Advancing nonlinear dynamics of coffee berry disease through robust dual-Network framework: Deep learning and random projection neural networks

• Innovative dual-framework approach implemented to develop a robust modeling of coffee berry disease dynamics and control • A stochastic Random Projection Neural Network and advanced Deep Neural Networks are used • Detail simulation with comprehensive error analysis is presented • The proposed intelligent scheme consistently achieve errors as low as 10 − 2 - 10 − 15 outperforming the existing conventional method Coffee production faces significant global challenges, with climate change exerting both direct and indirect impacts. These include reduced crop yield and quality, as well as altered patterns of pest and disease outbreaks, notably increasing the prevalence of plant infections. Among these, Coffee Berry Disease (CBD) poses a substantial threat to coffee crop health and productivity. The urgency of developing advanced analytical frameworks to understand and mitigate such impacts has become critical. In the present study, we propose a novel knowledge-driven neuro-computational modeling framework for analyzing the nonlinear transmission dynamics and control of CBD. The model incorporates a long-term system assessment through analytical derivation of the basic reproduction number and equilibrium states, providing insight into disease persistence and elimination thresholds. To enhance predictive accuracy and computational robustness, we introduce an innovative dual neural network architecture by integrating a stochastic Random Projection Neural Network (RPNN) with a Deep Neural Network (DNN). The RPNN utilizes Gaussian activation functions and demonstrates superior capability in capturing the nonlinear behavior of biological systems governed by ordinary differential equations (ODEs), achieving residual errors below 10 − 15 . Performance comparisons with standard solvers such as ode15s and ode23t indicate that the RPNN achieves significantly lower L 2 -norm errors ( 7.9432 × 10 − 5 ) compared to 8.3700 × 10 − 2 and 9.7365 × 10 − 3 respectively. Furthermore, the deep surrogate model incorporates Tanh and ReLU activation functions within hidden layers to boost generalization and training efficiency. This hybrid framework not only strengthens model fidelity under uncertainty but also facilitates the development of sustainable and data-driven disease management strategies. The proposed methodology holds potential for broader application in environmental modeling and precision agriculture, providing an intelligent tool for monitoring and controlling plant epidemics such as CBD.