Mathematical model and optimal control analysis of coffee berry disease

Abstract

Coffee berry disease (CBD) caused by Colletotrichum kahawae is a major challenge to Ara bica coffee production in African countries. In this dissertation, we studied mathematical models designed to describe the dynamics of plant pathogen and CBD infection to forecast the possible features and establish mitigation strategies for its spread. First, we showed the positivity, existence, uniqueness and positivity of solution, feasible region, equilibria and ba sic reproduction numbers of the models. Thus, the models turned out to be both biologically meaningful and mathematically well-posed. The local stability of the equilibria is shown via Routh-Hurwitz criteria, while the global stability of the equilibria is proved by using a Lyapunov function. Using center manifold theory, we proved that the model exhibits forward bifurcation. Sensitivity indices of basic reproduction numbers at minimum temperature and rainfall, and maximum temperature and rainfall are determined. The first model is extended to the optimal control problem using quarantine and chemical controls. The next models are extended to the optimal control problem with cost-effectiveness using genetic resistance, chemical control, and cultural practice in the presence of temperature and rainfall variability. The optimal control problem was analyzed with Pontryagin’s Minimum Principle (PMP). Numerical simulations were performed at minimum temperature and rainfall, and maximum temperature and rainfall. Furthermore, we studied the cost-effectiveness of strategies to determine the best approach to minimize the burden of the disease and the cost of interventions. The simulation resuls of the first model shows that a combination of quarantine and chemical controls strategies are very effective to eradicate the disease. The simulation resuls of the remaining models show that a combination of genetic resistance, chemical, and cultural control strategies are very effective to eradicate the disease.