Mathematical analysis of the role of host-to-host transmission of Maize Streak Virus Disease with Atangana-Baleanu derivative

Abstract

AbstractIn this article a deterministic model for Maize Streak Virus Disease (MSVD) using a fractional-order differential equation with the Atangana-Baleanu Caputo-type operator is developed. Focusing on the role of host-to-host transmission, the it is shown that the presence and stability of equilibria depends on maize field carrying capacity and half-saturation constant of susceptible maize. The MSVD-free equilibrium is globally asymptotically stable when the basic reproduction number is below unity. Local stability conditions for endemic equilibria are established using Lyapunov second technique and Routh-Hurwitz criteria. Matrix-based formulae are also presented for determining bifurcation and it is shown that the model exhibits forward bifurcation. Sensitivity analysis reveals the significant impact of the probability of infection between hosts on MSVD spread. A two-point Lagrange interpolation polynomial is developed for numerical solutions of the model, enabling exploration of theoretical findings and assessment of how epidemiological factors influence MSVD propagation. The paper contributes a comprehensive understanding of the disease's behavior under various conditions.

Keywords

• Epidemiology
• Maize Streak Virus Disease
• leafhopper
• basic reproduction number