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

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.

Modeling the transmission dynamics and control of cassava mosaic disease with non-cassava host plants

“…The transmission dynamics and control of CMD have been studied using a variety of mathematical models (Chapwanya & Dumont, 2019). However, most of these models did not account for the presence of non-cassava host plants in their model formulation and analyses.…”

“…In Tanzania, cassava is a crucial subsistence crop, especially in mostly dryland where cereal crops fail to thrive . The existence and persistence of plant pests and diseases, such as Cassava Mosaic Disease (CMD) and Cassava Brown Streak Disease (CBSD) hinder the production and cause an average of 34 million tonnes of cassava yields to be lost annually (Chapwanya & Dumont, 2019).…”