Mathematics Commons^™

An Epidemic Model Structured By The Time Since Last Infection, Jorge Alturo Alfaro Murillo

Open Access Dissertations

Epidemiological models structured by time since infection have their origin in the seminal work of 1927 by Kermack and McKendrick. Compared to ordinary differential equations (ODE) models, they are able to capture differences in infectivity of the individuals in a more suitable manner. Their use declined in the second half of the 20th century, probably because the theory for ODE models is more robust, complete and has proved successful in providing insights and predictions for many epidemiological problems. Nevertheless, it is important to understand in what occasions the inclusion of time since infection may alter the outcomes in a significant …

Mexican-American Children's Perspectives: Neighborhood Characteristics And Physical Activity In Texas-Mexico Border Colonias, Nelda Mier, Chanam Lee, Matthew Lee Smith, Xiaohui Wang, Elias H. Avila-Rodriguez, Laura Trevino, Marcia G. Ory

School of Mathematical & Statistical Sciences Faculty Publications

The qualitative study described in this article investigated perceptions about environmental factors influencing physical activity (PA) among children from underserved neighborhoods known as colonias in the U.S.-Mexico border. Ten focus groups were conducted with 67 Mexican-American colonia children ages 8 to 13 living in one of the poorest border counties in the U.S. Analyses indicated that PA among children was influenced by neighborhood characteristics, including litter, speeding cars, unleashed dogs, and dark streets. The children also underlined intrapersonal and social environmental factors. Findings may inform policy makers and public health professionals about ways to promote PA among underserved children through …

Mexican-American Children’S Perspectives: Neighborhood Characteristics And Physical Activity In Texas-Mexico Border Colonias, Nelda Mier, Chanam Lee, Matthew Lee Smith, Xiaohui Wang, David Irizarry, Elias H. Avila-Rodriguez, Laura Trevino, Marcia G. Ory

School of Mathematical & Statistical Sciences Faculty Publications

The qualitative study described in this article investigated perceptions about environmental factors infl uencing physical activity (PA) among children from underserved neighborhoods known as colonias in the U.S.-Mexico border. Ten focus groups were conducted with 67 Mexican-American colonia children ages 8 to 13 living in one of the poorest border counties in the U.S. Analyses indicated that PA among children was influenced by neighborhood characteristics, including litter, speeding cars, unleashed dogs, and dark streets. The children also underlined intrapersonal and social environmental factors. Findings may inform policy makers and public health professionals about ways to promote PA among underserved children …

Using Optimal Control Theory To Optimize The Use Of Oxygen Therapy In Chronic Wound Healing, Donna Lynn Daulton

Masters Theses & Specialist Projects

Approximately 2 to 3 million people in the United States suffer from chronic wounds, which are defined as wounds that do not heal in 30 days time; an estimated $25 billion per year is spent on their treatment in the United States. In our work, we focused on treating chronic wounds with bacterial infections using hyperbaric and topical oxygen therapies.

We used a mathematical model describing the interaction between bacteria, neutrophils and oxygen. Optimal control theory was then employed to study oxygen treatment strategies with the mathematical model. Existence of a solution was shown for both therapies. Uniqueness was also …

A Mathematical Model For Antibiotic Resistance In A Hospital Setting With A Varying Population, Edward H. Snyder

Electronic Theses and Dissertations

Antibiotic-resistant bacteria(ARB) is causing increased health risk and cost to society. Mathematical models have been developed to study the transmission of resistant bacteria and the efficacy of preventive measures to slow its spread within a hospital setting. The majority of these models have assumed a constant total hospital population with the admission and discharge rates being equal throughout the duration. But a typical hospital population varies from day to day and season to season. In this thesis, we apply variable admission and discharge daily rates to existing deterministic and stochastic models which examine the transmission of single and dual resistant …

Concurrent Neurological And Behavioral Assessment Of Number Line Estimation Performance In Children And Adults, Joseph Michael Baker

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

Understanding the brain’s response to common math-learning activities may help improve math education. For example, by imaging the brains of typically developing children and adults throughout a number line estimation task, it is possible to establish a baseline of what “typical” brains do in such situations. Thus, comparisons may be made to determine the degree to which brain functioning differs between typical and atypical math learners. Moreover, by identifying methods that may increase the brain’s response to real-world math activities, it may be possible to improve the math learning process for typical and atypical learners alike.

