Applied Mathematics Commons^™

Multilateration Index., Chip Lynch

Electronic Theses and Dissertations

We present an alternative method for pre-processing and storing point data, particularly for Geospatial points, by storing multilateration distances to fixed points rather than coordinates such as Latitude and Longitude. We explore the use of this data to improve query performance for some distance related queries such as nearest neighbor and query-within-radius (i.e. “find all points in a set P within distance d of query point q”). Further, we discuss the problem of “Network Adequacy” common to medical and communications businesses, to analyze questions such as “are at least 90% of patients living within 50 miles of a covered emergency …

From Reaction Kinetics To Dementia: A Simple Dimer Model Of Alzheimer’S Disease Etiology, Michael R. Lindstrom, Manuel B. Chavez, Elijah A. Gross-Sable, Eric Y. Hayden, David B. Teplow

School of Mathematical & Statistical Sciences Faculty Publications

Oligomers of the amyloid β-protein (Aβ) have been implicated in the pathogenesis of Alzheimer’s disease (AD) through their toxicity towards neurons. Understanding the process of oligomerization may contribute to the development of therapeutic agents, but this has been difficult due to the complexity of oligomerization and the metastability of the oligomers thus formed. To understand the kinetics of oligomer formation, and how that relates to the progression of AD, we developed models of the oligomerization process. Here, we use experimental data from cell viability assays and proxies for rate constants involved in monomerdimer-trimer kinetics to develop a simple mathematical model …

Multiple Baseline Interrupted Time Series: Describing Changes In New Mexico Medicaid Behavioral Health Home Patients’ Care, Jessica Reno

Mathematics & Statistics ETDs

In 2016, the CareLink New Mexico behavioral health homes program began enrolling Medicaid recipients with the goal of increasing care coordination, improving access to services, and decreasing long-term costs of care for adults with serious mental illness (SMI) and children with severe emotional disturbance (SED). To evaluate these aims, a retrospective interrupted time series study using Medicaid claims data was designed. First, a comparable subset of non-enrolled individuals was selected from the pool of Medicaid recipients with SMI or SED using propensity score matching. Then, segmented regression was applied to three outcomes: total Medicaid charges, number of outpatient behavioral health …

Understanding Covid-19 Dynamics And The Effects Of Interventions In The Philippines: A Mathematical Modelling Study, Jamie M. Caldwell, Elvira P. De Lara-Tuprio, Timothy Robin Y. Teng, Ma. Regina Justina E. Estuar, Raymond Francis R. Sarmiento, Milinda Abayawardana B. Eng, Robert Neil F. Leong, Richard T. Gray, James G. Wood, Linh-Vi Le, Emma S. Mcbryde, Romain Ragonnet, James M. Trauer

Mathematics Faculty Publications

Background

COVID-19 initially caused less severe outbreaks in many low- and middle-income countries (LMIC) compared with many high-income countries; possibly because of differing demographics; socioeconomics; surveillance; and policy responses. Here; we investigate the role of multiple factors on COVID-19 dynamics in the Philippines; a LMIC that has had a relatively severe COVID-19 outbreak.

Methods

We applied an age-structured compartmental model that incorporated time-varying mobility; testing; and personal protective behaviors (through a “Minimum Health Standards” policy; MHS) to represent the first wave of the Philippines COVID-19 epidemic nationally and for three highly affected regions (Calabarzon; Central Visayas; and the National Capital …

Mathematical Modeling, Analysis, And Simulation Of The Covid-19 Pandemic With Behavioral Patterns And Group Mixing, Comfort Ohajunwa, Padmanabhan Seshaiyer

Spora: A Journal of Biomathematics

Due to the rise of COVID-19 cases, many mathematical models have been developed to study the disease dynamics of the virus. However, despite its role in the spread of COVID-19, many SEIR models neglect to account for human behavior. In this project, we develop a novel mathematical modeling framework for studying the impact of mixing patterns and social behavior on the spread of COVID-19. Specifically, we consider two groups, one exhibiting normal behavior who do not reduce their contacts and another exhibiting altered behavior who reduce their contacts by practicing non-pharmaceutical interventions such as social distancing and self-isolation. The dynamics …

Research Focus: Pattern Recognition

In The Loop

A CDM health informatics team joins a global race to advance COVID-19 diagnostics through X-ray insights.

Optimal Analytical Methods For High Accuracy Cardiac Disease Classification And Treatment Based On Ecg Data, Jianwei Zheng

Computational and Data Sciences (PhD) Dissertations

This work constitutes six projects. In the first project, a newly inaugurated research database for 12-lead electrocardiogram signals was created under the auspices of Chapman University and Shaoxing People's Hospital (Shaoxing Hospital Zhejiang University School of Medicine). This database aims to enable the scientific community in conducting new studies on arrhythmia and other cardiovascular conditions. In the second project, we created a new 12-lead ECG database under the auspices of Chapman University and Ningbo First Hospital of Zhejiang University that aims to provide high quality data enabling detection of the distinctions between idiopathic ventricular arrhythmia from right ventricular outflow tract …

Predicting Suboptimal Care In Insured Nebraskans With Known And Suspected Chronic Conditions., Avery Wallace

