Fractional Modeling and Stability Analysis of Tomato Yellow Leaf Curl Virus Disease: Insights for Sustainable Crop Protection

Tomato Yellow Leaf Curl Virus (TYLCV) has recently caused severe economic losses in global tomato production. According to the International Plant Protection Convention (IPPC), yield reductions of 50–60% have been reported in several regions, including the Caribbean, Central America, and South Asia, with losses in sensitive cultivars reaching up to 90–100%. In developing countries, TYLCV and mixed infections affect more than seven million hectares of tomato-growing land annually. In this study, we construct and analyze a nonlinear dynamic model describing the transmission of TYLCV, incorporating the Caputo fractional-order derivative operator. The existence and uniqueness of solutions to the proposed model are rigorously established. Equilibrium points are identified, and the Jacobian determinant approach is applied to compute the basic reproduction number, $R_0$. Suitable Lyapunov functions are formulated to analyze the global asymptotic stability of both the disease-free and endemic equilibria. The model is numerically solved using the Grünwald–Letnikov-based nonstandard finite difference method, and simulations assess how the memory index and preventive strategies influence disease propagation. The results reveal critical factors governing TYLCV transmission and suggest effective intervention measures to guide sustainable crop protection policies.