Résumé
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.