Predictive mathematical modeling and control strategies for banana bunchy top virus via Levenberg–Marquardt backpropagation

Banana Bunchy Top Disease (BBTD), caused by Banana Bunchy Top Virus (BBTV) with banana aphid Pentalonia nigronervosa as the major route of transmission, is a major concern to banana production due to the interactions between plant and vector populations involved in transmission, as well as the potential presence of delayed and memory-dependent effects during the progression of infection and the transmission process. No known previously developed mathematical approaches to date typically provide a single conceptual framework of coupled temporal effects, epidemic threshold and stability condition, together with the analysis of synergistic combinations of control measures. In this work, we construct a nonlinear fractional-order model of BBTV transmission based on the Caputo fractional derivative(CFD), consisting of susceptible, exposed, infected, and recovered banana plants in conjunction with susceptible and infected aphid vectors, and analyze it mathematically. It is proved to be well-posed via the Banach Fixed Point Theorem, while the epidemic threshold and bifurcation of the model are investigated from the basic reproduction number obtained based on the next-generation matrix. The model is extended to include optimal control representing preventive plant protection, aphid vector control, and removal or quarantine of infected plants. The controlled model is simulated numerically through a predictor-corrector Adams–Bashforth–Moulton scheme, and then trained as an artificial neural network to explore the predictive effectiveness of the model. The numerical simulations of the model reveal that coordinated intervention strategies effectively reduce the infected plant and aphid vector population, while the fractional-order model can produce a relatively slow and smooth propagation trend compared to the integer-order model, reflecting the memory and hereditary effects. The ANN simulation indicates satisfactory prediction performance to the numerical solutions. Therefore, the mathematical structure of the coupled fractional-order memory-dependent model, together with the stability analysis, the optimal control strategy, the numerical simulation, and the prediction of the artificial neural network, can lay the mathematical foundations for the analysis of transmission of BBTV and help evaluate integrated intervention strategies.