Fractional-Order Epidemiological Model for Banana Bunchy Top Disease Integrating Memory Effects and Optimal Control Strategies

Banana Bunchy Top Disease (BBTD) is caused by Banana Bunchy Top Virus (BBTV), poses a significant threat to global banana farming and results in substantial yield losses and economic instability for smallholder farmers. Extensively, Classical compartmental models are used in plant diseases while overlooking the hereditary effects intrinsic to biological systems. Throughout this paper, an innovative fractional-order epidemiological model for BBTD is formulated using Caputo-type derivatives to integrate memory effects in plant–vector interactions. In this model, the host plant population is partitioned into five distinct compartments—susceptible, exposed, infected, treated, and recovered—whereas the vectors are classified into susceptible, infectious, and removed states. By applying the next-generation matrix, the local stability of the disease-free equilibrium is established. The sensitivity analysis of BBTD reveals that transmission and progression parameters act as the essential determinants of disease persistence within the ecosystem. The Numerical simulations are executed using the modified Euler method that illustrates the impact of fractional-order dynamics includes infection peaks, treatment effectiveness, and recovery delays. Using Optimal control strategies and Pontryagin’s Maximum Principle, preventive measures, vector management, and treatment interventions for BBTD are developed. These strategies demonstrate that integrated controls significantly reduce the infection prevalence while maintaining cost-effectiveness. These findings underscore the efficacy of fractional calculus in plant disease epidemiology, offering superior predictive precision and actionable insights for sustainable, long-term BBTD management.