Applied Mathematics Commons^™

A Stochastic Epidemiological Model Of The Response Of American Chestnut Populations To Fungal Blight, Kelsey Lieberman, Rebecca Rouleau, Anita Davelos Baines, Martin Allen

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Mathematical Medicine: Modeling Disease And Treatment, Lisette Depillis

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Numerically Solving A System Of Pdes Modeling Chronic Wounds Treated With Oxygen Therapy, Stefan Stryker

Mahurin Honors College Capstone Experience/Thesis Projects

Chronic wounds such as diabetic foot ulcers are the leading cause of non-traumatic amputations in developed countries. For researchers to better understand the physiology of these wounds, a mathematical model describing oxygen levels at the wound site can be used to help predict healing responses. The model utilizes equations that are modified from work by Guffey (2015) that consists of four variables – oxygen, bacteria, neutrophils, and chemoattractant within a system of partial differential equations. Our research focuses on numerically solving these partial differential equations using a finite volume approach. This numerical solver will be important for future research in …

Uncovering Functional Relationships In Leukemia, Reginald Mcgee

Biology and Medicine Through Mathematics Conference

No abstract provided.

Modeling Hiv Dynamics Following 3bnc117 Antibody Infusion, Samantha Erwin

Biology and Medicine Through Mathematics Conference

No abstract provided.

On The Analysis Of The Sir Epidemic Model For Small Networks: An Application In Hospital Settings, Martin Lopez-Garcia

Biology and Medicine Through Mathematics Conference

No abstract provided.

Analyzing Sexual Transmission In The Spread Of The Zika Virus In Colombia, Victoria M. Kelley

Biology and Medicine Through Mathematics Conference

No abstract provided.

High Performance Computation Of Cardiac Models In Real-Time Using Webgl, Abouzar Kaboudian, Flavio H. Fenton

Biology and Medicine Through Mathematics Conference

No abstract provided.

Applying Fmri Complexity Analyses To The Single-Subject: A Case Study For Proposed Neurodiagnostics, Anca R. Radulescu, Emily R. Hannon

Biology and Medicine Through Mathematics Conference

No abstract provided.

An Interdisciplinary Approach To Computational Neurostimulation, Madison Guitard

Biology and Medicine Through Mathematics Conference

No abstract provided.

Evolution Of Influenza H3n2: A Random Walk In High Dimensions, James R. Moore

Biology and Medicine Through Mathematics Conference

No abstract provided.

A Model For A Parameter Related To Free Virus Production From Infected Target Cells, Evan C. Haskell

Biology and Medicine Through Mathematics Conference

No abstract provided.

The Kinetics Of Type I Interferons During Influenza Virus Infection, Margaret A. Myers

Biology and Medicine Through Mathematics Conference

No abstract provided.

Dynamics Of Fluorescent Imaging In Glob-Driven Breakup, Lan Zhong, Christiaan Ketelaar, Richard J. Braun, Carolyn G. Begley, Peter Ewen King-Smith

Biology and Medicine Through Mathematics Conference

No abstract provided.

Control Policies And Sensitivity Analysis In A Cutaneous Leishmaniasis Model: A Case Study In Cusco Region, Peru., Rocio M. Caja-Rivera, Ignacio Barradas

Biology and Medicine Through Mathematics Conference

No abstract provided.

Shear Driven Micro-Fluidic Pump For Cardiovascular Applications, Nihad E. Daidzic

Aviation Department Publications

A valveless shear-driven micro-fluidic pump design (SDMFP) for hemodynamic applications is presented in this work. One of the possible medical and biomedical applications is in-vivo hemodynamic (human blood circulation) support/assist. One or more SDMFPs can be inserted/implanted into vascular lumens in a form of a stent/duct in series and/or in parallel (bypass duct) to support blood circulation in-vivo. A comprehensive review of various micro-pump designs up to about mid 2000’s is given in [1,2]. Many of micropump designs considered are not suitable for in-vivo or even in-vitro medical/biomedical applications.

Operating principles, design, and SDMFP features are given in [3]. A …

Computational Fluid Dynamics In A Terminal Alveolated Bronchiole Duct With Expanding Walls: Proof-Of-Concept In Openfoam, Jeremy Myers

Theses and Dissertations

Mathematical Biology has found recent success applying Computational Fluid Dynamics (CFD) to model airflow in the human lung. Detailed modeling of flow patterns in the alveoli, where the oxygen-carbon dioxide gas exchange occurs, has provided data that is useful in treating illnesses and designing drug-delivery systems. Unfortunately, many CFD software packages have high licensing fees that are out of reach for independent researchers. This thesis uses three open-source software packages, Gmsh, OpenFOAM, and ParaView, to design a mesh, create a simulation, and visualize the results of an idealized terminal alveolar sac model. This model successfully demonstrates that OpenFOAM can be …

