Application of Mathematical Epidemiology to crop vector-borne diseases. The cassava mosaic virus disease case

Michael Chapwanya (1) , Yves Dumont (2, 1, 3)

1 University of Pretoria [South Africa]
2 UMR AMAP - Botanique et Modélisation de l'Architecture des Plantes et des Végétations
3 LIRIMA - Laboratoire International de Recherche en Informatique et Mathématiques Appliquées

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: Cassava; Cassava mosaic disease; Vector borne disease; Plant-Insect interaction; crop growth; Ordinary differential equations; Qualitative Analysis; Hopf bifurcation; Sensitivity analysis; Roguing; Numerical simulations

Domaines: Systèmes dynamiques [math.DS]; Mathématiques [math]; Sciences de l'environnement

Michael Chapwanya, Yves Dumont. Application of Mathematical Epidemiology to crop vector-borne diseases. The cassava mosaic virus disease case. Miranda I. Teboh-Ewungkem; Gideon Akumah Ngwa. Infectious Diseases and our Planet, 7, Springer, 2021, Mathematics of Planet Earth, 978-3-030-50825-8. ⟨10.1007/978-3-030-50826-5_4⟩. ⟨hal-02401399⟩