of a host-pathogen model Article - Janvier 2019

Roumen Anguelov, Rebecca Bekker, Yves Dumont

Roumen Anguelov, Rebecca Bekker, Yves Dumont, « Bi-stable dynamics of a host-pathogen model  », BIOMATH, janvier 2019, p. 1901029. ISSN 1314-684X

Abstract

Crop host-pathogen interaction have been a main issue for decades, in particular for food security. In this paper, we focus on the modeling and long term behavior of soil-borne pathogens. We first develop a new compartmental temporal model, which exhibits bi-stable asymptotical dynamics. To investigate the long term behavior, we use LaSalle Invariance Principle to derive sufficient conditions for global asymptotic stability of the pathogen free equilibrium and monotone dynamical systems theory to provide sufficient conditions for permanence of the system. Finally, we develop a partially degenerate reaction diffusion system, providing a numerical exploration based on the results obtained for the temporal system. We show that a traveling wave solution may exist where the speed of the wave follows a power law.

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