Optimal Control of Begomovirus–Whitefly Dynamics in Tomato Crops

Abstract

Tomato Yellow Leaf Curl Virus (TYLCV), transmitted by the whitefly Bemisia tabaci, poses a significant
threat to global tomato production. We propose a nonlinear epidemiological model describing the coupled dynamics of tomato plants, whitefly vectors, and TYLCV transmission. The basic reproduction number, R0, is derived to characterize the threshold dynamics of the system. The stability of the disease-free equilibrium is established in terms of this threshold parameter.
The model is extended to incorporate time-dependent control variables representing biological control, removal of infected plants, resistant tomato varieties, and insect-proof nets. An optimal control problem is formulated and analyzed using Pontryagin’s Maximum Principle to minimize both infection levels and implementation costs.
Numerical simulations indicate that the combined application of all control measures provides the most effective strategy, particularly under high-transmission conditions. In contrast, strategies relying solely on resistant varieties may increase selective pressure on vector populations and compromise long-term sustainability. Furthermore, early implementation of individual control measures is shown to significantly reduce disease spread.
These results highlight the importance of integrated and optimized management strategies for the sustainable control of TYLCV.