Role of vector resistance and grafting infection in Huanglongbing control models

Citrus huanglongbing (HLB) is one of the most devastating diseases affecting citrus almost worldwide due to the lack of a cure. To better understand the impact of insecticide resistance and grafting infection on the spread of HLB disease, a vector-borne compartmental model is formulated to describe the transmission dynamics of HLB between citrus and Asian citrus psyllid (ACP). The basic reproduction number R(0) is computed by using the next generation matrix approach, which is a threshold value of the uniform persistence and disappearance of HLB disease. By applying the sensitivity analysis of R(0), we obtain some parameters with the most significant influence on the transmission dynamics of HLB. Moreover, we also obtain that grafting infection has the least influence on the transmission dynamics of HLB. Additionally, a time-dependent control model of HLB to minimize the cost of implementing control efforts and infected trees and ACPs is formulated. By using Pontryagin's Minimum Principle, we obtain the optimal integrated strategy and prove the uniqueness of optimal control solution. The simulation results illustrate that the strategy involving two time-dependent optimal controls is the most effective to suppress the spread of the disease. However, insecticide spraying is more effective measure compared with infected tree removing.