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Full-Text Articles in Mathematics

Functional Data Analysis Of Covid-19, Nichole L. Fluke Nov 2022

Functional Data Analysis Of Covid-19, Nichole L. Fluke

Mathematics & Statistics ETDs

This thesis deals with Functional Data Analysis (FDA) on COVID data. The Data involves counts for new COVID cases, hospitalized COVID patients, and new COVID deaths. The data used is for all the states and regions in the United States. The data starts in March 1st, 2020 and goes through March 31st, 2021. The FDA smooths the data and looks to see if there are similarities or differences between the states and regions in the data. The data also shows which states and regions stand out from the others and which ones are similar. Also shown …


Statistical Analysis Methods Applied To Early Outpatient Covid-19 Treatment Case Series Data, Eleftherios Gkioulekas, Peter A. Mccullough, Vladimir Zelenko Aug 2022

Statistical Analysis Methods Applied To Early Outpatient Covid-19 Treatment Case Series Data, Eleftherios Gkioulekas, Peter A. Mccullough, Vladimir Zelenko

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

When confronted with a public health emergency, significant innovative treatment protocols can sometimes be discovered by medical doctors at the front lines based on repurposed medications. We propose a statistical framework for analyzing the case series of patients treated with such new protocols, that enables a comparison with our prior knowledge of expected outcomes, in the absence of treatment. The goal of the proposed methodology is not to provide a precise measurement of treatment efficacy, but to establish the existence of treatment efficacy, in order to facilitate the binary decision of whether the treatment protocol should be adopted on an …


Machine Learning Model Comparison And Arma Simulation Of Exhaled Breath Signals Classifying Covid-19 Patients, Aaron Christopher Segura Aug 2022

Machine Learning Model Comparison And Arma Simulation Of Exhaled Breath Signals Classifying Covid-19 Patients, Aaron Christopher Segura

Mathematics & Statistics ETDs

This study compared the performance of machine learning models in classifying COVID-19 patients using exhaled breath signals and simulated datasets. Ground truth classification was determined by the gold standard Polymerase Chain Reaction (PCR) test results. A residual bootstrapped method generated the simulated datasets by fitting signal data to Autoregressive Moving Average (ARMA) models. Classification models included neural networks, k-nearest neighbors, naïve Bayes, random forest, and support vector machines. A Recursive Feature Elimination (RFE) study was performed to determine if reducing signal features would improve the classification models performance using Gini Importance scoring for the two classes. The top 25% of …


Mathematical Modeling Of Seir Model With Generalized Incidence Function And The Extension To Covid-19 Model, Shymaa Mohammad Dadoa Aug 2022

Mathematical Modeling Of Seir Model With Generalized Incidence Function And The Extension To Covid-19 Model, Shymaa Mohammad Dadoa

Theses

The COVID-19 pandemic had shown the importance of the SEIR model in predicting the outcome of the disease spread and to find the best strategies to contain the pandemic. As this type of model has a limited number of compartments, many other models were derived from the SEIR model to cover, to the maximum, the complex dynamics of the disease spread. These extensions of the SEIR model bring natural validity questions: How can we validate these models? and how far/close are these extended models from giving us real insights into the pandemic?

This thesis investigates the SEIR epidemic model and …


What In The World Just Happened? Students’ Self-Regulation In Asynchronous Precalculus During The Covid-19 Pandemic, Whitney George, Keith Gallagher Jul 2022

What In The World Just Happened? Students’ Self-Regulation In Asynchronous Precalculus During The Covid-19 Pandemic, Whitney George, Keith Gallagher

Journal of Humanistic Mathematics

We describe students’ learning practices in an online asynchronous PreCalculus course during Fall 2020, the first complete semester of distance learning induced by the COVID-19 pandemic. Results were compiled using a thematic analysis of a questionnaire administered to 43 students enrolled in PreCalculus at a university in the Midwest (United States). Students were given opportunities for active learning and various synchronous Q&A sessions, yet they primarily learned through watching videos and reading worked examples, minimizing interactions with the instructor and available tutors. The questionnaire results show that students knew active learning was helpful, but they were unable to curtail unproductive …


Networks Of Necessity: Simulating Covid-19 Mitigation Strategies For Disabled People And Their Caregivers, Thomas E. Valles, Hannah Shoenhard, Joseph Zinski, Sarah Trick, Mason A. Porter, Michael R. Lindstrom May 2022

Networks Of Necessity: Simulating Covid-19 Mitigation Strategies For Disabled People And Their Caregivers, Thomas E. Valles, Hannah Shoenhard, Joseph Zinski, Sarah Trick, Mason A. Porter, Michael R. Lindstrom

