Mathematical model with memory effects targets banana bunchy top virus spread

Banana bunchy top disease, caused by the banana bunchy top virus and transmitted primarily by the banana aphid Pentalonia nigronervosa, remains a major threat to banana production. A new study published in Chemical and Biological Technologies in Agriculture presents a mathematical framework designed to capture how the virus spreads through coupled populations of banana plants and their insect vector, with particular attention to delayed and memory-dependent effects that arise during infection and transmission.

The research team, led by D. Prabu and P. Jalapathy with colleagues including Syeda Fatima Ayub, S. Sridhar, K. Loganathan and Aiedh Mrisi Alharthi, constructed a nonlinear fractional-order model of virus transmission based on the Caputo fractional derivative. The model tracks susceptible, exposed, infected and recovered banana plants alongside susceptible and infected aphid vectors, allowing the dynamics of both host and vector populations to be analyzed within a single coupled system.

A key motivation for using a fractional-order formulation is its ability to represent memory and hereditary effects, which the authors argue are absent from previously developed mathematical approaches. According to the abstract, no earlier framework had typically combined coupled temporal effects, an epidemic threshold, a stability condition and the analysis of synergistic combinations of control measures in one conceptual structure.

The model was shown to be mathematically well-posed via the Banach Fixed Point Theorem. The researchers obtained the basic reproduction number based on the next-generation matrix and used it to investigate the epidemic threshold and bifurcation behavior of the system.

Beyond the baseline model, the team extended the framework to include optimal control terms representing three intervention types: preventive plant protection, control of the aphid vector, and removal or quarantine of infected plants. This allowed the authors to evaluate how coordinated combinations of these measures perform against the disease, rather than assessing each strategy in isolation.

Numerical simulations of the controlled model were carried out using a predictor-corrector Adams-Bashforth-Moulton scheme. The simulations indicated that coordinated intervention strategies effectively reduce both the infected plant population and the infected aphid vector population. The fractional-order model also produced a relatively slow and smooth propagation trend compared with an equivalent integer-order model, which the authors attribute to the memory and hereditary effects captured by the fractional derivative.

According to the study, the network simulation showed satisfactory prediction performance relative to the numerical solutions of the model, suggesting the approach could serve as a predictive tool alongside the underlying differential equations.

The authors state that the combination of the coupled fractional-order memory-dependent model, its stability analysis, the optimal control strategy, the numerical simulation and the neural network prediction can lay mathematical foundations for analyzing BBTV transmission and help evaluate integrated intervention strategies. As with any modeling study, the findings reflect simulated dynamics rather than field trials, and the practical value of the framework will depend on how well its parameters and predicted intervention effects match real-world banana-aphid-virus systems.

Subject of Research: Mathematical modeling of banana bunchy top virus transmission and control strategies

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

Article References: Prabu, D., Jalapathy, P., Ayub, S. F., Sridhar, S., Loganathan, K., & Alharthi, A. M. (2026). Predictive mathematical modeling and control strategies for banana bunchy top virus via Levenberg–Marquardt backpropagation. Chemical and Biological Technologies in Agriculture. https://doi.org/10.1186/s40538-026-01125-5

Image Credits: AI Generated

DOI: 10.1186/s40538-026-01125-5

Keywords: banana bunchy top virus, mathematical modeling, fractional calculus, Caputo derivative, basic reproduction number, optimal control, aphid vector, artificial neural network, Levenberg–Marquardt backpropagation, plant disease epidemiology, Predictive, mathematical