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Studying the effects of viruses and toxins on honey bees is important in order to understand the danger these important pollinators are exposed to. Hives exist in various environments, and different colonies are exposed to varying environmental conditions and dangers. To properly study the changes and effects of seasonality and pesticides on the population dynamics of honey bees, the presence of each of these threats must be considered. This study aims to analyze how infected colonies grapple more deeply with changing, seasonal environments, and how toxins in pesticides affect population dynamics. Thus, it addresses the following questions: How do viruses within a colony affect honey bee population dynamics when the environment is seasonal? How can the effects of pesticides be modeled to better understand the spread of toxins? This project is a continuation of my own undergraduate work in a previous class, MAT 350: Techniques and Applications of Applied Mathematics, with Dr. Yun Kang, and also utilizes previous research conducted by graduate students. Original research focused on the population dynamics of honey bee disease interactions (without considering seasonality), and a mathematical modeling approach to analyze the effects of pesticides on honey bees. In order to pursue answers to the main research questions, the model for honey bee virus interaction was adapted to account for seasonality. The adaptation of this model allowed the new model to account for the effects of seasonality on infected colony population dynamics. After adapting the model, simulations with arbitrary data were run using RStudio in order to gain insight into the specific ways in which seasonality affected the interaction between a honey bee colony and viruses. The second portion of this project examines a system of ordinary differential equations that represent the effect of pesticides on honey bee population dynamics, and explores the process of this model’s formulation. Both systems of equations used as the basis for each model’s research question are from previous research reports. This project aims to further that research, and explore the applications of applied mathematics to biological issues.
colony collapse. This paper aims to understand how these different factors contribute to the decline of honeybee populations by using two separate approaches: data analysis and mathematical modeling. The data analysis examines the relative impacts of mites, pollen, mites, and viruses on honeybee populations and colony collapse. From the data, low initial bee populations lead to collapse in September while mites and viruses can lead to collapse in December. Feeding bee colonies also has a mixed effect, where it increases both bee and mite populations. For the model, we focus on the population dynamics of the honeybee-mite interaction. Using a system of delay differential equations with five population components, we find that bee colonies can collapse from mites, coexist with mites, and survive without them. As long as bees produce more pupa than the death rate of pupa and mites produce enough phoretic mites compared to their death rates, bees and mites can coexist. Thus, it is possible for honeybee colonies to withstand mites, but if the parasitism is too large, the colony will collapse. Provided
this equilibrium exists, the addition of mites leads to the colony moving to the interior equilibrium. Additionally, population oscillations are persistent if they occur and are connected to the interior equilibrium. Certain parameter values destabilize bee populations, leading to large
oscillations and even collapse. From these parameters, we can develop approaches that can help us prevent honeybee colony collapse before it occurs.