Analyzing the Memory‐Based Transmission Dynamics of Coffee Berry Disease using Caputo Derivative

Abstract In recent years, the incidence of plant diseases caused by bacterial, fungal, and environmental factors has steadily increased, affecting plants at various stages of agricultural production. Plant diseases not only reduce food production and quality but also pose significant social, health, and economic challenges. Mathematical modeling provides a method to analyze and predict the spread and impact of plant diseases. In this study, a mathematical model is suggested to describe the transmission dynamics of coffee berry disease (CBD). The model is extended in the sense of the Caputo derivative to improve accuracy and provide more realistic scenarios for coffee berry disease. A detailed analysis of the key mathematical properties of the model is presented. The conditions of local and global stability of the equilibrium points are analyzed. The existence and uniqueness of the model solution are presented, considering the fixed‐point theory. Parameter sensitivity is also examined. The numerical simulations are carried out to illustrate the practical application of fractional derivatives in the study of plant epidemiology.