Analysis and optimal control of a Huanglongbing mathematical model with resistant vector

Huanglongbing (HLB) is an incurable disease that affects citrus trees. To better understand the transmission of HLB, the mathematical model is developed to investigate the transmission dynamics of the disease between Asian citrus psyllid (ACP) and citrus trees. Through rigorous mathematical derivations, we derive the expression of the basic reproduction number (R ₀) of HLB. The findings show that the disease-free equilibrium is locally asymptotically stable if R ₀ < 1, and if R ₀ > 1 the system is uniformly persistent. By applying the global sensitivity analysis of R ₀, we can obtain some parameters that have the greatest influence on the HLB transmission dynamics. Additionally, the optimal control theory is used to explore the corresponding optimal control problem of the HLB model. Numerical simulations are conducted to reinforce the analytical results. These theoretical and numerical results provide useful insights for understanding the transmission dynamics of HLB and may help policy makers to develop intervention strategies for the disease.