Modelling coffee leaf rust dynamics to control its spread. (English) Zbl 1473.35594
Summary: Coffee leaf rust (CLR) is one of the main diseases that affect coffee plantations worldwide. It is caused by the fungus Hemileia vastatrix. Damages induce severe yield losses (up to 70%). Its control mainly relies on cultural practices and fungicides, the latter having harmful ecological impact and important cost. Our goal is to understand the propagation of this fungus in order to propose a biocontrol solution, based on a mycoparasite that inhibits H. vastatrix reproduction. We develop and explore a spatio-temporal model that describes CLR propagation in a coffee plantation during the rainy and dry seasons. We show the existence of a solution and prove that there exists two threshold parameters, the dry and rainy basic reproduction numbers, that determine the stability of the equilibria for the dry and rainy season subsystems. To illustrate these theoretical results, numerical simulations are performed, using a non-standard finite method to integrate the pest model. We also numerically investigate the biocontrol impact. We determine its efficiency threshold in order to ensure CLR eradication.
MSC:
| 35Q92 | PDEs in connection with biology, chemistry and other natural sciences |
| 35K57 | Reaction-diffusion equations |
| 93D05 | Lyapunov and other classical stabilities (Lagrange, Poisson, \(L^p, l^p\), etc.) in control theory |
| 65M06 | Finite difference methods for initial value and initial-boundary value problems involving PDEs |
| 92D30 | Epidemiology |
| 92C80 | Plant biology |
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