Applied Mathematics Commons^™

Combating Covid On College Campuses: The Impact Of Structural Changes On Viral Transmissions, Jared Knofczynski, Aria Killebrew Bruehl, Ben Warner, Ryne Shelton

altREU Projects

One of the most significant issues in the COVID-19 pandemic is the reopening of schools while minimizing the transmission of coronavirus. Opportunities for evaluating the effectiveness of policies that might be utilized at such institutions are limited, as the necessary empirical data has not been gathered yet. Agent-based modeling, where various entities within an environment are simulated as agents, offers an opportunity to examine the effectiveness of various policies in a way that drastically minimizes the health and economic risks involved. Agent-based modeling is common within biology, ecology and other fields; and has seen some use within the coronavirus literature. …

Statistical Methods For Resolving Intratumor Heterogeneity With Single-Cell Dna Sequencing, Alexander Davis

Dissertations and Theses (Open Access)

Tumor cells have heterogeneous genotypes, which drives progression and treatment resistance. Such genetic intratumor heterogeneity plays a role in the process of clonal evolution that underlies tumor progression and treatment resistance. Single-cell DNA sequencing is a promising experimental method for studying intratumor heterogeneity, but brings unique statistical challenges in interpreting the resulting data. Researchers lack methods to determine whether sufficiently many cells have been sampled from a tumor. In addition, there are no proven computational methods for determining the ploidy of a cell, a necessary step in the determination of copy number. In this work, software for calculating probabilities from …

"A Comparison Of Variable Selection Methods Using Bootstrap Samples From Environmental Metal Mixture Data", Paul-Yvann Djamen

Mathematics & Statistics ETDs

In this thesis, I studied a newly developed variable selection method SODA, and three customarily used variable selection methods: LASSO, Elastic net, and Random forest for environmental mixture data. The motivating datasets have neuro-developmental status as responses and metal measurements and demographic variables as covariates. The challenges for variable selections include (1) many measured metal concentrations are highly correlated, (2) there are many possible ways of modeling interactions among the metals, (3) the relationships between the outcomes and explanatory variables are possibly nonlinear, (4) the signal to noise ratio in the real data may be low. To compare these methods …

Projecting The Covid-19 Weekly Deaths And Hospitalizations For Jefferson County, Kentucky, Seyed Karimi, Natalie Dupre, W. Paul Mckinney, Bert B. Little, Naiya Patel, Sarah Moyer

The University of Louisville Journal of Respiratory Infections

Introduction: The trends in the numbers of active hospitalizations and fatalities caused by the COVID-19 in Jefferson County, Kentucky, were projected over the period May 7 to August 20, 2020.

Methods: The projections provided in this report are from a susceptible-exposed-infectious-recovered (SEIR) model. The model was calibrated using the COVID-19 transmission dynamics parameters from relevant literature and clinical dynamics parameters from the county’s data. The model was used to measure the impact of public health policy interventions designed to contain the infection. The policy was modeled by its intervention day and impact on the transmission of the virus such that …

An Improved Method For Spectroscopic Quality Classification, Elizabeth G. Mayer

Mathematics & Statistics ETDs

Spectral quality classification is a vital step in data cleaning before the

analysis of magnetic resonance spectroscopy (MRS) data can be done. This

analysis compares five methods of quality classification; three of these are

legacy methods, Maudsley et al. (2006), Zhang et al. (2018), and

Bustillo et al. (2020), and two newly created methods that used a random forests

classifier (RFC) to inform their classifications. We found that the random forest

classifier was the most accurate at predicting spectra quality (balanced

accuracy for RF of 88% vs legacy of 70%, 72%, or 72%). A

Random-Forests-Informed Filtering method (RFIFM) for quality …

Covid-19 Peak Immunity Values Seem To Follow Lognormal Distribution, Julio Urenda, Olga Kosheleva, Vladik Kreinovich, Tonghui Wang

Departmental Technical Reports (CS)

For the current pandemic, an important open problem is immunity: do people who had this disease become immune against further infections? In the immunity study, it is important to know how frequent are different levels of immunity, i.e., what is the probability distribution of the immunity levels. Different people have different rates of immunity dynamics: for some, immunity gets to the level faster, for others the immunity effect is slower. Similarly, in some patients, immunity stays longer, it others, it decreases faster. In view of this, an important characteristic is peak immunity. A recent study provides some statistics on the …

The Role Of Diversity Amplification For Personal Protection Control Strategies In Vector-Borne Disease Models, Jeffery Demers, Sharon Bewick, Justin M. Calabrese, William F. Fagan

Biology and Medicine Through Mathematics Conference

No abstract provided.

Density-Dependent Development Impacts The Success Of Wolbachia-Based Mosquito Control Programs, Alyssa Petroski, Lauren M. Childs, Michael Andrew Robert

Biology and Medicine Through Mathematics Conference

No abstract provided.

