Bi-stable dynamics of a host-pathogen model

Anguelov Roumen, Bekker Rebecca, Dumont Yves. 2018. Bi-stable dynamics of a host-pathogen model. Biomath Communications, 5 (1), suppl. BIOMATH 2018, 1 p. Biomath 2018 : International Conference on Mathematical Methods and Models in Biosciences and a School for Young Scientists, Sofia, Bulgarie, 24 Juin 2018/29 Juin 2018.

Résumé : We discuss a model of the spread of a soil pathogen in roots. The model can be considered an extension of the compartmental model of [1] by including compartments for the pathogen. In this way we can consider the spread of the infection through the spatial diffusion of the free (unattached) pathogen, which we believe is a more realistic approach. We show that for the space independent model the pathogen free equilibrium (PFE) is always asymptotically stable, and the persistence of the infection occurs only in the setting of bi-stability. Condition for global asymptotic stability of PFE are derived using two methods: (i) Lyapunov function, and (ii) construction of a monotone system that approximates the model from above. These methods lead to two sets of sufficient conditions for the global stability. The parameter values satisfying these conditions have some overlap. However, there are values that satisfy one set and not the other. Numerical investigation of the long term behaviour of the system with spatial diffusion is carried out.

Mots-clés libres : Soil-borne disease, Mathematical modelling, Epidemiology, Ordinary differential equation, Partially degenerate reaction diffusion system, Numerical simulations

Classification Agris : H20 - Maladies des plantes
P34 - Biologie du sol

Champ stratégique Cirad : Axe 4 (2014-2018) - Santé des animaux et des plantes

Auteurs et affiliations

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

Source : Cirad-Agritrop (https://agritrop.cirad.fr/589358/)

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