Brain imaging devices such …

Self-Directed Learning Readiness And Self-Determination For Selected Rehabilitation Professional Students: The Impact Of Clinical Education, Shelley S. Payne, Peter Rundquist, William V. Harper, Julie Gahimer

Mathematics Faculty Scholarship

In a time of rapidly changing medical information, practitioners must have learning skills that enable them to be effective life-long learners. A part of an examination of a final clinical internship for rehabilitation professionals was a pre-post measure of learner self-direction and self-determination. Two instruments, the Self-Directed Learning Readiness Scale (SDLRS) and the Academic Motivation Scale (AMS- reported as Self-Determination Index (SDI) were used with a sample of Doctorate of Physical Therapy (DPT) and Master of Occupational Therapy (MOT) students. Pre-testing occurred just prior to and post-testing just after the subjects’ final clinical assignments. Both groups increased mean scores from …

Volume 05, Ian Karamarkovich, Jessica Cox, Kyle Fowlkes, Allison Pawlowski, Kaitlin Major, Carrie Dunham, Kelsey Scheitlin, Kathryn Grayson, Ashley Johnson, Jennifer Nehrt, Kelsey Stolzenbach, Kristin Mcquarrie, Sara Nelson, Melisa Michelle, Jessica Sudlow, Perry Bason, Danielle Dmuchawski, Mariah Asbell, Matthew Sakach, Timothy Smith Jr., Annaliese Troxell, T. Dane Summerell, Sarah Ganrude, Malina Rutherford, Hannah Hopper, John Berry Jr., James Early, Colleen Festa, Chelsea D. Taylor, Michelle Maddox, Kaitlyn Smith, Sarah Schu, Cabell Edmunds, Katherine Grayson, Kayla Tornai

Incite: The Journal of Undergraduate Scholarship

Introduction from Dean Dr. Charles Ross

The Tallis House as an Extension of Emily Tallis in McEwan's Atonement by Ian Karamarkovich

Graphic Design by Jessica Cox

Graphic Design by Kyle Fowlkes

Graphic Design by Allison Pawlowski

Incorporating Original Research in The Classroom: A Case Study Analyzing the Influence of the Chesapeake Bay on Local Temperatures by Kaitlin Major, Carrie Dunham and Dr. Kelsey Scheitlin

Graphic Design by Kathryn Grayson

Graphic Design by Ashley Johnson

Facing the Music: Environmental Impact Assessment of Building A Concert Hall on North Campus by Jennifer Nehrt, Kelsey Stolzenbach And Dr. Kelsey Scheitlin

Art by Kristin …

Transmission Rate In Partial Differential Equation In Epidemic Models, Alaa Elkadry

Theses, Dissertations and Capstones

The rate at which susceptible individuals become infected is called the transmission rate. It is important to know this rate in order to study the spread and the effect of an infectious disease in a population. This study aims at providing an understanding of estimating the transmission rate from mathematical models representing the population dynamics of an infectious diseases using two different methods. Throughout, it is assumed that the number of infected individuals is known. In the first chapter, it includes historical background for infectious diseases and epidemic models and some terminology needed to understand the problems. Specifically, the partial …

High Jump Analysis, Paige Cooke

Undergraduate Journal of Mathematical Modeling: One + Two

This project presents a mathematical analysis of the high jump, a popular track and field event. The first and second stages of the high jump correspond to the athlete’s run along two distinct trajectories. The third stage is the actual jump. We propose an individual model for each of these stages and show how to combine these models to study the dynamics of the entire high jump.

A Single-Parameter Model Of The Immune Response To Bacterial Invasion, Lester Caudill

Department of Math & Statistics Faculty Publications

The human immune response to bacterial pathogens is a remarkably complex process, involving many different cell types, chemical signals, and extensive lines of communication. Mathematical models of this system have become increasingly high-dimensional and complicated, as researchers seek to capture many of the major dynamics. In this paper, we argue that, in some important instances, preference should be given to low-dimensional models of immune response, as opposed to their high-dimensional counterparts. One such model is analyzed and shown to reflect many of the key phenomenological properties of the immune response in humans. Notably, this model includes a single parameter values, …

A Comparison Of Two Teaching Methods For Pediatric Medication Administration: Multimedia And Text-Based Modules, Renee Granados

Doctoral Dissertations

A Comparison of Two Teaching Methods for Pediatrics: Multimedia and Text-based Modules to Teach Pediatric Medication Administration

Nurse educators are in a position to design and develop effective methods that consider the cognitive structures and how the mind processes information to teach pediatric medication content to nursing students. The majority of methods teaching medication administration use only one mode: the visual mode. One mode to present leaning material does not take advantage of the additive effects of using two modes to present learning material.

