Math. Model. Nat. Phenom.
Volume 16, 2021
Mathematical Models and Methods in Epidemiology
|Number of page(s)||25|
|Published online||28 April 2021|
Modelling coffee leaf rust dynamics to control its spread
Université Côte d’Azur, Inria, INRAE, CNRS, Sorbonne Université, BIOCORE,
Sophia Antipolis, France.
2 Department of Mathematics and Computer Science, University of Douala, Cameroon.
3 Université Côte d’Azur, INRAE, CNRS, ISA, Sophia Antipolis, France.
4 IRD, Sorbonne Université, UMMISCO, Bondy, France.
* Corresponding author: firstname.lastname@example.org
Accepted: 11 March 2021
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.
Mathematics Subject Classification: 35K57 / 93D05 / 65M06 / 92D30
Key words: Spatio-temporal model / coffee leaf rust / basic reproduction number / stability
© The authors. Published by EDP Sciences, 2021
This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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