American Institute of Mathematical Sciences

September  2017, 22(7): 2879-2905. doi: 10.3934/dcdsb.2017155

Asymptotic behaviour of an age and infection age structured model for the propagation of fungal diseases in plants

 1 UMR CNRS 5251 IMB, Université de Bordeaux, 3ter Place de la Victoire, 33076 Bordeaux, France 2 UMI-IRD-209 UMMISCO and LANI, UFR de Sciences Appliquées et de Technologie, Université Gaston Berger, B.P. 234 Saint-Louis, Sénégal

* Corresponding author: J.-B. Burie

Received  June 2016 Revised  March 2017 Published  May 2017

A mathematical model describing the propagation of fungal diseases in plants is proposed. The model takes into account both chronological age and age since infection. We investigate and fully characterize the large time behaviour of the solutions. Existence of a unique endemic stationary state is ensured by a threshold condition: $\mathcal R_0>1$. Then using Lyapounov arguments, we prove that if $\mathcal R_0 ≤ 1$ the disease free stationary state is globally stable while when $\mathcal R_0>1$, the unique endemic stationary state is globally stable with respect to a suitable set of initial data.

Citation: Jean-Baptiste Burie, Arnaud Ducrot, Abdoul Aziz Mbengue. Asymptotic behaviour of an age and infection age structured model for the propagation of fungal diseases in plants. Discrete & Continuous Dynamical Systems - B, 2017, 22 (7) : 2879-2905. doi: 10.3934/dcdsb.2017155
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