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ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Optimal Control Strategies for Coffee Berry Disease with Cost-Effectiveness Analysis in the Presence of Climatic Variability

Journal of Applied Nonlinear Dynamics 12(2) (2023) 191--211 | DOI:10.5890/JAND.2023.06.001

Abdisa Shiferaw Melese$^{1}$, Oluwole Daniel Makinde$^{2}$, Legesse Lemecha Obsu$^{1}$

$^{1}$ Department of Applied Mathematics, Adama Science and Technology University, Adama, Ethiopia

$^{2}$ Faculty of Military Science, Stellenbosch University, Stellenbosch, South Africa

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Abstract

This paper aims to tackle an important problem - the optimization of measures applied to fight disease in one of the most important economically plant cultures: coffee. This is done by formulating a mathematical model of coffee berry disease \textit{(Colletotrichum kahawae)} with optimal controls which consist of coffee berry and vector population with the interaction of pathogen, temperature variability, and rainfall pattern. First, we investigate the positivity and boundedness of solutions of the proposed model with the absence of controls. Then, optimal control strategies are studied to minimize the burden of coffee berry disease (CBD) and the cost of interventions. The characterization of optimal trajectories is also analytically derived using Pontryagin's Minimum Principle. Finally, we performed numerical simulations to investigate the impact of control strategies in combating CBD. Furthermore, we studied the cost-effectiveness of our control strategies to determine the best approach to minimize the disease burden. The finding of this study shows that any combination of genetic resistance variety, chemical and cultural control strategies are very effective to combat the disease.

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