Capstone Experience: Master of Public Health

Health insurance companies have a goal of improving population health for their members (people who the company insures). As a health insurance company, [Company] has ample data on the health of its members that can be utilized to improve the health, and by extension lives of the people they insure. Although [Company] does not deliver care, they communicate with their members and physicians to identify ways to improve the health of the member. Of specific interest are members with known chronic conditions who are receiving suboptimal care, as well as members who have undiagnosed chronic conditions. Two chronic conditions were …

Predicting Tumor Response To Radiotherapy Based On Estimation Of Non-Treatment Parameters, Yutian Huang, Allison L. Lewis

Spora: A Journal of Biomathematics

Though clinicians can now collect detailed information about a variety of tumor characteristics as a tumor evolves, it remains difficult to predict the efficacy of a given treatment prior to administration. Additionally, the process of data collection may be invasive and expensive. Thus, the creation of a framework for predicting patient response to treatment using only information collected prior to the start of treatment could be invaluable. In this study, we employ ordinary differential equation models for tumor growth and utilize synthetic data from a cellular automaton model for calibration. We investigate which parameters have the most influence upon treatment …

Modeling Covid-19 Infection Rates Using Sir And Arima Models, Janelle Domantay, Ilya Pivavaruk, Victor Taksheyev

Undergraduate Research Symposium Posters

With the onset of the COVID-19 pandemic, it has become of increasing interest to both monitor and predict the growth of its infection rates. In order to analyze the accuracy of epidemiological prediction, we consider two different models for prediction, the Susceptible Infected and Removed (SIR), and Autoregressive Integrated Moving Average (ARIMA) models. Using a dataset of Clark County COVID-19 infections, we create various ARIMA and SIR models that attempt to predict the progression of COVID-19 infections whilst comparing these predictions to the dataset. We observed that the ARIMA model performed more accurately overall, having a much lower Root Mean …

Modeling Of Covid-19 Utilizing Various Compartmental Models To Predict Infection Rates Throughout Michigan, Colleen M. Staniszewski

Honors Theses

Compartmental modeling is a method of employing math to create a visual representation of a disease interacting with a select population, typically used in epidemiology analyses. This project applies compartmental modeling equations to data collected on the various aspects of COVID-19 in Michigan. Comparing current data to past predictive models, as well as the visual representations that were developed through the various compartmental modeling methods, allows an assessment of the effects of the preventative measures taken by the state, the various rates at which the infection is able to spread, as well as the potential path and spread of the …

Sars-Cov-2 And Rohingya Refugee Camp, Bangladesh: Uncertainty And How The Government Took Over The Situation, Md. Md. Kamrujjaman, Md. Shahriar Mahmud, Shakil Ahmed, Md. Omar Qayum, Mohammad Morshad Alam, Md. Nazmul Hassan, Md. Rafiul Islam, Kaniz Fatema Nipa, Ummugul Bulut

Mathematics Faculty Publications (Archived)

Background: Bangladesh hosts more than 800,000 Rohingya refugees from Myanmar. The low health immunity, lifestyle, access to good healthcare services, and social-security cause this population to be at risk of far more direct effects of COVID-19 than the host population. Therefore, evidence-based forecasting of the COVID-19 burden is vital in this regard. In this study, we aimed to forecast the COVID-19 obligation among the Rohingya refugees of Bangladesh to keep up with the disease outbreak’s pace, health needs, and disaster preparedness. Methodology and Findings: To estimate the possible consequences of COVID-19 in the Rohingya camps of Bangladesh, we used a …

Long-Term Dynamics Of The Kidney Disease Epidemic Among Hiv-Infected Individuals, Heather Gudaz, Henry A. Ogu, Elissa J. Schwartz

Spora: A Journal of Biomathematics

One of many risks facing HIV+ individuals is the development of kidney dysfunction and end stage kidney disease (ESKD). A differential equation-based mathematical model was developed to assess the impact of antiretroviral therapy on the progression to kidney disease and on reducing mortality due to kidney failure. Analytical and numerical predictions of long-term HIV+ ESKD prevalence show that therapy can lead to either extremely low levels of disease prevalence or increased prevalence, depending on drug efficacy levels and mechanisms of action. Maintenance of HIV+ ESKD prevalence below one individual is possible with sufficient efficacy (e.g., 99%) against the progression from …

Sars-Cov-2 Pandemic Analytical Overview With Machine Learning Predictability, Anthony Tanaydin, Jingchen Liang, Daniel W. Engels

SMU Data Science Review

Understanding diagnostic tests and examining important features of novel coronavirus (COVID-19) infection are essential steps for controlling the current pandemic of 2020. In this paper, we study the relationship between clinical diagnosis and analytical features of patient blood panels from the US, Mexico, and Brazil. Our analysis confirms that among adults, the risk of severe illness from COVID-19 increases with pre-existing conditions such as diabetes and immunosuppression. Although more than eight months into pandemic, more data have become available to indicate that more young adults were getting infected. In addition, we expand on the definition of COVID-19 test and discuss …

