This study used a system of delay differential equations (DDE) to construct a time-delayed vector-host dengue epidemic model that accounts for inhibitory impact rates, immunity loss rates, and partial immunity rates. The model's solution is investigated and is determined to be positive and bounded. Using the next-generation matrix technique, the reproduction number is utilized to assess the model's stability. The virus-free equilibrium points were found to be locally asymptotically unstable. The existence of endemic equilibrium stability with and without time delay was investigated; as a result, endemic equilibrium points were locally stable with delay under certain conditions. For dengue transmission sensitivity analysis, the epidemiological model was analyzed. Finally, our theoretical results are validated by numerical simulations.

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.