Geodesic
Modelling coffee leaf rust dynamics to control its spread
Clotilde Djuikem1 ; Frédéric Grognard1 ; Roger Tagne Wafo2 ; Suzanne Touzeau1, 3 ; Samuel Bowong2, 4
1 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.
Mathematical modelling of natural phenomena, Tome 16 (2021), article no. 26 Cet article a éte moissonné depuis la source EDP Sciences

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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.
DOI : 10.1051/mmnp/2021018

Clotilde Djuikem 1 ; Frédéric Grognard 1 ; Roger Tagne Wafo 2 ; Suzanne Touzeau 1, 3 ; Samuel Bowong 2, 4

1 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. 
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Clotilde Djuikem; Frédéric Grognard; Roger Tagne Wafo; Suzanne Touzeau; Samuel Bowong. Modelling coffee leaf rust dynamics to control its spread. Mathematical modelling of natural phenomena, Tome 16 (2021), article  no. 26. doi: 10.1051/mmnp/2021018

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