Neither “Post-War” Nor Post-Pregnancy Paranoia: How America’S War On Drugs Continues To Perpetuate Disparate Incarceration Outcomes For Pregnant, Substance-Involved Offenders, Becca S. Zimmerman

Pitzer Senior Theses

This thesis investigates the unique interactions between pregnancy, substance involvement, and race as they relate to the War on Drugs and the hyper-incarceration of women. Using ordinary least square regression analyses and data from the Bureau of Justice Statistics’ 2016 Survey of Prison Inmates, I examine if (and how) pregnancy status, drug use, race, and their interactions influence two length of incarceration outcomes: sentence length and amount of time spent in jail between arrest and imprisonment. The results collectively indicate that pregnancy decreases length of incarceration outcomes for those offenders who are not substance-involved but not evenhandedly -- benefitting white …

Impact Of Vaccine Supplies And Delays On Optimal Control Of The Covid-19 Pandemic: Mapping Interventions For The Philippines, Carlo Delfin S. Estadilla, Joshua Uyheng, Elvira P. De Lara-Tuprio, Timothy Robin Y. Teng, Jay Michael R. Macalalag, Ma. Regina Justina E. Estuar

Mathematics Faculty Publications

Background

Around the world, controlling the COVID-19 pandemic requires national coordination of multiple intervention strategies. As vaccinations are globally introduced into the repertoire of available interventions, it is important to consider how changes in the local supply of vaccines, including delays in administration, may be addressed through existing policy levers. This study aims to identify the optimal level of interventions for COVID-19 from 2021 to 2022 in the Philippines, which as a developing country is particularly vulnerable to shifting assumptions around vaccine availability. Furthermore, we explore optimal strategies in scenarios featuring delays in vaccine administration, expansions of vaccine supply, and …

Grouping Algorithms For Informative Array Testing In Disease Surveillance, David Sokolov

Graduate Theses, Dissertations, and Problem Reports (ETD)

In order to maintain normal operations and prevent unnecessary morbidity and mortality during times of disease outbreak, institutions find a need to conduct frequent and widespread testing of their constituents, often under significantly limited testing resource constraints. Faced with the challenge of how best to allo- cate these limited resources to maximum effect, institutions are increasingly turning to group (or “pooled”) testing, which involves testing strategically-chosen groups of patient samples rather than individual samples, producing significant testing resource savings under certain regimes of disease prevalence. While group test- ing can be conducted without any a priori knowledge of individual disease …

Bivariate Markov Chain Model Of Irritable Bowel Syndrome (Ibs) Subtypes And Abdominal Pain, Ricardo Reyna Jr.

Theses and Dissertations

Researchers use stochastic models like continuous-time Markov chains (CTMC) to model progression of morbidities of public health impact, like HIV and Hepatitis C. Most of the research in that area is done for a single disease. In this research, we use a bivariate continuous-time Markov chain (CTMC) to model progression of co-morbidities. In particular, we use a bivariate CTMC to model the joint progression of Irritable Bowel Syndrome (IBS) and abdominal pain. Symptoms of IBS are known to change throughout the duration of the disorder. Hence, patients are normally asked to make a journal of the stool type, symptoms, and …

Strange Periodic Behavior In An Epilepsy Model, David Chan, Candace Kent, William Strasser

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Applying Immuno-Epidemiology Principles To Violence, Anna H. Sisk, Nina H. Fefferman, Judy Day, Patricia Bamwine

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Analyzing The Control Measures For The Homeless Population And Quantifying Their Impact On The Covid-19 Epidemic In New York City, Steven Manns

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Mathematical Modeling And Analysis Of The Zika Virus Epidemic With Human Mobility And Parameter Estimation For Localities In Puerto Rico, Carmen Caiseda

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Modeling And Preparedness: The Transmission Dynamics Of Covid-19 Outbreak In Provinces Of Ecuador, Carlos E. Bustamante Orellana, Jordy Cevallos-Chavez, Cesar Montalvo, Jeff Sulliavan, Edwin Michael, Anuj Mubayi

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

A Teaching Module For Mathematical Epidemiology Using Matlab Or R, Glenn Ledder

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Assess The Impacts Of Human Mobility Change On Covid-19 Using Differential Equations With Google Community Mobility Data, Nao Yamamoto

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Mathematical Modeling, Analysis, And Simulation Of The Covid-19 Pandemic With Behavioral Patterns, Risk Perception, And Group Mixing, Comfort Ohajunwa, Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Deep Learning With Physics Informed Neural Networks For The Airborne Spread Of Covid-19 In Enclosed Spaces, Udbhav Muthakana, Padmanabhan Seshaiyer, Maziar Raissi, Long Nguyen

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

In Silico Modelling For The Treatment Of Gastric Cancer, Leonardo F. Martinez, Diana Gamboa, Paul A. Valle

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Mathematical Modelling And In Silico Experimentation To Estimate The Quantity Of Covid-19 Infected Individuals In Tijuana, México, Karla A. Encinas, Luis N. Coria, Paul A. Valle

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Testing The Effect Of Acetaminophen Overdose On The Liver And The Role Of Biomarkers To Predict Death Or Survival, Christine Brasic

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.