Modeling Citrus Huanglongbing transmission within an orchard and its optimal control

Citrus Huanglongbing (HLB) is the most devastating citrus disease worldwide. In this paper, a deterministic dynamical model is proposed to explore the transmission dynamics of HLB between citrus tree and Asian citrus psyllid (ACP). Using the theory of dynamical system, the dynamics of the model are rigorously analyzed. The results show that the disease-free equilibrium is globally asymptotically stable when the basic reproduction number $\mathscr{R}_0 < 1$, and when $\mathscr{R}_0 > 1$ the system is uniformly persistent. Applying the global sensitivity analysis of $\mathscr{R}_0$, some parameters that have the greatest impact on HLB transmission dynamics are obtained. Furthermore, the optimal control theory is applied to the model to study the corresponding optimal control problem. Both analytical and numerical results show that: (1) the infected ACP plays a decisive role in the transmission of HLB in citrus trees, and eliminating the ACP will be helpful to curtail the spread of HLB; (2) optimal control strategy is superior to the constant control strategy in decreasing the prevalence of the diseased citrus trees, and the cost of implementing optimal control is much lower than that of the constant control strategy; and (3) spraying insecticides is more effective than other control strategies in reducing the number of ACP in the early phase of the transmission of HLB. These theoretical and numerical results may be helpful in making public policies to control HLB in orchards more effectively.