Dynamics of a citrus disease model with intercropping and insecticides: application to Huanglongbing

Huanglongbing (HLB) is one of the most widespread vector-borne plant diseases, transmitted by psyllids. It is often referred to as a “cancer” for citrus trees. In recent years, biologists have focused on the role of intercropping strategies to control the spread of HLB. In this paper, we formulate an HLB transmission model with intercropping and insecticide spraying strategies. We establish a threshold value $\mathcal{R}_{0}$ to determine whether or not the HLB will be uniformly persistent. For the HLB model, it shows rich dynamics, for instance, the existence of Hopf bifurcation and backward bifurcation which reveals a subthreshold condition that still enables spread of the HLB. We also discuss the effects of intercropping and spraying insecticides on disease propagation. Numerical simulations demonstrate that $\mathcal{R}_{0}$ is most sensitive to the total number of intercropped citrus trees with non-rutaceae plants, which indicates that intercropping is an effective control measure.