The purpose of the study was to compare the effectiveness of two teaching methods to present …

The Two-Phase Arterial Blood Flow With Or Without A Catheter And In The Presence Of A Single Or Multi Stenosis, Ani E. Garcia, Daniel N. Riahi

School of Mathematical & Statistical Sciences Faculty Publications

We consider the problem of blood flow in an artery with or without a catheter and in the presence of single or multi stenosis whose shape is based on the available experimental data for the stenosis in a human’s artery. The presence of stenosis in the artery, which locally narrows portion of the artery, can be a result of fatty materials such as cholesterol in the blood. The use of catheter is important as a standard tool for diagnosis and treatment in patience whose blood flow passage in the artery is affected adversely by the presence of the stenosis within …

High Prevalence Of Subclinical Atherosclerosis By Carotid Ultrasound Among Mexican Americans: Discordance With 10-Year Risk Assessment Using The Framingham Risk Score, Susan T. Laing, Beverly Smulevitz, Kristina Vatcheva, Anne R. Rentfro, David D. Mcpherson, Susan P. Fisher-Hoch, Joseph B. Mccormick

School of Mathematical & Statistical Sciences Faculty Publications

Background: Framingham risk scores (FRS) were validated in a mostly Caucasian population. Evaluation of subclinical atherosclerosis by carotid ultrasound may improve ascertainment of risk in nonwhite populations. This study aimed to evaluate carotid intima-media thickness (cIMT) and carotid plaquing among Mexican Americans, and to correlate these markers with coronary risk factors and the FRS.

Methods/results: Participants (n = 141) were drawn from the Cameron County Hispanic Cohort. Carotid artery ultrasound was performed and cIMT measured. Carotid plaque was defined as areas of thickening >50% of the thickness of the surrounding walls. Mean age was 53.1 ± 11.7 years (73.8% female). …

Missed Opportunities For Diagnosis And Treatment Of Diabetes, Hypertension, And Hypercholesterolemia In A Mexican American Population, Cameron County Hispanic Cohort, 2003-2008, Susan P. Fisher-Hoch, Kristina Vatcheva, Susan T. Laing, Monir Hossain, M Hossein Rahbar, Craig Hanis, H Shelton Brown, Anne R. Rentfro, Belinda M. Reininger, Joseph B. Mccormick

School of Mathematical & Statistical Sciences Faculty Publications

Introduction

Diabetes, hypertension, and hypercholesterolemia are common chronic diseases among Hispanics, a group projected to comprise 30% of the US population by 2050. Mexican Americans are the largest ethnically distinct subgroup among Hispanics. We assessed the prevalence of and risk factors for undiagnosed and untreated diabetes, hypertension, and hypercholesterolemia among Mexican Americans in Cameron County, Texas.

Methods

We analyzed cross-sectional baseline data collected from 2003 to 2008 in the Cameron County Hispanic Cohort, a randomly selected, community-recruited cohort of 2,000 Mexican American adults aged 18 or older, to assess prevalence of diabetes, hypertension, and hypercholesterolemia; to assess the extent to …

Halcomb, Warren G. (Sc 587), Manuscripts & Folklife Archives

Manuscript Collection Finding Aids

Finding aid and scan (Click on "additional files" below) for Manuscripts Small Collection 587. Ciphering book of Warren G. Halcomb’s of Caswell County, North Carolina, which he kept from 11 September 1809 to 15 July 1815. Other entries in the book include a few family names and dates, personal business notes, and a recipe for the cure of rheumatism. Loose items, 1840-1854, found in the book concern the slave trade, 1840 and 1849.

Interactive Concept To Aid In Understanding Dimensional Analysis, Alicia Hicks

Symposium 2012

Many students struggle with learning how to utilize dimensional analysis. This confusion is due to not understanding the concept of dose per volume, leading to difficulty when starting the sequencing. This could be one of the contributing causes to medication errors in clinical practice. Does using models, such as Play-doh and pebbles, help students learn the concept of milligrams per milliliters when calculating dosages using dimensional analysis method? A series of pre- and post-tests are used to measure learning growth in each of the treatment groups. Three treatment groups were utilized: Control: one group had no intervention between the pre …

Using Mathematics To Gain Insights Into Biology: An Application In Respiratory Mechanics, William Matern

Inquiry Journal 2012

No abstract provided.

