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Bi-stable dynamics of a host-pathogen model

Anguelov Roumen, Bekker Rebecca, Dumont Yves. 2019. Bi-stable dynamics of a host-pathogen model. Biomath, 8 (1):1901029, 17 p.

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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.

Mots-clés Agrovoc : Relation hôte pathogène, Modèle de simulation, Pathologie végétale, Transmission des maladies

Mots-clés libres : Host-pathogen interactions, Modelling, Monotone system, Bi-stability, Lasalle invariance principle, Partially degenerate reaction-diffusion, Travelling wave

Classification Agris : H20 - Plant diseases
U10 - Mathematical and statistical methods
P34 - Soil biology

Champ stratégique Cirad : CTS 4 (2019-) - Santé des plantes, des animaux et des écosystèmes

Auteurs et affiliations

  • Anguelov Roumen, University of Pretoria (ZAF)
  • Bekker Rebecca, University of Pretoria (ZAF)
  • Dumont Yves, CIRAD-BIOS-UMR AMAP (FRA) ORCID: 0000-0003-4817-685X - auteur correspondant

Source : Cirad-Agritrop (https://agritrop.cirad.fr/590849/)

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