Electronic Thesis and Dissertation Repository

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.