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Ordinary Differential Equations and Applied Dynamics Commons™
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Articles 1 - 10 of 10
Full-Text Articles in Ordinary Differential Equations and Applied Dynamics
A Physiologically-Based Pharmacokinetic Model For Vancomycin, Rebekah White
A Physiologically-Based Pharmacokinetic Model For Vancomycin, Rebekah White
Undergraduate Honors Theses
Vancomycin is an antibiotic used for the treatment of systemic infections. It is given
intravenously usually every twelve or twenty-four hours. This particular drug has a
medium level of boundedness, with approximately fty percent of the drug being free
and thus physiologically eective. A physiologically-based pharmacokinetic (PBPK)
model was used to better understand the absorption, distribution, and elimination of
the drug. Using optimal parameters, the model could be used in the future to test
how various factors, such as BMI or excretion levels, might aect the concentration
of the antibiotic.
Numerical Solutions Of Generalized Burgers' Equations For Some Incompressible Non-Newtonian Fluids, Yupeng Shu
Numerical Solutions Of Generalized Burgers' Equations For Some Incompressible Non-Newtonian Fluids, Yupeng Shu
University of New Orleans Theses and Dissertations
The author presents some generalized Burgers' equations for incompressible and isothermal flow of viscous non-Newtonian fluids based on the Cross model, the Carreau model, and the Power-Law model and some simple assumptions on the flows. The author numerically solves the traveling wave equations for the Cross model, the Carreau model, the Power-Law model by using industrial data. The author proves existence and uniqueness of solutions to the traveling wave equations of each of the three models. The author also provides numerical estimates of the shock thickness as well as maximum strain $\varepsilon_{11}$ for each of the fluids.
Comparison Of Two Parameter Estimation Techniques For Stochastic Models, Thomas C. Robacker
Comparison Of Two Parameter Estimation Techniques For Stochastic Models, Thomas C. Robacker
Electronic Theses and Dissertations
Parameter estimation techniques have been successfully and extensively applied to deterministic models based on ordinary differential equations but are in early development for stochastic models. In this thesis, we first investigate using parameter estimation techniques for a deterministic model to approximate parameters in a corresponding stochastic model. The basis behind this approach lies in the Kurtz limit theorem which implies that for large populations, the realizations of the stochastic model converge to the deterministic model. We show for two example models that this approach often fails to estimate parameters well when the population size is small. We then develop a …
Mathematical Notions Of Resilience: The Effects Of Disturbancei In One-Dimensional Nonlinear Systems, Stephen Ligtenberg
Mathematical Notions Of Resilience: The Effects Of Disturbancei In One-Dimensional Nonlinear Systems, Stephen Ligtenberg
Honors Projects
No abstract provided.
Mathematical Modeling And Optimal Control Of Alternative Pest Management For Alfalfa Agroecosystems, Cara Sulyok
Mathematical Modeling And Optimal Control Of Alternative Pest Management For Alfalfa Agroecosystems, Cara Sulyok
Mathematics Honors Papers
This project develops mathematical models and computer simulations for cost-effective and environmentally-safe strategies to minimize plant damage from pests with optimal biodiversity levels. The desired goals are to identify tradeoffs between costs, impacts, and outcomes using the enemies hypothesis and polyculture in farming. A mathematical model including twelve size- and time-dependent parameters was created using a system of non-linear differential equations. It was shown to accurately fit results from open-field experiments and thus predict outcomes for scenarios not covered by these experiments.
The focus is on the application to alfalfa agroecosystems where field experiments and data were conducted and provided …
Solutions Of A Logistic Equation On Varying Time Scales: A Quantitative And Qualitative Analysis, Alexandria Amity Amorim
Solutions Of A Logistic Equation On Varying Time Scales: A Quantitative And Qualitative Analysis, Alexandria Amity Amorim
Theses, Dissertations and Capstones
Time Scale Calculus, introduced by Dr. Stefan Hilger in 1988, combines the study of differential and difference equations into a single topic. We begin with an introduction of sets used in this field, time scales, and build up to the definition of the exponential function on a time scale. The main focus of this work is a study of the solutions of a particular logistic dynamic equation on varying time scales. We study both the analytical and graphical solutions of this equation. Analytical solutions are worked out using theorems from Time Scale Calculus, including properties of the exponential function. Graphical …
A Mathematical Model Of The Effect Of Aspirin On Blood Clotting, Breeana J. Johng
A Mathematical Model Of The Effect Of Aspirin On Blood Clotting, Breeana J. Johng
Scripps Senior Theses
In this paper, we provide a mathematical model of the effect of aspirin on blood clotting. The model tracks the enzyme prostaglandin H synthase and an important blood clotting factor, thromboxane A2, in the form of thromboxane B2. Through model analysis, we determine conditions under which the reactions of prostaglandin H synthase are self-sustaining. Lastly, through numerical simulations, we demonstrate that the model accurately captures the steady-state chemical concentrations of interest in blood, both with and without aspirin treatment.
An Applied Mathematics Approach To Modeling Inflammation: Hematopoietic Bone Marrow Stem Cells, Systemic Estrogen And Wound Healing And Gas Exchange In The Lungs And Body, Racheal L. Cooper
An Applied Mathematics Approach To Modeling Inflammation: Hematopoietic Bone Marrow Stem Cells, Systemic Estrogen And Wound Healing And Gas Exchange In The Lungs And Body, Racheal L. Cooper
Theses and Dissertations
Mathematical models apply to a multitude physiological processes and are used to make predictions and analyze outcomes of these processes. Specifically, in the medical field, a mathematical model uses a set of initial conditions that represents a physiological state as input and a set of parameter values are used to describe the interaction between variables being modeled. These models are used to analyze possible outcomes, and assist physicians in choosing the most appropriate treatment options for a particular situation. We aim to use mathematical modeling to analyze the dynamics of processes involved in the inflammatory process.
First, we create a …
A Survey Of Mathematical Models Of Dengue Fever, Iurii Bakach
A Survey Of Mathematical Models Of Dengue Fever, Iurii Bakach
Electronic Theses and Dissertations
In this paper, we compare and contrast five models of Dengue fever. We evaluate each model using different scenarios and identify the strenghts and wecknesses of each of the model
A Comparison Of Obesity Interventions Using Energy Balance Models, Marcella Torres
A Comparison Of Obesity Interventions Using Energy Balance Models, Marcella Torres
Theses and Dissertations
An energy balance model of human metabolism developed by Hall et al. is extended to compare body composition outcomes among standard and proposed obesity interventions. Standard interventions include a drastic diet or a drastic diet with endurance training. Outcomes for these interventions are typically poor in clinical studies. Proposed interventions include a gradual diet and the addition of resistance training to preserve lean mass and metabolic rate. We see that resistance training, regardless of dietary strategy, achieves these goals. Finally, we observe that the optimal obesity intervention for continued maintenance of a healthy body composition following a diet includes a …