Title: Modelling and optimal control analysis of coffee berry disease with cost-effectiveness in the presence of temperature variability

Authors: Abdisa Shiferaw Melese; Oluwole Daniel Makinde; Legesse Lemecha Obsu

Addresses: Department of Applied Mathematics, Adama Science and Technology University, Adama, 1888, Ethiopia ' Faculty of Military Science, Stellenbosch University, Stellenbosch, 7395, South Africa ' Department of Applied Mathematics, Adama Science and Technology University, Adama, 1888, Ethiopia

Abstract: In this paper, we propose and analyse a nonlinear deterministic mathematical model for the impact of temperature variability on coffee berry disease in coffee plants. In the analysis of the model, we derived the basic reproduction numbers at minimum temperature T₀ and maximum temperature T_m which help us in establishing the local and global stability of disease-free and endemic equilibrium points. The global stability of endemic equilibrium is determined by using a Lyapunov function. We proved that the model exhibits forward and backward bifurcation by the concept of centre manifold theory. Sensitivity indices are also discussed. We extend the proposed model into the optimal control problem by incorporating three controls. We also analyse the necessary conditions for the optimal control of the disease by applying Pontryagin minimum principle. In addition, we investigate the cost-effective analysis to determine the most effective strategy with minimum costs. Finally, we present the numerical simulations.

Keywords: mathematical model; coffee berry; optimal control; costeffectiveness; temperature variability.

DOI: 10.1504/IJCSM.2023.133525

International Journal of Computing Science and Mathematics, 2023 Vol.18 No.1, pp.17 - 31

Received: 05 Sep 2020
Accepted: 10 Jan 2022
Published online: 19 Sep 2023 *

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