Physical Sciences and Mathematics Commons^™

Modeling Leafhopper Populations And Their Role In Transmitting Plant Diseases., Ji Ruan

Electronic Thesis and Dissertation Repository

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 …