Application of mathematical epidemiology to crop vector-borne diseases: The cassava mosaic virus disease case

Chapwanya Michael, Dumont Yves. 2021. Application of mathematical epidemiology to crop vector-borne diseases: The cassava mosaic virus disease case. In : Infectious diseases and our planet. Teboh-Ewungkem Miranda I. (ed.), Ngwa Gideon Akumah (ed.). Cham : Springer, pp. 57-95. (Mathematics of Plant Earth, 7) ISBN 978-3-030-50826-8

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Abstract : In this chapter, an application of Mathematical Epidemiology to crop vector-borne diseases is presented to investigate the interactions between crops, vectors, and virus. The main illustrative example is the cassava mosaic disease (CMD). The CMD virus has two routes of infection: through vectors and also through infected crops. In the field, the main tool to control CMD spreading is roguing. The presented biological model is sufficiently generic and the same methodology can be adapted to other crops or crop vector-borne diseases. After an introduction where a brief history of crop diseases and useful information on Cassava and CMD is given, we develop and study a compartmental temporal model, taking into account the crop growth and the vector dynamics. A brief qualitative analysis of the model is provided, i.e., existence and uniqueness of a solution, existence of a disease-free equilibrium, and existence of an endemic equilibrium. We also provide conditions for local (global) asymptotic stability and show that a Hopf Bifurcation may occur, for instance, when diseased plants are removed. Numerical simulations are provided to illustrate all possible behaviors. Finally, we discuss the theoretical and numerical outputs in terms of crop protection.

Mots-clés Agrovoc : Manihot esculenta, Virus mosaïque manioc, Virus des végétaux, Modèle mathématique, Maladie des plantes, Maladie transmise par vecteur, Épidémiologie, Relation hôte pathogène, Protection des plantes

Mots-clés libres : Cassava, Cassava mosaic disease, Plant growth, Bemisia tabaci, Modeling, Ordinary differential equation, Qualitative analysis, Periodic equilibrium, Hopf bifurcation, Numerical simulations

Classification Agris : H20 - Plant diseases
U10 - Computer science, mathematics and statistics

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