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Abstract

A major strategy to prevent the spread of COVID-19 is the limiting of in-person contacts. However, limiting contacts is impractical or impossible for the many disabled people who do not live in care facilities but still require caregivers to assist them with activities of daily living. We seek to determine which interventions can best prevent infections of disabled people and their caregivers. To accomplish this, we simulate COVID-19 transmission with a compartmental model that includes susceptible, exposed, asymptomatic, symptomatically ill, hospitalized, and removed/recovered individuals. The networks on which we simulate disease spread incorporate heterogeneity in the risk levels of …


An Application Of Matrices To The Spread Of The Covid 19, Selena Suarez May 2022

An Application Of Matrices To The Spread Of The Covid 19, Selena Suarez

Theses and Dissertations

We represented a restaurant seating arrangement using matrices by using 0 entry for someone without covid and 1 entry for someone with covid. Using the matrices we found the best seating arrangements to lessen the spread of covid. We also investigated if there was a factor needed to create a formula that could calculate the matrix that shows who would be affected with covid with each seating arrangement. However, there did not seem to be a clear pattern within the factors. Aside from covid applications, we also investigated the symmetries in seating arrangements and the possible combinations with these arrangements …


Remotely Close: An Investigation Of The Student Experience In First-Year Mathematics Courses During The Covid-19 Pandemic, Sawyer Smith Apr 2022

Remotely Close: An Investigation Of The Student Experience In First-Year Mathematics Courses During The Covid-19 Pandemic, Sawyer Smith

Honors Theses

The realm of education was shaken by the onset of the COVID-19 pandemic in 2020. It had drastic effects on the way that courses were delivered to students, and the way that students were getting their education at the collegiate level. At the University of Nebraska – Lincoln, the pandemic dramatically changed the way that first-year mathematics courses looked for students. By Spring 2021, students had the opportunity to take their first-year math courses either in-person or virtually. This project sought to identify differences between the two methods of course delivery during the Spring 2021 semester, regarding interaction with peers …


On The Mathematics Of Social Distancing, Robert Haas Jan 2022

On The Mathematics Of Social Distancing, Robert Haas

Journal of Humanistic Mathematics

Early in the COVID-19 pandemic, when spring began to make itself felt, photos showed New Yorkers enjoying the outdoors, while properly socially distanced, by sitting on the grass in a square lattice of circles. But the planners should have consulted a mathematician for the design, because significantly more people (over 15% more) could enjoy the same area safely if the circles were closer packed into a hexagonal lattice.


Covid-19, Vaccines, And Decision Theory, Michael A. Lewis Jan 2022

Covid-19, Vaccines, And Decision Theory, Michael A. Lewis

Journal of Humanistic Mathematics

In this piece, I delve into some thoughts I've had about decision theory. These have been inspired by the vaccine rollout phase of the COVID-19 Pandemic. I focus on decision making under uncertainty, as it relates to the decision to get vaccinated or not.


Mindfully Navigating The Wind And Water: Defining The Currents Of Metaphors That Interfere With Excellence In Mathematics Education, Rob Blom, Olivia Lu, Chunlei Lu Jan 2022

Mindfully Navigating The Wind And Water: Defining The Currents Of Metaphors That Interfere With Excellence In Mathematics Education, Rob Blom, Olivia Lu, Chunlei Lu

Journal of Humanistic Mathematics

We bring to the forefront of educational thought a specific attitude toward the COVID-19 crisis that harnesses the symbolism of wind and water to navigate the cultural storm interfering upon our mathematical and pedagogical craft. The purpose of our paper is to open up space for opportunities in mathematics education using integral mindfulness as the rudder to readjust our bearings. More specifically, through conceptual analyses and making explicit the currents of change, disorder, and technology, we can apply discernment to these metaphors that intersect our pedagogy to re-align efforts and attitudes toward an integrated (aperspectival) culture of mathematics education. Through …


Unmotivated, Depressed, Anxious: Impact Of The Covid-19 Emergency Transition To Remote Learning On Undergraduates’ Math Anxiety, Melinda Lanius, Tiffany Frugé Jones, Samantha Kao, Tynan Lazarus, Alex Farrell Jan 2022

Unmotivated, Depressed, Anxious: Impact Of The Covid-19 Emergency Transition To Remote Learning On Undergraduates’ Math Anxiety, Melinda Lanius, Tiffany Frugé Jones, Samantha Kao, Tynan Lazarus, Alex Farrell

