In this project we focus on COVID-19 in a university setting. Arizona State University has a very large population on the Tempe Campus. With the emergence of diseases such as COVID-19, it is very important to track how such a disease spreads within that type of community. This is vital for containment measures and the safety of everyone involved. We found in the literature several epidemiology models that utilize differential equations for tracking a spread of a disease. However, our goal is to provide a granular look at how disease may spread through contact in a classroom. This thesis models a single ASU classroom and tracks the spread of a disease. It is important to note that our variables and declarations are not aligned with COVID-19 or any other specific disease but are chosen to exemplify the impact of some key parameters on the epidemic size. We found that a smaller transmissibility alongside a more spread-out classroom of agents resulted in fewer infections overall. There are many extensions to this model that are needed in order to take what we have demonstrated and align those ideas with COVID-19 and it’s spread at ASU. However, this model successfully demonstrates a spread of disease through single-classroom interaction, which is the key component for any university campus disease transmission model.
We present an age- and stage-structured population model to study some methods of control of one of the most important grapevine pests, the European grapevine moth. We consider control by insecticides that reduce either the proportion of surviving eggs, larvae or both, as well as chemicals that cause mating disruption, thereby reducing the number of eggs laid. We formulate optimal control problems with cost functionals related to real-life costs in the wine industry, and we prove that these problems admit a unique solution. We also provide some numerical examples from simulation.