Analytical Perspectives and Numerical Simulations of a Mathematical Model for Spatiotemporal Dynamics of Citrus Greening

In this study, we propose a compartmental mathematical model that considers two interacting populations (citrus plants and insect vectors) and investigate the transmission dynamics of Huanglongbing in citrus crops. This disease is caused by the bacterium Candidatus Liberibacter asiaticus and is vectored by the psyllid Diaphorina citri. The disease is modeled under the following three main assumptions: there is vital dynamics with constant recruitment rates of citrus plants, the force of infection in both populations is a spatially dependent function varying with geographic location, and there is a spatial displacement of the vectors. In the main results of the paper, we formulate a coupled ordinary and partial differential equation system with initial and zero flux boundary conditions, establish the existence and uniqueness of solutions to the proposed model by applying semigroup theory, and introduce a numerical approximation of the system. Moreover, we develop a stability and persistence analysis. From the analytical point of view, we calculate the basic reproduction number R0 and prove three facts: the disease-free equilibrium is globally asymptotically stable when R0<1; the disease-free equilibrium is globally asymptotically stable when R0>1; and the hybrid system exhibits uniform persistence of infection when R0>1. In addition, we present some numerical examples.