Mathematical Models Of The Inflammatory Response In The Lungs, Sarah B. Minucci

Theses and Dissertations

Inflammation in the lungs can occur for many reasons, from bacterial infections to stretch by mechanical ventilation. In this work we compare and contrast various mathematical models for lung injuries in the categories of acute infection, latent versus active infection, and particulate inhalation. We focus on systems of ordinary differential equations (ODEs), agent-based models (ABMs), and Boolean networks. Each type of model provides different insight into the immune response to damage in the lungs. This knowledge includes a better understanding of the complex dynamics of immune cells, proteins, and cytokines, recommendations for treatment with antibiotics, and a foundation for more …

Multi-Scale Cardiovascular Flow Analysis By An Integrated Meshless-Lumped Parameter Model, Leonardo A. Bueno, Eduardo A. Divo, Alain J. Kassab

Publications

A computational tool that integrates a Radial basis function (RBF)-based Meshless solver with a Lumped Parameter model (LPM) is developed to analyze the multi-scale and multi-physics interaction between the cardiovascular flow hemodynamics, the cardiac function, and the peripheral circulation. The Meshless solver is based on localized RBF collocations at scattered data points which allows for automation of the model generation via CAD integration. The time-accurate incompressible flow hemodynamics are addressed via a pressure-velocity correction scheme where the ensuing Poisson equations are accurately and efficiently solved at each time step by a Dual-Reciprocity Boundary Element method (DRBEM) formulation that takes advantage …

Modelling Random Antibody Adsorption And Immunoassay Activity, Dana Mackey, Eilis Kelly, Robert Nooney

Articles

One of the primary considerations in immunoassay design is optimizing the concentration of capture antibody in order to achieve maximal antigen binding and, subsequently, improved sensitivity and limit of detection. Many immunoassay technologies involve immobilization of the antibody to solid surfaces. Antibodies are large molecules in which the position and accessibility of the antigen-binding site depend on their orientation and packing density. In this paper we propose a simple mathematical model, based on the theory known as random sequential adsorption (RSA), in order to calculate how the concentration of correctly oriented antibodies (active site exposed for subsequent reactions) evolves during …

Simulating The Spread Of The Common Cold, R. Corban Harwood

Faculty Publications - Department of Mathematics

This modeling scenario guides students to simulate and investigate the spread of the common cold in a residence hall. An example floor plan is given, but the reader is encouraged to use a more relevant example. In groups, students run repeated simulations, collect data, derive a differential equation model, solve that equation, estimate parameter values by hand and through regression, visually evaluate the consistency of the model with their data, and present their results to the class.

Network Inference Driven Drug Discovery, Gergely Zahoránszky-Kőhalmi, Tudor I. Oprea, Cristian G. Bologa, Subramani Mani, Oleg Ursu

Biomedical Sciences ETDs

The application of rational drug design principles in the era of network-pharmacology requires the investigation of drug-target and target-target interactions in order to design new drugs. The presented research was aimed at developing novel computational methods that enable the efficient analysis of complex biomedical data and to promote the hypothesis generation in the context of translational research. The three chapters of the Dissertation relate to various segments of drug discovery and development process.

The first chapter introduces the integrated predictive drug discovery platform „SmartGraph”. The novel collaborative-filtering based algorithm „Target Based Recommender (TBR)” was developed in the framework of this …

Influence Of Preventive Measures To Eradicate The Spread Of The Zika Arbovirus, Pradyuta Padmanabhan, Padmanabhan Seshaiyer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Impact Of Devil Facial Tumor Disease On The Tasmanian Devil Age Structure, Christopher Bruno, Vashni Vasquez

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

The Kinetics Of Type 1 Interferons During Influenza Virus Infection, Margaret A. Myers

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Neural Networks: Using Biomarkers To Inform Diagnosis, Classification Of Disease And Approach To Therapy, Paula Grajdeanu

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Optimal Control Of Vaccination Rate In An Epidemiological Model Of Clostridium Difficile Transmission, Brittany Stephenson

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Mathematical Modeling Of Vaccine Noncompliance, Jordan A. Bauer

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Understanding Adipocyte Dynamics Through Mathematical Modeling, Katrina Johnson, Fred Adler

Annual Symposium on Biomathematics and Ecology Education and Research

No abstract provided.

Optimal Control Analysis Of Ebola Disease With Control Strategies Of Quarantine And Vaccination, Muhammad Dure Ahmad, Muhammad Usman, Adnan Khan, Mudassar Imran

Mathematics Faculty Publications

The 2014 Ebola epidemic is the largest in history, affecting multiple countries in West Africa. Some isolated cases were also observed in other regions of the world.