OPTIMAL CONTROL AND COST-EFFECTIVENESS ANALYSIS OF AN INTEGRATED INTERVENTION MODEL INCORPORATING VECTOR PREFERENCE FOR MOSO BAMBOO SOOTY MOLD DISEASE

Understanding the transmission mechanisms of Moso bamboo sooty mold disease and the vector preference behavior of its vector insect (bamboo aphid) is of great significance for developing cost-effective integrated pest management strategies. This study constructs a compartmental model that incorporates vector preference to describe the transmission dynamics of the disease between bamboo plants and bamboo aphids. Through rigorous mathematical derivation, an explicit expression for the basic reproduction number $\mathcal{R}_0$ of the disease is obtained. Global sensitivity analysis identified the key parameters that most significantly influence the dynamics of disease transmission. Theoretical and numerical findings indicate: (ⅰ) When $\mathcal{R}_0 <1$, the disease-free equilibrium of model (2.1) is globally asymptotically stable (GAS); when $\mathcal{R}_0 > 1$, the system is uniformly persistent and possesses a unique positive equilibrium, which is GAS. (ⅱ) Under identical state variables and parameter values in this model, compared to the model ignoring vector preference $(\phi=1)$, the model incorporating vector preference $(\phi>1)$ overestimates the disease’s potential transmission capacity while simultaneously underestimating the actual infection scale. (ⅲ) Spraying insecticides and injecting nutrient solutions are long-term control measures that should be implemented throughout the entire disease management process. In contrast, using yellow adhesive traps to capture pests and removing bamboo plants exhibiting symptoms of sooty mold are short-term control strategies suitable for use during the early stages of an outbreak. Considering the cost-effectiveness of labor and materials, these measures can be discontinued in later stages. (ⅳ) According to the optimal control model for the disease and related numerical simulation results, the integrated control measure combining insecticide spraying with nutrient solution injection is found to be the most cost-effective among all strategies. This study provides a theoretical basis and decision-making support for the prevention and control of the disease.