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.

中文翻译：

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果园内柑橘黄龙病传播模型及其优化控制。

柑橘黄龙病（HLB）是全球最具破坏性的柑橘病。本文提出了一种确定性动力学模型，以研究HLB在柑橘树与亚洲柑橘木虱（ACP）之间的传播动力学。利用动力学系统理论，对模型的动力学进行了严格的分析。结果表明，当基本繁殖数$ \ mathscr {R} _0 <1 $时，无病平衡全局渐近稳定；而当$ \ mathscr {R} _0> 1 $时，系统是一致持久的。应用$ \ mathscr {R} _0 $的全局灵敏度分析，可以获得一些对HLB传输动力学影响最大的参数。此外，将最优控制理论应用于模型以研究相应的最优控制问题。分析和数值结果均表明：（1）被感染的ACP在柑橘中HLB的传播中起决定性作用，消除ACP将有助于抑制HLB的传播；（2）最优控制策略在降低患病柑橘树的流行方面优于恒定控制策略，实施最优控制的成本要比恒定控制策略低得多；（3）在减少HLB传播的早期阶段，喷洒杀虫剂比其他控制策略更有效地减少ACP的数量。这些理论和数值结果可能有助于制定公共政策来更有效地控制果园中的HLB。（2）最优控制策略在降低患病柑橘树的流行方面优于恒定控制策略，实施最优控制的成本要比恒定控制策略低得多；（3）喷洒杀虫剂比其他控制策略更有效地减少HLB传播早期的ACP数量。这些理论和数值结果可能有助于制定公共政策来更有效地控制果园中的HLB。（2）最优控制策略在降低患病柑橘树的流行方面优于恒定控制策略，实施最优控制的成本要比恒定控制策略低得多；（3）喷洒杀虫剂比其他控制策略更有效地减少HLB传播早期的ACP数量。这些理论和数值结果可能有助于制定公共政策来更有效地控制果园中的HLB。（3）喷洒杀虫剂比其他控制策略更有效地减少HLB传播早期的ACP数量。这些理论和数值结果可能有助于制定公共政策来更有效地控制果园中的HLB。（3）喷洒杀虫剂比其他控制策略更有效地减少HLB传播早期的ACP数量。这些理论和数值结果可能有助于制定公共政策来更有效地控制果园中的HLB。