Applied Mathematics Commons^™

Computational Analysis Of The Sir Mathematical Model For The Dengue Fever, Joseph Phillip Diaz

Theses and Dissertations

Dengue fever is a disease affecting people in more than 100 countries. Here we consider a host and vector model for the transmission of dengue fever. This SIR model consists of three compartments of susceptible, infective and removed for host (human) and two compartments of susceptible and infective for vector (dengue mosquitos). These five compartments yield five coupled nonlinear ordinary differential equations (ODEs). After non-dimensionalization, we have a system of three nonlinear ODEs. Reproductive number and two equilibrium points are calculated for various cases. Simulation is carried out for susceptible, infective and removed and the results are presented in graphical …

Partial Covariance Based Functional Connectivity Computation Using Ledoit-Wolf Covariance Regularization, Matthew R. Brier, Anish Mitra, John E. Mccarthy, Beau M. Ances, Abraham Z. Snyder

Mathematics Faculty Publications

Highlights •We use the well characterized matrix regularization technique described by Ledoit and Wolf to calculate high dimensional partial correlations in fMRI data. •Using this approach we demonstrate that partial correlations reveal RSN structure suggesting that RSNs are defined by widely and uniquely shared variance. •Partial correlation functional connectivity is sensitive to changes in brain state indicating that they contain functional information. Functional connectivity refers to shared signals among brain regions and is typically assessed in a task free state. Functional connectivity commonly is quantified between signal pairs using Pearson correlation. However, resting-state fMRI is a multivariate process exhibiting a …

Local And Distributed Pib Accumulation Associated With Development Of Preclinical Alzheimer's Disease, Matthew R. Brier, John E. Mccarthy, Tammie L.S. Benzinger, Ari Stern, Yi Su, Karl A. Friedrichsen, John C. Morris, Beau M. Ances, Andrei G. Vlassenko

Mathematics Faculty Publications

Amyloid-beta plaques are a hallmark of Alzheimer's disease (AD) that can be assessed by amyloid imaging (e.g., Pittsburgh B compound [PiB]) and summarized as a scalar value. Summary values may have clinical utility but are an average over many regions of interest, potentially obscuring important topography. This study investigates the longitudinal evolution of amyloid topographies in cognitively normal older adults who had normal (N = 131) or abnormal (N = 26) PiB scans at baseline. At 3 years follow-up, 16 participants with a previously normal PiB scan had conversion to PiB scans consistent with preclinical AD. We investigated the multivariate …

Comparison Of Fecal Microbiota In Children With Autism Spectrum Disorders And Neurotypical Siblings In The Simons Simplex Collection, Joshua S. Son, Ling J. Zheng, Leahana M. Rowehl, Ellen Li, Xinyu Tian, Yuanhao Zhang, Wei Zhu, Leighann Litcher-Kelly, Kenneth D. Gadow, Grace Gathungu, Charles E. Robertson, Diana Ir, Daniel N. Frank

Department of Applied Mathematics & Statistics Faculty Publications

In order to assess potential associations between autism spectrum disorder (ASD) phenotype, functional GI disorders and fecal microbiota, we recruited simplex families, which had only a single ASD proband and neurotypical (NT) siblings, through the Simons Simplex Community at the Interactive Autism Network (SSC@IAN). Fecal samples and metadata related to functional GI disorders and diet were collected from ASD probands and NT siblings of ASD probands (age 7–14). Functional gastrointestinal disorders (FGID) were assessed using the parent-completed ROME III questionnaire for pediatric FGIDs, and problem behaviors were assessed using the Child Behavior Check List (CBCL). Targeted quantitative polymerase chain reaction …

A Machine Learning Approach To Post-Market Surveillance Of Medical Devices, Jonathan Bates, Shu-Xia Li, Craig Parzynski, Ronald Coifman, Harlan Krumholz, Joseph Ross

Yale Day of Data

Post-market surveillance is a collection of processes and activities used by product manufacturers and regulators, such as the U.S. Food and Drug Administration (FDA) to monitor the safety and effectiveness of medical devices once they are available for use “on the market”. These activities are designed to generate information to identify poorly performing devices and other safety problems, accurately characterize real-world device performance and clinical outcomes, and facilitate the development of new devices, or new uses for existing devices. Typically, a device is monitored by comparing adverse events in the exposed population to a matched unexposed population. This research considers …

Collaboration And Health Care Diagnostics: An Agent Based Model Simulation, Sebastian Linde, George K. Thiruvathukal

George K. Thiruvathukal

This paper presents a simple ABM simulation that seeks to provide insight into the public health benefits that derive from greater collaboration among health care professionals. In particular, the paper compares the efficiency, delivery and timeliness of health care diagnostics under two contrasting paradigms–one in which collaboration is encouraged, and an- other where it is not. The preliminary results of this study suggest that while the effect of cooperation on aggregate public health depends on the patient search algorithm employed, its effect on overall efficiency and timeliness of health care diagnostics and treatment is significant and pos- itive. Since the …

Population Modeling For Resource Allocation And Antimicrobial Stewardship, Jason Bintz

Doctoral Dissertations

This dissertation contains two types of population models with applications in conservation biology and epidemiology. In particular, it considers models for resource allocation and antimicrobial stewardship.

In a population model with a parabolic differential equation and density dependent growth, we study the problem of allocating resources to maximize the net benefit in the conservation of a single species while the cost of the resource allocation is minimized. The net benefit is measured in terms of maximizing population abundance and the goal of maximizing abundance is divided between the goal of maximizing the overall abundance across space and time and the …

A Hierarchical Graph For Nucleotide Binding Domain 2, Samuel Kakraba

Electronic Theses and Dissertations

One of the most prevalent inherited diseases is cystic fibrosis. This disease is caused by a mutation in a membrane protein, the cystic fibrosis transmembrane conductance regulator (CFTR). CFTR is known to function as a chloride channel that regulates the viscosity of mucus that lines the ducts of a number of organs. Generally, most of the prevalent mutations of CFTR are located in one of two nucleotide binding domains, namely, the nucleotide binding domain 1 (NBD1). However, some mutations in nucleotide binding domain 2 (NBD2) can equally cause cystic fibrosis. In this work, a hierarchical graph is built for NBD2. …

The Relationship Among Math Anxiety, Mathematical Performance, And Math Education In Undergraduate Nursing Students, Joshua D. Beall, Troy Roebuck, Paul Penkalsky

Williams Honors College, Honors Research Projects

Although nurses spend up to 40% of their day calculating and administering medication doses, undergraduate nursing students often perform poorly on nursing math exams. The purpose of this study was (a) to examine the relationship among mathematical education, performance, and anxiety and (b) to compare the mathematical education, performance, and anxiety in sophomore and senior baccalaureate nursing students at a public university in the Midwest. This cross-sectional, descriptive study was guided by Bandura's self-efficacy theory. Math performance was measured with an 11-item math instrument, math education was measured with number of math courses, and math anxiety was measured with Fennema–Sherman …

Multistrain Infections In Metapopulations, Sydney Garmer, Rachel Lynn, Dan Rossi, Alex Capaldi

Alex Capaldi