Revision as of 12:16, 25 September 2026

Abstract

Maize streak disease (MSD) remains a major constraint to maize production, particularly in sub-Saharan Africa, where its spread is strongly influenced by environmental, agronomic, and vector-related factors. This paper develops a stochastic delayed model for MSD transmission dynamics. The model incorporates a discrete time delay to represent incubation and vector-mediated transmission, while stochastic perturbations are included to describe environmental variability and random fluctuations in disease spread. The qualitative analysis shows that the model is biologically well posed, with positive and bounded solutions. The disease-free and endemic equilibria are derived, and the effective reproduction number is obtained using the next-generation matrix method. Also, the sensitivity of parameters is studied rigorously using the given data. The stochastic formulation leads to a modified threshold, indicating that random perturbations can reduce disease persistence and may contribute to disease extinction under suitable conditions. The standard numerical method, Euler–Maruyama, and the nonstandard numerical method, namely the nonstandard finite difference (NSFD) method, are used to solve the stochastic MSD model due to the unavailability of a closed-form solution for the model. Unfortunately, the Euler–Maruyama method has some limitations and is dependent on the discretization step size, whereas the NSFD method is independent and provides more reliable results. Moreover, numerical simulations based on a stochastic nonstandard finite difference scheme are used to illustrate the theoretical results and the effects of key parameters, including transmission rate, delay, and insecticide efficacy. The limited MSD data from 2020–2025 are used only for illustrative trend analysis. Overall, the proposed stochastic delayed model provides a useful framework for understanding MSD dynamics and assessing insecticide-based control strategies under uncertainty.OPEN ACCESS Received: 25/04/2026 Accepted: 17/06/2026 Published: 21/09/2026

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