In Chapters 2 and 3, I demonstrate how this approach provides novel insights into factors that shape the flexibility and robustness of task organization in harvester ant colonies (Pogonomyrmex barbatus). My results show that the degree to which colonies can respond to work in fluctuating environments depends on how individuals weigh the costs of activity and update their behavior in response to social information. In Chapter 4, I introduce a mathematical framework to study the emergence of collective organization in heterogenous groups. My approach, which is based on the theory of multi-agent systems, focuses on myopic agents whose behavior emerges out of an independent valuation of alternative choices in a given work environment. The product of this dynamic is an equilibrium organization in which agents perform different tasks (or abstain from work) with an analytically defined set of threshold probabilities. The framework is minimally developed, but can be extended to include other factors known to affect task decisions including individual experience and social facilitation. This research contributes a novel approach to developing (and analyzing) models of task organization that can be applied in a broader range of contexts where animals cooperate.
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.
The first model considers a monotherapy employing the immune checkpoint inhibitor anti-PD-1. The dynamics both with and without anti-PD-1 are studied, and mathematical analysis is performed in the case when no anti-PD-1 is administrated. Simulations are carried out to explore the effects of continuous treatment versus intermittent treatment. The outcome of the simulations does not demonstrate elimination of the tumor, suggesting the need for a combination type of treatment.
An extension of the aforementioned model is deployed to investigate the pairing of an immune checkpoint inhibitor anti-PD-L1 with an immunostimulant NHS-muIL12. Additionally, a generic drug-free model is developed to explore the dynamics of both exponential and logistic tumor growth functions. Experimental data are used for model fitting and parameter estimation in the monotherapy cases. The model is utilized to predict the outcome of combination therapy, and reveals a synergistic effect: Compared to the monotherapy case, only one-third of the dosage can successfully control the tumor in the combination case.
Finally, the treatment impact of oncolytic virus therapy in a previously developed and fit model is explored. To determine if one can trust the predictive abilities of the model, a practical identifiability analysis is performed. Particularly, the profile likelihood curves demonstrate practical unidentifiability, when all parameters are simultaneously fit. This observation poses concerns about the predictive abilities of the model. Further investigation showed that if half of the model parameters can be measured through biological experimentation, practical identifiability is achieved.