Honey Bee Population Dynamics and Neonicotinoids

Honey bees (Apis mellifera) are responsible for pollinating nearly 80\% of all pollinated plants, meaning humans depend on honey bees to pollinate many staple crops. The success or failure of a colony is vital to global food production. There are various complex factors that can contribute to a colony's failure, including pesticides. Neonicotoids are a popular pesticide that have been used in recent times. In this study we concern ourselves with pesticides and its impact on honey bee colonies. Previous investigations that we draw significant inspiration from include Khoury et Al's \emph{A Quantitative Model of Honey Bee Colony Population Dynamics}, Henry et Al's \emph{A Common Pesticide Decreases Foraging Success and Survival in Honey Bees}, and Brown's \emph{ Mathematical Models of Honey Bee Populations: Rapid Population Decline}. In this project we extend a mathematical model to investigate the impact of pesticides on a honey bee colony, with birth rates and death rates being dependent on pesticides, and we see how these death rates influence the growth of a colony. Our studies have found an equilibrium point that depends on pesticides. Trace amounts of pesticide are detrimental as they not only affect death rates, but birth rates as well.