Investigating the Dynamics of Bayoud Disease in Date Palm Trees and Optimal Control Analysis

Abstract

The fungus Fusarium oxysporum (f.sp. albedinis) causes Bayoud disease. It is one of the epiphytotic diseases that affects a wide range of palm species and has no known cure at present. However, preventive measures can be taken to reduce the effects of the disease. Bayoud disease has caused enormous economic losses due to decreased crop yield and quality. Therefore, it is essential to develop a mathematical model for the dynamics of the disease to propose some affordable methods for disease management. In this study, we propose a novel mathematical model that describes the transmission dynamics of the disease in date palm trees. The model incorporates various factors such as the contact rate of the fungi with date palm trees, the utilization of fungicides, and the introduction of a quarantine compartment to prevent disease dissemination. We first prove a few key properties of the proposed model to ensure that the model is well-posed and suitable for numerical investigations. We establish that the model has a unique positive solution that is bounded and stable over time. We use sensitivity analysis to identify the parameters that have the greatest effect on the reproduction number R0 and illustrate this effect graphically. We then formulate an optimal control problem to identify the most suitable and cost-effective disease control approaches. As a first approach, we solely focus on the application of fungicide to susceptible trees and determine the best spray rates for a greater decrease in exposed and infected trees. Secondly, we emphasize quarantining exposed and infected trees at optimal quarantine rates. Finally, we explore the combined effect of fungicide spraying and isolating infected trees on disease control. The findings of the last approach turn out to be the most rewarding and cost-effective for minimizing infections in date palm trees.