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Ordinary Differential Equations and Applied Dynamics

University of Richmond

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From Big Farm To Big Pharma: A Differential Equations Model Of Antibiotic-Resistant Salmonella In Industrial Poultry Populations, Rilyn Mckallip Apr 2023

From Big Farm To Big Pharma: A Differential Equations Model Of Antibiotic-Resistant Salmonella In Industrial Poultry Populations, Rilyn Mckallip

Honors Theses

Antibiotics are used in poultry production as prophylaxis, curative treatment, and growth promotion. The first use is as prophylaxis, or prevention of common bacterial diseases. The crowded conditions in concentrated animal feeding operations necessitate management of infectious disease to ensure overall animal health and the profitability of such operations. In these farms, between 20,000 and 125,000 birds are raised in shed-like enclosures [3], with an average of less than one square foot of space per chicken [34]. Antibiotics are currently used in chicken farms to manage and prevent common bacterial diseases such as respiratory and digestive tract infections, as well …

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A Hybrid Agent-Based And Differential Equations Model For Simulating Antibiotic Resistance In A Hospital Ward, Lester Caudill, Barry Lawson Dec 2013

A Hybrid Agent-Based And Differential Equations Model For Simulating Antibiotic Resistance In A Hospital Ward, Lester Caudill, Barry Lawson

Department of Math & Statistics Faculty Publications

Serious infections due to antibiotic-resistant bacteria are pervasive, and of particular concern within hospital units due to frequent interaction among health-care workers and patients. Such nosocomial infections are difficult to eliminate because of inconsistent disinfection procedures and frequent interactions among infected persons, and because ill-chosen antibiotic treatment strategies can lead to a growth of resistant bacterial strains. Clinical studies to address these concerns have several issues, but chief among them are the effects on the patients involved. Realistic simulation models offer an attractive alternative. This paper presents a hybrid simulation model of antibiotic resistant infections in a hospital ward, combining …

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Reconstruction Of An Unknown Boundary Portion From Cauchy Data In N- Dimensions, Kurt Bryan, Lester Caudill Feb 2005

Reconstruction Of An Unknown Boundary Portion From Cauchy Data In N- Dimensions, Kurt Bryan, Lester Caudill

Department of Math & Statistics Faculty Publications

We consider the inverse problem of determining the shape of some inaccessible portion of the boundary of a region in n dimensions from Cauchy data for the heat equation on an accessible portion of the boundary. The inverse problem is quite ill-posed, and nonlinear. We develop a Newton-like algorithm for solving the problem, with a simple and efficient means for computing the required derivatives, develop methods for regularizing the process, and provide computational examples.

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Isospectral Sets For Fourth-Order Ordinary Differential Operators, Lester Caudill, Peter A. Perry, Albert W. Schueller Jul 1998

Isospectral Sets For Fourth-Order Ordinary Differential Operators, Lester Caudill, Peter A. Perry, Albert W. Schueller

Department of Math & Statistics Faculty Publications

Let L(p)u = D4u - (p1u’)’ + p2u be a fourth-order differential operator acting on L2[0; 1] with p ≡ (p1; p2) belonging to L2ℝ[0, 1] x L2ℝ[0, 1] and boundary conditions u(0) = u''(0) = u(1) = u''(1) = 0. We study the isospectral set of L(p) when L(p) has simple spectrum. In particular we show that for such p …

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