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Full-Text Articles in Physical Sciences and Mathematics
An Application Of Differential Mathematical Modeling Techniques To Study The Ongoing Rabies Epizootic In China, Christopher Turner
An Application Of Differential Mathematical Modeling Techniques To Study The Ongoing Rabies Epizootic In China, Christopher Turner
Electronic Theses and Dissertations
Rabies remains a global public health issue with a wide variety of neurological symptoms such as confusion, slight paralysis, hypersalivation, and hydrophobia. Rabies is usually fatal once symptoms appear. Many species are reservoirs for rabies, such as foxes, racoons, and wild dogs, which in turn can transmit the disease to humans, leading to complex transmission chains. There is a long latent period of rabies, between 1 to 3 months after infection, which further complicates control efforts. Mathematical modeling is a valuable tool in the study of infectious disease outbreaks and there have been many models applied to rabies outbreaks. However, …
A Practical Extension To The Ab/Ba Design, My T.A Nguyen
A Practical Extension To The Ab/Ba Design, My T.A Nguyen
Electronic Theses and Dissertations
In this work, we take a close look at a general extension to the traditional AB/BA
crossover design that is commonly used in clinical trials to determine the effectiveness
of new candidate drugs. While the traditional crossover design requires each patient
in the study to be measured on both treatment A and treatment B, we consider the
possibility of additional measurements being available on each patient. This produces
designs such as the AABB/BBAA design which has been used in previous studies.
A general test statistic will be derived to test for treatment effects as well as its
corresponding power function …
The Effect Of Initial Conditions On The Weather Research And Forecasting Model, Aaron D. Baker
The Effect Of Initial Conditions On The Weather Research And Forecasting Model, Aaron D. Baker
Electronic Theses and Dissertations
Modeling our atmosphere and determining forecasts using numerical methods has been a challenge since the early 20th Century. Most models use a complex dynamical system of equations that prove difficult to solve by hand as they are chaotic by nature. When computer systems became more widely adopted and available, approximating the solution of these equations, numerically, became easier as computational power increased. This advancement in computing has caused numerous weather models to be created and implemented across the world. However a challenge of approximating these solutions accurately still exists as each model have varying set of equations and variables to …
A Novel Mathematical Model Of The Trojan Y-Chromosome Strategy With Optimal Control, Christopher Turner
A Novel Mathematical Model Of The Trojan Y-Chromosome Strategy With Optimal Control, Christopher Turner
Electronic Theses and Dissertations
Invasive species are a prevalent problem all over the world. Controlling and eradicating an invasive species is an even more diffcult problem. The Trojan Y Chromosome (TYC) eradication strategy is one control method. This method alters the female to male sex ratio by introducing sex reversed males called supermales. These sex reversed males can only produce male progeny. Mathematical models of this strategy have shown that a population can be driven to extinction with a continuous supply of these sex reversed males. There are many different mathematical models of this strategy, but most have serious flaws, such as negative solutions …
Theoretical Analysis Of Nonlinear Differential Equations, Emily Jean Weymier
Theoretical Analysis Of Nonlinear Differential Equations, Emily Jean Weymier
Electronic Theses and Dissertations
Nonlinear differential equations arise as mathematical models of various phenomena. Here, various methods of solving and approximating linear and nonlinear differential equations are examined. Since analytical solutions to nonlinear differential equations are rare and difficult to determine, approximation methods have been developed. Initial and boundary value problems will be discussed. Several linear and nonlinear techniques to approximate or solve the linear or nonlinear problems are demonstrated. Regular and singular perturbation theory and Magnus expansions are our particular focus. Each section offers several examples to show how each technique is implemented along with the use of visuals to demonstrate the accuracy, …