Asymptotic behaviour of an age and infection age structured model for the propagation of fungal diseases in plants
| Autor: | Arnaud Ducrot, Jean-Baptiste Burie, Abdoul Aziz Mbengue |
|---|---|
| Přispěvatelé: | Institut de Mathématiques de Bordeaux (IMB), Université Bordeaux Segalen - Bordeaux 2-Université Sciences et Technologies - Bordeaux 1-Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux (Bordeaux INP)-Centre National de la Recherche Scientifique (CNRS) |
| Jazyk: | angličtina |
| Rok vydání: | 2017 |
| Předmět: |
Applied Mathematics
010102 general mathematics Infection age Disease free Chronological age 01 natural sciences 010101 applied mathematics Combinatorics Set (abstract data type) Lyapunov functional Discrete Mathematics and Combinatorics [MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP] 0101 mathematics Structured model Stationary state ComputingMilieux_MISCELLANEOUS Mathematics |
| Zdroj: | Discrete and Continuous Dynamical Systems-Series B Discrete and Continuous Dynamical Systems-Series B, American Institute of Mathematical Sciences, 2017, 22 (7), pp.2879-2905. ⟨10.3934/dcdsb.2017155⟩ |
| ISSN: | 1531-3492 1553-524X |
| DOI: | 10.3934/dcdsb.2017155⟩ |
| Popis: | 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: \begin{document}$\mathcal R_0>1$\end{document} . Then using Lyapounov arguments, we prove that if \begin{document}$\mathcal R_0 ≤ 1$\end{document} the disease free stationary state is globally stable while when \begin{document}$\mathcal R_0>1$\end{document} , the unique endemic stationary state is globally stable with respect to a suitable set of initial data. |
| Databáze: | OpenAIRE |
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