Transmission dynamics and optimal control of stage-structured HLB model.

Citrus Huanglongbing (HLB) is one of severe quarantine diseases affecting citrus pro-duction both in abroad and domestic. Based on the mechanism and characteristics of citrus HLB transmission, we establish a vector-borne model with stage structure and integrated strategy and inves-tigate the effect of the strategy in controlling the spread of HLB. By calculating, we obtain the basic reproductive number R0, and prove that the disease can be eradicated if R0 < 1, whereas the disease will persist if R0 > 1. Meanwhile, we apply the optimal control theory to obtain an optimal integrated strategy. Finally, we use our model to simulate the data of the numbers of inspected and infected citrus trees in "Yuan Orchard", located in Ganzhou City, Jiangxi Province in the southeast of P.R China. We also give some numerical simulations for our theoretical findings.