A Robust Memory-Based Neuro-Computational Analysis of Coffee Berry Disease Using Fractional Calculus and Deep Learning Approach

Coffee plants are susceptible to a variety of diseases that threaten the quantity and quality of coffee production. Coffee berry disease (CBD) poses a significant threat to global coffee production, particularly in Africa, and creates a potential risk of expansion into coffee-growing regions in Latin America and Asia. This study explores a novel hybrid computational modeling using fractional calculus and deep learning techniques to model the complex dynamics of CBD. The Caputo operator-based Euler scheme is used to solve the model numerically and to generate synthetic datasets by considering various values of fractional order. Further, the dynamics of disease transmission are numerically studied using a deep neural network by comparing solutions across all compartments through convergence testing, regression metrics, and error distribution. To minimize the mean squared error, we employ a fractional Euler iterative scheme, allocating 70% of the data for training and 15% each for validation and testing. Numerical performance is demonstrated under five fractional-order scenarios α=0.80,0.85,0.90,0.95,1 using distinct initial conditions. The results obtained from the present approach align precisely with the benchmark data. The best validation performance is archived to 10−10, and with minimum absolute error 10−8. The outcomes of the scheme are rigorously presented numerically and tabulated. We believe that the integration of a deep neural network that implements Tanh and ReLU activations in its hidden layers to study CBD is a novel attempt in the modeling of infectious diseases. This hybrid neuro-computing paradigm delivers both improved accuracy and computational efficiency, providing a better understanding of CBD and thereby helping to set effective control interventions.