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

TL;DR

This paper develops a mathematical model to understand and control the spread of cassava mosaic disease, considering crop growth, vector dynamics, and intervention strategies, with potential applications to other crop diseases.

Contribution

It introduces a generic compartmental model for crop vector-borne diseases, incorporating disease transmission, crop growth, and control measures like roguing, with stability analysis and numerical simulations.

Findings

Existence of disease-free and endemic equilibria.

Conditions for local and global stability of equilibria.

Potential for Hopf bifurcation affecting disease dynamics.

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.