Degree
Master of Science
Program
Applied Mathematics
Supervisor
Dr. Xingfu Zou
Abstract
This M.Sc. thesis focuses on the interactions between crops and leafhoppers.
Firstly, a general delay differential equations system is proposed, based on the infection age structure, to investigate disease dynamics when disease latencies are considered. To further the understanding on the subject, a specific model is then introduced. The basic reproduction numbers $\cR_0$ and $\cR_1$ are identified and their threshold properties are discussed. When $\cR_0 < 1$, the insect-free equilibrium is globally asymptotically stable. When $\cR_0 > 1$ and $\cR_1 < 1$, the disease-free equilibrium exists and is locally asymptotically stable. When $\cR_1>1$, the disease will persist.
Secondly, we derive another general delay differential equations system to examine how different life stages of leafhoppers affect crops. The basic reproduction numbers $\cR_0$ is determined: when $\cR_01$, a positive equilibrium appears. To investigate the qualitative behaviours of this equilibrium, two special cases based on the monotonicity of birth rates of leafhoppers with respect to the adult population are studied.
Recommended Citation
Ruan, Ji, "Modeling leafhopper populations and their role in transmitting plant diseases." (2013). Electronic Thesis and Dissertation Repository. 1556.
https://ir.lib.uwo.ca/etd/1556
Included in
Agricultural Economics Commons, Bioinformatics Commons, Biology Commons, Dynamic Systems Commons, Non-linear Dynamics Commons, Ordinary Differential Equations and Applied Dynamics Commons, Parasitology Commons, Partial Differential Equations Commons