Transmission dynamics of a Huanglongbing model with cross protection

Huanglongbing (HLB) is one of the most common widespread vector-borne transmission diseases through psyllid, which is called a kind of cancer of plant disease. In recent years, biologists have focused on the role of cross protection strategy to control the spread of HLB. In this paper, according to transmission mechanism of HLB, a deterministic model with cross protection is formulated. A threshold value R-0 is established to measure whether or not the disease is uniformly persistent. The existence of a backward bifurcation presents a further sub-threshold condition below R-0 for the spread of the disease. We also discuss the effects of cross protection and removing infected trees in spreading the disease. Numerical simulations suggest that cross protection is a promotion control measure, and replanting trees is bad for HLB control.