Journal of Humanistic Mathematics

In summer 2020, we invited the 6761 undergraduate students who took a Spring 2020 math course at the University of Arizona to participate in a survey, with 13% responding. We asked about their experience with the emergency transition to remote learning and measured their math anxiety before and after the transition using the well-established Abbreviated Math Anxiety Scale(AMAS). “Unmotivated, depressed, anxious” are the words one undergraduate used to describe their emergency transition to remote learning. Our results indicate that limited access to quality technology and inadequate communication with an instructor were the two greatest predictors for an increase in math …


Using A Stochastic Continuous-Time Markov Chain Model To Examine Alternative Timing And Duration Of The Covid-19 Lockdown In Kuwait: What Can Be Done Now?, Mustafa Al-Zoughool, Tamer Oraby, Harri Vainio, Janvier Gasana, Joseph C. Longenecker, Walid Al Ali, Mohammad Alseaidan, Susie Elsaadany, Michael G. Tyshenko Jan 2022

Using A Stochastic Continuous-Time Markov Chain Model To Examine Alternative Timing And Duration Of The Covid-19 Lockdown In Kuwait: What Can Be Done Now?, Mustafa Al-Zoughool, Tamer Oraby, Harri Vainio, Janvier Gasana, Joseph C. Longenecker, Walid Al Ali, Mohammad Alseaidan, Susie Elsaadany, Michael G. Tyshenko

School of Mathematical and Statistical Sciences Faculty Publications and Presentations

Background

Kuwait had its first COVID-19 in late February, and until October 6, 2020 it recorded 108,268 cases and 632 deaths. Despite implementing one of the strictest control measures-including a three-week complete lockdown, there was no sign of a declining epidemic curve. The objective of the current analyses is to determine, hypothetically, the optimal timing and duration of a full lockdown in Kuwait that would result in controlling new infections and lead to a substantial reduction in case hospitalizations.

Methods

The analysis was conducted using a stochastic Continuous-Time Markov Chain (CTMC), eight state model that depicts the disease transmission and …


Finding The Best Predictors For Foot Traffic In Us Seafood Restaurants, Isabel Paige Beaulieu Jan 2022

Finding The Best Predictors For Foot Traffic In Us Seafood Restaurants, Isabel Paige Beaulieu

Honors Theses and Capstones

COVID-19 caused state and nation-wide lockdowns, which altered human foot traffic, especially in restaurants. The seafood sector in particular suffered greatly as there was an increase in illegal fishing, it is made up of perishable goods, it is seasonal in some places, and imports and exports were slowed. Foot traffic data is useful for business owners to have to know how much to order, how many employees to schedule, etc. One issue is that the data is very expensive, hard to get, and not available until months after it is recorded. Our goal is to not only find covariates that …


Collected Papers (On Physics, Artificial Intelligence, Health Issues, Decision Making, Economics, Statistics), Volume Xi, Florentin Smarandache Jan 2022

Collected Papers (On Physics, Artificial Intelligence, Health Issues, Decision Making, Economics, Statistics), Volume Xi, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This eleventh volume of Collected Papers includes 90 papers comprising 988 pages on Physics, Artificial Intelligence, Health Issues, Decision Making, Economics, Statistics, written between 2001-2022 by the author alone or in collaboration with 84 co-authors from 19 countries.


Collected Papers (On Neutrosophics, Plithogenics, Hypersoft Set, Hypergraphs, And Other Topics), Volume X, Florentin Smarandache Jan 2022

Collected Papers (On Neutrosophics, Plithogenics, Hypersoft Set, Hypergraphs, And Other Topics), Volume X, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

This tenth volume of Collected Papers includes 86 papers in English and Spanish languages comprising 972 pages, written between 2014-2022 by the author alone or in collaboration with 105 co-authors from 26 countries.


Exo-Sir: An Epidemiological Model To Analyze The Impact Of Exogenous Spread Of Infection, Nirmal Kumar Sivaraman, Manas Gaur, Shivansh Baijal, Sakthi Balan Muthiah, Amit Sheth Jan 2022

Exo-Sir: An Epidemiological Model To Analyze The Impact Of Exogenous Spread Of Infection, Nirmal Kumar Sivaraman, Manas Gaur, Shivansh Baijal, Sakthi Balan Muthiah, Amit Sheth

Publications

Epidemics like Covid-19 and Ebola have impacted people's lives significantly. The impact of mobility of people across the countries or states in the spread of epidemics has been significant. The spread of disease due to factors local to the population under consideration is termed the endogenous spread. The spread due to external factors like migration, mobility, etc. is called the exogenous spread. In this paper, we introduce the Exo-SIR model, an extension of the popular SIR model and a few variants of the model. The novelty in our model is that it captures both the exogenous and endogenous spread of …