Analysis of Huanglongbing transmission model with vector preferences and heterogeneous environments

The world citrus industry is confronting an unprecedented challenge from citrus Huanglongbing (HLB). With no resistant commercial citrus varieties or curable chemicals currently available, HLB remains the top threat to the world citrus industry. In this paper, two dynamic models of citrus HLB are proposed based on the preference and diffusion of citrus psyllids. The first model is a single-patch model of HLB with vector preference. The basic reproduction number of the model is calculated, and dynamic properties of the single-patch model, including the existence and local stability of the disease-free equilibrium, are analyzed. By sensitivity analysis, the parameters that have a significant impact on the basic reproduction number are identified. Numerical simulations are conducted to demonstrate that the preference of citrus psyllids is not conducive to disease prevention. Considering the diffusion of citrus psyllids between two patches, a two-patch diffusion model of HLB with preference is formulated. The global basic reproduction number of the diffusion model is determined, and the global stability of the disease-free equilibrium is established under certain conditions. Finally, numerical simulation results explore how the preference behavior of the vector and the coupling strength between two patches affect the HLB transmission.