Attraction-Repulsion Taxis Mechanisms In A Predator-Prey Model, Evan C. Haskell

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Model-Based Investigation Of The Role Of Density Dependence In Juvenile Mosquito Development And Survival, Melody Walker Ms, Lauren M. Childs, Michael A. Robert

Biology and Medicine Through Mathematics Conference

No abstract provided.

Mathematical Modeling Of Gliding Motility And Its Regulation In Myxococcus Xanthus, Yirui Chen

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Mathematical Framework To Augment Metrics Of Small Intestinal Health, Cara J. Sulyok, Judy Day, Suzanne Lenhart

Biology and Medicine Through Mathematics Conference

No abstract provided.

Emergence, Mechanics, And Development: How Behavior And Geometry Underlie Cowrie Seashell Form, Michael G. Levy, Michael R. Deweese

Biology and Medicine Through Mathematics Conference

No abstract provided.

Mathematical Modeling Of The Car T-Cell Therapy, Emek Kose, Elizabeth Zollinger, Samantha Elliott

Biology and Medicine Through Mathematics Conference

No abstract provided.

Parameter Estimation For Tear Film Thinning, Rayanne Luke

Biology and Medicine Through Mathematics Conference

No abstract provided.

The Role Of Variation In Mate Choice And Wolbachia Infection On Aedes Aegypti Population Dynamics, Bernardo Ameneyro

Biology and Medicine Through Mathematics Conference

No abstract provided.

Using Network Modeling To Understand The Relationship Between Sars-Cov-1 And Sars-Cov-2, Elizabeth Brooke Haywood, Nicole A. Bruce

Biology and Medicine Through Mathematics Conference

No abstract provided.

Exploring The Effect Of The Nestling Recruitment Curve On Enzootic West Nile Virus Transmission, Emily B. Horton

Biology and Medicine Through Mathematics Conference

No abstract provided.

Modeling The Effects Of Fentanyl And Narcan On The Opioid Epidemic In Allegheny County Using Mathematics, Lindsay Moskal, Lauren Sines, Rachael Neilan Ph.D.

Undergraduate Research and Scholarship Symposium

Starting in the 1990s, physicians across the United States have increasingly prescribed opioid pain relievers, which has given rise to the current opioid epidemic. As a result, there has been a drastic increase in the number of overdose fatalities. In 2017, the number of opioid overdose deaths peaked and the U.S. declared the crisis as a public health emergency. One state that has contributed significantly to this epidemic is Pennsylvania, which ranks first for the greatest number of overdose deaths and third for the highest death rate. In fact, Allegheny County has witnessed an overdose death rate that is three …

Modeling The Effects Of Fentanyl And Narcan On The Opioid Epidemic In Allegheny County Using Mathematics, Lindsay Moskal, Lauren Sines, Rachael Neilan Ph.D.

Undergraduate Research and Scholarship Symposium

Starting in the 1990s, physicians across the United States have increasingly prescribed opioid pain relievers, which has given rise to the current opioid epidemic. As a result, there has been a drastic increase in the number of overdose fatalities. In 2017, the number of opioid overdose deaths peaked and the U.S. declared the crisis as a public health emergency. One state that has contributed significantly to this epidemic is Pennsylvania, which ranks first for the greatest number of overdose deaths and third for the highest death rate. In fact, Allegheny County has witnessed an overdose death rate that is three …

A Study Of Addiction: The Opioid Epidemic, An Analysis At The State And County Level, Jamey Van Dyke

Undergraduate Theses

Addictive diseases such as those stemming from the use of alcohol, cocaine and opioids lead to serious negative consequences at both the individual and societal level. Over the last two decades, there has been a significant increase in opioid prescriptions and addiction. The potential for addiction is related to factors that include genetics, prescriber behavior, user behavior and characteristics, in addition to environmental and systemic determinants. One measure of the seriousness of the opioid epidemic is the number of overdose deaths. In 2017, drug overdoses killed over seventy thousand Americans, and overdose deaths are projected to increase in the future. …

483— Effectiveness Of Mmr Vaccination In Orthodox Jewish Neighborhoods, Meenu Mundackal

GREAT Day Posters

Measles is a highly contagious disease, where large outbreaks arise by direct contact between susceptible (unvaccinated) and infectious individuals. Many Orthodox Jewish neighborhoods were affected by measles from 2018-2019. To quantify the vaccination effort on this susceptible population, a retrospective analysis was used to study the NYC and Rockland County populations using a differential equations model. A subsequent model, known as a realistically-structured network model, studied only the NYC population, in relation to typical household size. Vaccination strategies were applied to three cohorts: unvaccinated family members, members with 1 prior MMR dose, and members with 2 prior MMR doses. The …

484— Modeling Social Distancing Methods And Their Effectiveness In Combating The Spread Of Ebola, Rachel Fair