Electrocardiographic Abnormalities Among Mexican Americans: Correlations With Diabetes, Obesity, And The Metabolic Syndrome, Saulette R. Queen, Beverly Smulevitz, Anne R. Rentfro, Kristina Vatcheva, David D. Mcpherson, Susan P. Fisher-Hoch, Joseph B. Mccormick, Susan T. Laing

School of Mathematical & Statistical Sciences Faculty Publications

Background: Resting ischemic electrocardiographic abnormalities have been associated with cardiovascular mortality. Simple markers of abnormal autonomic tone have also been associated with diabetes, obesity, and the metabolic syndrome in some populations. Data on these electrocardiographic abnormalities and correlations with coronary risk factors are lacking among Mexican Americans wherein these conditions are prevalent.

Objective: This study aimed to evaluate the prevalent resting electrocardiographic abnormalities among community-dwelling Mexican Americans, and correlate these findings with coronary risk factors, particularly diabetes, obesity, and the metabolic syndrome.

Methods: Study subjects (n=1280) were drawn from the Cameron County Hispanic Cohort comprised of community-dwelling Mexican Americans living …

Improved Left Ventricular Mass Quantification With Partial Voxel Interpolation – In-Vivo And Necropsy Validation Of A Novel Cardiac Mri Segmentation Algorithm, Noel C.F. Codella, Hae Yeoun Lee, David S. Fieno, Debbie W. Chen, Sandra M. Hurtado Rua, Minisha Kochar, John Paul Finn, Robert Judd, Parag Goyal, Jesse Schenendorf, Matthew D. Cham, Richard B. Devereux, Martin Prince, Yi Wang, Jonathan W. Weinsaft

Mathematics and Statistics Faculty Publications

Background—CMR typically quantifies LV mass (LVM) via manual planimetry (MP), but this approach is time consuming and does not account for partial voxel components - myocardium admixed with blood in a single voxel. Automated segmentation (AS) can account for partial voxels, but this has not been used for LVM quantification. This study used automated CMR segmentation to test the influence of partial voxels on quantification of LVM. Methods and Results—LVM was quantified by AS and MP in 126 consecutive patients and 10 laboratory animals undergoing CMR. AS yielded both partial voxel (AS_PV) and full voxel (AS_FV) …

Changes Across 25 Years Of Statistics In Medicine, Johanna S. Hardin

Pomona Faculty Publications and Research

[This piece is a series of interviews with giants in the field of medicine on their views of how statistics is changing medicine. I interviewed the editor of the New England Journal of Medicine, a preeminent doctor/researcher of lung cancer, the director of the LA County Department of Public Health, and a Harvard statistician who sits on the editorial board of the New England Journal of Medicine.]

Medicine, Statistics, And Education: The Inextricable Link, Katharine K. Brieger '11, Johanna S. Hardin

Pomona Faculty Publications and Research

No abstract provided.

Volume 04, Matt Szemborski, Phillip Van Ness, Sarah Croughwell, Sarah Mayfield, Alyssa Strackbein, Marley Kimmel, Stephanie Skipp, Jamie Yurasits, Katherine Taggart, Alex Leonhart, Kristen Rawls, Andrew Armes, Amanda Haymens, Allison Paqlowski, Erica May, Stephanie Lane, Luke Acree, Cassandra L. Wilson, Stephanie Pishock, Erica Hopson, K. Juston Osborne, Katheryn Grayson, Kyle Fowlkes, Jessica Cox, Kaity Byrum, John-Harwood Scott, Ashley Johnson, Samantha Hockman, Emily Staskiel, Nancy Macdonald, R. Kruger Bressin, Benjamin P. Bilodeau, Andrea Irby, Kristin Macquarrie, Sarah Bietsch, Elizabeth Bednar

Incite: The Journal of Undergraduate Scholarship

Please note that part of pages 92-95 are redacted, in the digital copy, due to a misprint of the original printed article.

Introduction from Dean Dr. Charles Ross

The Internal Other: Transculturation and Postcolonial Magical Realism in Rushdie’s Midnight’s Children by Matt Szemborski

Photography by Phillip Van Ness

Photography “Waterfall” by Sarah Croughwell

Romancing the Bite: Statistical Analysis of Young Adult Vampire Novels by Sarah Mayfield

Photography by Alyssa Strackbein

Photography by Marley Kimmel

Wine and Society in the Viceroyalty of Peru by Stephanie Skipp

Analysis of Claud Monet’s Impression, Sunrise by Jamie Yurasits

Exploring Meaning: The Lindisfarne Gospels by …

An Epidemiological Model Of Rift Valley Fever With Spatial Dynamics, Tianchan Niu, Holly D. Gaff, Yiannis E. Papelis, David M. Hartley

