Threshold dynamics and intervention strategy optimization in a maize-vector delayed system for streak virus disease

Maize streak virus disease (MSVD), primarily transmitted by leafhoppers, is an important viral disease of maize. The delay involved in vector-mediated transmission may affect the disease epidemic patterns and control timing. In this study, a delayed transmission model coupling the interaction of maize and vector interaction is formulated, aiming to reveal the mechanism of delay on disease epidemic patterns and optimal control strategies. Theoretical analysis shows that delay does not alter the stability threshold of disease-free equilibrium. However, when the basic reproduction number exceeds one, increasing the delay will induce Hopf bifurcation, and the system will transform from steady-state convergence to periodic oscillation. Upon this foundation, an optimal control model with three measures, including preventive control through weeding, removal of infected maize plants, and chemical control through pesticide spraying, are investigated. Numerical simulations indicate that increasing the delay postpones the action window and reduces peak intensity of three control measures, whereas its influences depend on the initial infection status of vector leafhoppers. When infected leafhoppers are absent initially, an increase in delay inhibits the evolution of MSVD. In contrast, when infected leafhoppers are already present, it promotes the spread of MSVD among maize. Under optimal control, the three measures exhibit a temporal structure of removal first, spraying second, and weeding last under optimal control, which provides clear operational guidance for phased prevention and control under limited resources. These results reveal that the interplay between transmission delay and initial vector infection fundamentally shapes the effectiveness of each control measure, implying that the optimal timing and priority of removal, spraying, and weeding must be dynamically aligned with the specific phase of disease progression.