Modeling the impact of climate change on tick population dynamics and tick-borne disease spread

There is increasing evidence that Lyme disease is an emerging threat for public health in Canada. In this dissertation, we study the impact of climate change on establishment/extinction of the Lyme disease tick vector Ixodes scapularis and Lyme pathogen Borrelia burgdorferi in the Canadian landscape by utilizing mathematical techniques and computer simulations. We develop principal mathematical frameworks using ordinary differential equations with periodic coefficients, partial differential equations with seasonality and a periodic system of delay differential equations with periodic delay. We develop analysis and tools to predict the long-term status of Lyme disease transmission dynamics in the vector population. We determine factors, which are of interest to public health policy makers, for Lyme disease prevention and control in Canada in varying environmental conditions. We provide the theoretical foundation of a risk map of Lyme disease in Canada.