This thesis project is part of a larger collaboration documenting the history of the ASU Biodesign Clinical Testing Laboratory (ABCTL). There are many different aspects that need to be considered when transforming to a clinical testing laboratory. This includes the different types of tests performed in the laboratory. In addition to the diagnostic polymerase chain reaction (PCR) test that is performed detecting the presence of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), antibody testing is also performed in clinical laboratories. Antibody testing is used to detect a previous infection. Antibodies are produced as part of the immune response against SARS-CoV-2. There are many different forms of antibody tests and their sensitives and specificities have been examined and reviewed in the literature. Antibody testing can be used to determine the seroprevalence of the disease which can inform policy decisions regarding public health strategies. The results from antibody testing can also be used for creating new therapeutics like vaccines. The ABCTL recognizes the shifting need of the community to begin testing for previous infections of SARS-CoV-2 and is developing new forms of antibody testing that can meet them.

In this project, I examined the relationship between lockdowns implemented by COVID-19 and the activity of animals in urban areas. I hypothesized that animals became more active in urban areas during COVID-19 quarantine than they were before and I wanted to see if my hypothesis could be researched through Twitter crowdsourcing. I began by collecting tweets using python code, but upon examining all data output from code-based searches, I concluded that it is quicker and more efficient to use the advanced search on Twitter website. Based on my research, I can neither confirm nor deny if the appearance of wild animals is due to the COVID-19 lockdowns. However, I was able to discover a correlational relationship between these two factors in some research cases. Although my findings are mixed with regard to my original hypothesis, the impact that this phenomenon had on society cannot be denied.

Actuaries can analyze healthcare trends to determine if rates are reasonable and if reserves are adequate. In this talk, we will provide a framework of methods to analyze the healthcare trend during the pandemic. COVID-19 may influence future healthcare cost trends in many ways. First, direct COVID-19 costs may increase the amount of total experienced healthcare costs. However, with the implementation of social distancing, the amount of regularly scheduled care may be deferred to a future date. There are also many unknown factors regarding the transmission of the virus. Implementing epidemiology models allows us to predict infections by studying the dynamics of the disease. The correlation between infection amounts and hospitalization occupancies provide a methodology to estimate the amount of deferred and recouped amounts of regularly scheduled healthcare costs. Thus, the combination of the models allows to model the healthcare cost trend impact due to COVID-19.

Optimal foraging theory provides a suite of tools that model the best way that an animal will <br/>structure its searching and processing decisions in uncertain environments. It has been <br/>successful characterizing real patterns of animal decision making, thereby providing insights<br/>into why animals behave the way they do. However, it does not speak to how animals make<br/>decisions that tend to be adaptive. Using simulation studies, prior work has shown empirically<br/>that a simple decision-making heuristic tends to produce prey-choice behaviors that, on <br/>average, match the predicted behaviors of optimal foraging theory. That heuristic chooses<br/>to spend time processing an encountered prey item if that prey item's marginal rate of<br/>caloric gain (in calories per unit of processing time) is greater than the forager's<br/>current long-term rate of accumulated caloric gain (in calories per unit of total searching<br/>and processing time). Although this heuristic may seem intuitive, a rigorous mathematical<br/>argument for why it tends to produce the theorized optimal foraging theory behavior has<br/>not been developed. In this thesis, an analytical argument is given for why this<br/>simple decision-making heuristic is expected to realize the optimal performance<br/>predicted by optimal foraging theory. This theoretical guarantee not only provides support<br/>for why such a heuristic might be favored by natural selection, but it also provides<br/>support for why such a heuristic might a reliable tool for decision-making in autonomous<br/>engineered agents moving through theatres of uncertain rewards. Ultimately, this simple<br/>decision-making heuristic may provide a recipe for reinforcement learning in small robots<br/>with little computational capabilities.

With the rise of fast fashion and its now apparent effects on climate change, there is an evident need for change in terms of how we as individuals use our clothing and footwear. Our team has created Ray Fashion Inc., a sustainable footwear company that focuses on implementing the circular economy to reduce the amount of waste generated in shoe creation. We have designed a sandal that accommodates the rapid consumption element of fast fashion with a business model that promotes sustainability through a buy-back method to upcycle and retain our materials.

The COVID-19 pandemic has resulted in preventative measures and has led to extensive changes in lifestyle for the vast majority of the American population. As the pandemic progresses, a growing amount of evidence shows that minority groups, such as the Deaf community, are often disproportionately and uniquely affected. Deaf people are directly affected in their ability to personally socialize and continue with daily routines. More specifically, this can constitute their ability to meet new people, connect with friends/family, and to perform in their work or learning environment. It also may result in further mental health changes and an increased reliance on technology. The impact of COVID-19 on the Deaf community in clinical settings must also be considered. This includes changes in policies for in-person interpreters and a rise in telehealth. Often, these effects can be representative of the pre-existing low health literacy, frequency of miscommunication, poor treatment, and the inconvenience felt by Deaf people when trying to access healthcare. Ultimately, these effects on the Deaf community must be taken into account when attempting to create a full picture of the societal shift caused by COVID-19.

This thesis is a supplement textbook designed with ASU’s MAT 370, or more generally, a course in introductory real analysis (IRA). With research in the realms of mathematics textbook creation and IRA pedagogy, this supplement aims to provide students or interested readers an additional presentation of the materials. Topics discussed include the real number system, some topology of the real line, sequences of real numbers, continuity, differentiation, integration, and the Fundamental Theorem of Calculus. Special emphasis was placed on worked examples of proven results and exercises with hints at the end of every chapter. In this respect, this supplement aims to be both versatile and self-contained for the different mathematics skill levels of readers.