Biological Sciences Faculty Publications

As a category A agent in the Center for Disease Control bioterrorism list, Rift Valley fever (RVF) is considered a major threat to the United States (USA). Should the pathogen be intentionally or unintentionally introduced to the continental USA, there is tremendous potential for economic damages due to loss of livestock, trade restrictions, and subsequent food supply chain disruptions. We have incorporated the effects of space into a mathematical model of RVF in order to study the dynamics of the pathogen spread as affected by the movement of humans, livestock, and mosquitoes. The model accounts for the horizontal transmission of …

Extenics In Higher Dimensions, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

Prof. Dr. Florentin Smarandache, during his research period in the Summer of 2012 at

the Research Institute of Extenics and Innovation Methods, from Guangdong University of

Technology, in Guangzhou, China, has introduced the Linear and Non-Linear Attraction

Point Principle and the Network of Attraction Curves, he has generalized the 1D Extension

Distance and the 1D Dependent Function to 2D, 3D, and in general to n-D Spaces, and he

generalized Qiao-Xing Li’s and Xing-Sen Li’s definitions of the Location Value of a Point

and the Dependent Function of a Point on a Single Finite Interval from one dimension (1D) …

Short-Term Plasticity At The Schaffer Collateral: A New Model With Implications For Hippocampal Processing, Andrew Hamilton Toland

Dissertations and Theses

A new mathematical model of short-term synaptic plasticity (STP) at the Schaffer collateral is introduced. Like other models of STP, the new model relates short-term synaptic plasticity to an interaction between facilitative and depressive dynamic influences. Unlike previous models, the new model successfully simulates facilitative and depressive dynamics within the framework of the synaptic vesicle cycle. The novelty of the model lies in the description of a competitive interaction between calcium-sensitive proteins for binding sites on the vesicle release machinery. By attributing specific molecular causes to observable presynaptic effects, the new model of STP can predict the effects of specific …

Gm-Csf Production Allows The Identification Of Immunoprevalent Antigens Recognized By Human Cd4+ T Cells Following Smallpox Vaccination, Valeria A. Judkowski, Alcinette Bunying, Feng Ge, Jon R. Appel, Kingyee Law, Atima Sharma, Claudia Raja-Gabaglia, Patricia Norori, Radleigh Santos, Marc Giulianotti, Mark K. Slifka, Daniel C. Douek, Barney S. Graham, Clemencia Pinilla

Mathematics Faculty Articles

The threat of bioterrorism with smallpox and the broad use of vaccinia vectors for other vaccines have led to the resurgence in the study of vaccinia immunological memory. The importance of the role of CD4+ T cells in the control of vaccinia infection is well known. However, more CD8+ than CD4+ T cell epitopes recognized by human subjects immunized with vaccinia virus have been reported. This could be, in part, due to the fact that most of the studies that have identified human CD4+ specific protein-derived fragments or peptides have used IFN-γ production to evaluate vaccinia specific T cell responses. …

Utilizing Induced Voxel Correlation In Fmri Analysis, Daniel B. Rowe, Andrew S. Nencka

Mathematics, Statistics and Computer Science Faculty Research and Publications

No abstract provided.

Mathematical Methods For Biosensor Models, Qi Wang

Doctoral

A biosensor is defined as a compact analytical device incorporating a biological sensing element integrated within a physico-chemical transducer whose aim is to produce optical or electronic signals proportional to the concentration of an analyte in a sample. Biosensors offer enormous potential to detect a wide range of analytes in health care, the food industry, environmental monitoring, security and defence. The beneficial impact on society as a result of the availability of such systems is immense, therefore investigating any strategy that could reduce development times and costs and reveal alternative designs is of utmost importance. In particular, mathematical modelling and …

Noise, Delays, And Resonance In A Neural Network, Austin Quan

HMC Senior Theses

A stochastic-delay differential equation (SDDE) model of a small neural network with recurrent inhibition is presented and analyzed. The model exhibits unexpected transient behavior: oscillations that occur at the boundary of the basins of attraction when the system is bistable. These are known as delay-induced transitory oscillations (DITOs). This behavior is analyzed in the context of stochastic resonance, an unintuitive, though widely researched phenomenon in physical bistable systems where noise can play in constructive role in strengthening an input signal. A method for modeling the dynamics using a probabilistic three-state model is proposed, and supported with numerical evidence. The potential …