Electronic Thesis and Dissertation Repository


Doctor of Philosophy


Applied Mathematics


Lindi Wahl

2nd Supervisor

Mair Zamir



The work herein falls under the umbrella of mathematical modeling of disease transmission. The majority of this document focuses on the extent to which infection undermines the strength of a honey bee colony. These studies extend from simple mass-action ordinary differential equations models, to continuous age-structured partial differential equation models and finally a detailed agent-based model which accounts for vector transmission of infection between bees as well as a host of other influences and stressors on honey bee colony dynamics. These models offer a series of predictions relevant to the fate of honey bee colonies in the presence of disease and the nonlinear effects of disease, seasonality and the complicated dynamics of honey bee colonies. We are also able to extract from these models metrics that preempt colony failure. The analysis of disease dynamics in age-structured honey bee colony models required the study of next generation operators (NGO) and the basic reproduction number, $R_0$, for partial differential equations. This led us to the development of a coherent path from the NGO to its discrete compartmental counterpart, the next generation matrix (NGM) as well as the derivation of new closed-form formulae for the NGO for specific classes of disease models.