GREAT Day Posters

Ebola Virus Disease (EVD) is a rare but severe disease that is transmitted among humans through direct-contact with, and close proximity to, infected bodily fluids. From 2014-16, West Africa experienced the largest Ebola outbreak ever recorded, infecting over 28,000 people, and killing over 11,000. Although the symptoms of EVD are treatable, the disease can be extremely deadly, with an average of 50% EVD cases resulting in fatality. In areas where healthcare is scarce and vaccinations are not readily available, the practices of social distancing and self-quarantining have been shown to be highly effective in combating the spread of EVD. To …

465— Modeling Vaccine Efficacy For Tuberculosis In A Prison Population, Kaitlyn Mundackal

GREAT Day Posters

Tuberculosis is a highly contagious disease and is particularly problematic in confined communities such as prisons. I simulated how Tuberculosis moves through a prison population and tested how much vaccination effort is needed to control its spread. To explore this, I tested adding ever increasing numbers of randomly placed edges in a network and determined the size of the largest component. Afterwards, I removed edges in the model using two different methods, one illustrating if the edges were removed randomly and the other starting with prisoners that had the most connections, to simulate the effect of vaccination. My results show …

A Study Of Cholera Transmission, Urmi Ghosh-Dastidar

Open Educational Resources

A recent cholera outbreak in Haiti brought public attention to this disease. Cholera, a diarrheal disease, is caused by an intestinal bacterium, and if not addressed in a timely manner may become fatal. During the project described here, the students will learn how to solve and address a practical problem such as cholera transmission using various mathematical tools. Students will learn to develop a differential equation model based on practical scenarios, analyze the model using mathematics as well as numerical simulation, and finally describe the results in words that are understandable by the people who are not specialists in this …

H-Discrete Fractional Model Of Tumor Growth And Anticancer Effects Of Mono And Combination Therapies, Kamala Dadashova

Masters Theses & Specialist Projects

In this thesis, we focus on h–discrete and h–discrete fractional representation of a pharmacokinetics-pharmacodynamics (PK-PD) model which describes tumor growth considering time on hNa, where h>0. First, we introduce some definitions, lemmas and theorems on both h–discrete and h–discrete fractional calculus in the preliminary section. In Chapter 3, we work on the PD model with delay by exam ining nabla h–discrete equations and nabla h–discrete fractional equations as well as variation of constants formulas, accordingly. We introduce our model and solve it using theorems we proved in the last section of the indicated chapter. When we do simulation for …

Mathematical Modelling Of The Tuberculosis Epidemiology, Ally Yeketi Ayinla

Student Works (2020-2029)

This project analyses the tuberculosis (TB) epidemic mathematically using compartmental modelling approach. Three models are presented to discuss drug susceptible and multi-drug resistant TB. The first model presented has 4 compartments; susceptible, exposed, infectious and recovered. The relevance of the exposed class in managing TB is analysed and found to be useful in delaying the eventual onset of the infection. Compared to previous researches, our results significantly show that when efforts are made such that no infected individual bypasses the exposed class and progresses directly to the infectious, the TB epidemic is successfully combatted. Also, the model is used to …

Use Of Kalman Filtering In State And Parameter Estimation Of Diabetes Models, Cassidy Le

HMC Senior Theses

Diabetes continues to affect many lives every year, putting those affected by it at higher risk of serious health issues. Despite many efforts, there currently is no cure for diabetes. Nevertheless, researchers continue to study diabetes in hopes of understanding the disease and how it affects people, creating mathematical models to simulate the onset and progression of diabetes. Recent research by David J. Albers, Matthew E. Levine, Andrew Stuart, Lena Mamykina, Bruce Gluckman, and George Hripcsak¹ has suggested that these models can be furthered through the use of Data Assimilation, a regression method that synchronizes a model with a …

Mechanisms Of Value-Biased Prioritization In Fast Sensorimotor Decision Making, Kivilcim Afacan-Seref

Dissertations and Theses

In dynamic environments, split-second sensorimotor decisions must be prioritized according to potential payoffs to maximize overall rewards. The impact of relative value on deliberative perceptual judgments has been examined extensively, but relatively little is known about value-biasing mechanisms in the common situation where physical evidence is strong but the time to act is severely limited. This research examines the behavioral and electrophysiological indices of how value biases split-second perceptual decisions and the possible mechanisms underlying the process. In prominent decision models, a noisy but statistically stationary representation of sensory evidence is integrated over time to an action-triggering bound, and value-biases …

The Application Of Machine Learning Models In The Concussion Diagnosis Process, Sujit Subhash

Masters Theses

“Concussions represent a growing health concern and are challenging to diagnose and manage. Roughly four million concussions are diagnosed every year in the United States. Although research into the application of advanced metrics such as neuroimages and blood biomarkers has shown promise, they are yet to be implemented at a clinical level due to cost and reliability concerns. Therefore, concussion diagnosis is still reliant on clinical evaluations of symptoms, balance, and neurocognitive status and function. The lack of a universal threshold on these assessments makes the diagnosis process entirely reliant on a physician’s interpretation of these assessment scores. This study …