Author: Jillian Claire Stupiansky

Publisher:

Published: 2013

Total Pages: 78

ISBN-13:

Huanglongbing (citrus greening) is a bacterial disease that has a significant impact on the citrus industry in Florida and poses a risk to the remaining citrus-producing regions of the United States. The work presented here centers around the development of a deterministic mathematical model that represents the spread of citrus greening disease within a single grove of trees. The system models both the tree and insect populations and incorporates a control strategy of roguing infected trees and replanting healthy trees. Initially, we will examine a system in which all interactions occur at a constant rate. In this case, the basic reproductive number, R[subscript small o], and its relation to the stability of the equilibria is discussed. In particular, theorems regarding extinction of the disease when R[subscript small o][less than or equal to] 1 and persistence of the disease when R[subscript small o][greater- than] 1 are proved. Variations on the rates of roguing are examined to provide insight into the effect of the control strategy on the level of healthy trees that can be maintained. A modification to the model is presented which allows for the possibility of the occurrence of a backward bifurcation. The original model is then modified to account for seasonal variation in the rate of transmission of the disease, and results pertaining to the stability of this new system are proved. Numerical studies are performed throughout to illustrate the theoretical findings. In addition, simulations of a stochastic model are explored, as this type of model may allow for the future incorporation of the economic impact of the disease.