Discrete mathematical modeling and optimal control for Bayoud disease of date palm

Abstract

In this work, we propose a discrete mathematical model that describes the Bayoud, the disease caused by the Fusarium oxysporum fungi [24], which spreads by contact between palm roots and the Fusarium oxysporum soil fungi, the susceptible palm (S), the infected (I), the recovered palm (R), the Fusarium oxysporum fungi (C). We also focus on the importance of treatments to find the optimal strategies to minimize the number of infected palms and also the number of Fusarium oxysporum fungi population and maximize the number of the recovered palm under treatment. We propose three optimal control strategies for this disease in order to slow down the growth of Fusarium oxysporum, the agent of Bayoud’s disease. The result of this optimal system is solved numerically by Matlab. Consequently, the obtained results confirm the performance of our optimization strategy.