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- Creators: Novak, Gail (Pianist)
ContributorsKierum, Caitlin (Contributor) / Novak, Gail (Pianist) (Performer) / Liang, Jack (Performer) / ASU Library. Music Library (Publisher)
Created2018-04-11
ContributorsLougheed, Julia (Performer) / Novak, Gail (Pianist) (Performer) / Bayer, Elizabeth Kennedy (Performer) / Clifton-Armenta, Tyler (Performer) / Park, Julie (Performer) / Javier de Alba, Francisco (Performer) / Vientos Dulces (Performer) / ASU Library. Music Library (Publisher)
Created2018-04-07
Description
Rabies disease remains enzootic among raccoons, skunks, foxes and bats in the United States. It is of primary concern for public-health agencies to control spatial spread of rabies in wildlife and its potential spillover infection of domestic animals and humans. Rabies is invariably fatal in wildlife if untreated, with a non-negligible incubation period. Understanding how this latency affects spatial spread of rabies in wildlife is the concern of chapter 2 and 3. Chapter 1 deals with the background of mathematical models for rabies and lists main objectives. In chapter 2, a reaction-diffusion susceptible-exposed-infected (SEI) model and a delayed diffusive susceptible-infected (SI) model are constructed to describe the same epidemic process -- rabies spread in foxes. For the delayed diffusive model a non-local infection term with delay is resulted from modeling the dispersal during incubation stage. Comparison is made regarding minimum traveling wave speeds of the two models, which are verified using numerical experiments. In chapter 3, starting with two Kermack and McKendrick's models where infectivity, death rate and diffusion rate of infected individuals can depend on the age of infection, the asymptotic speed of spread $c^\ast$ for the cumulated force of infection can be analyzed. For the special case of fixed incubation period, the asymptotic speed of spread is governed by the same integral equation for both models. Although explicit solutions for $c^\ast$ are difficult to obtain, assuming that diffusion coefficient of incubating animals is small, $c^\ast$ can be estimated in terms of model parameter values. Chapter 4 considers the implementation of realistic landscape in simulation of rabies spread in skunks and bats in northeast Texas. The Finite Element Method (FEM) is adopted because the irregular shapes of realistic landscape naturally lead to unstructured grids in the spatial domain. This implementation leads to a more accurate description of skunk rabies cases distributions.
ContributorsLiu, Hao (Author) / Kuang, Yang (Thesis advisor) / Jackiewicz, Zdzislaw (Committee member) / Lanchier, Nicolas (Committee member) / Smith, Hal (Committee member) / Thieme, Horst (Committee member) / Arizona State University (Publisher)
Created2013
Description
In complex consumer-resource type systems, where diverse individuals are interconnected and interdependent, one can often anticipate what has become known as the tragedy of the commons, i.e., a situation, when overly efficient consumers exhaust the common resource, causing collapse of the entire population. In this dissertation I use mathematical modeling to explore different variations on the consumer-resource type systems, identifying some possible transitional regimes that can precede the tragedy of the commons. I then reformulate it as a game of a multi-player prisoner's dilemma and study two possible approaches for preventing it, namely direct modification of players' payoffs through punishment/reward and modification of the environment in which the interactions occur. I also investigate the questions of whether the strategy of resource allocation for reproduction or competition would yield higher fitness in an evolving consumer-resource type system and demonstrate that the direction in which the system will evolve will depend not only on the state of the environment but largely on the initial composition of the population. I then apply the developed framework to modeling cancer as an evolving ecological system and draw conclusions about some alternative approaches to cancer treatment.
ContributorsKareva, Irina (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Collins, James (Committee member) / Nagy, John (Committee member) / Smith, Hal (Committee member) / Arizona State University (Publisher)
Created2012
Description
Bacteriophage (phage) are viruses that infect bacteria. Typical laboratory experiments show that in a chemostat containing phage and susceptible bacteria species, a mutant bacteria species will evolve. This mutant species is usually resistant to the phage infection and less competitive compared to the susceptible bacteria species. In some experiments, both susceptible and resistant bacteria species, as well as phage, can coexist at an equilibrium for hundreds of hours. The current research is inspired by these observations, and the goal is to establish a mathematical model and explore sufficient and necessary conditions for the coexistence. In this dissertation a model with infinite distributed delay terms based on some existing work is established. A rigorous analysis of the well-posedness of this model is provided, and it is proved that the susceptible bacteria persist. To study the persistence of phage species, a "Phage Reproduction Number" (PRN) is defined. The mathematical analysis shows phage persist if PRN > 1 and vanish if PRN < 1. A sufficient condition and a necessary condition for persistence of resistant bacteria are given. The persistence of the phage is essential for the persistence of resistant bacteria. Also, the resistant bacteria persist if its fitness is the same as the susceptible bacteria and if PRN > 1. A special case of the general model leads to a system of ordinary differential equations, for which numerical simulation results are presented.
ContributorsHan, Zhun (Author) / Smith, Hal (Thesis advisor) / Armbruster, Dieter (Committee member) / Kawski, Matthias (Committee member) / Kuang, Yang (Committee member) / Thieme, Horst (Committee member) / Arizona State University (Publisher)
Created2012
ContributorsCoffey, Brennan (Performer) / Novak, Gail (Pianist) (Performer) / ASU Library. Music Library (Publisher)
Created2021-04-26
ContributorsHolly, Sean (Performer) / Wright, Aaron (Performer) / Novak, Gail (Pianist) (Performer) / ASU Library. Music Library (Publisher)
Created2021-04-29
Description
Serge Galams voting systems and public debate models are used to model voting behaviors of two competing opinions in democratic societies. Galam assumes that individuals in the population are independently in favor of one opinion with a fixed probability p, making the initial number of that type of opinion a binomial random variable. This analysis revisits Galams models from the point of view of the hypergeometric random variable by assuming the initial number of individuals in favor of an opinion is a fixed deterministic number. This assumption is more realistic, especially when analyzing small populations. Evolution of the models is based on majority rules, with a bias introduced when there is a tie. For the hier- archical voting system model, in order to derive the probability that opinion +1 would win, the analysis was done by reversing time and assuming that an individual in favor of opinion +1 wins. Then, working backwards we counted the number of configurations at the next lowest level that could induce each possible configuration at the level above, and continued this process until reaching the bottom level, i.e., the initial population. Using this method, we were able to derive an explicit formula for the probability that an individual in favor of opinion +1 wins given any initial count of that opinion, for any group size greater than or equal to three. For the public debate model, we counted the total number of individuals in favor of opinion +1 at each time step and used this variable to define a random walk. Then, we used first-step analysis to derive an explicit formula for the probability that an individual in favor of opinion +1 wins given any initial count of that opinion for group sizes of three. The spatial public debate model evolves based on the proportional rule. For the spatial model, the most natural graphical representation to construct the process results in a model that is not mathematically tractable. Thus, we defined a different graphical representation that is mathematically equivalent to the first graphical representation, but in this model it is possible to define a dual process that is mathematically tractable. Using this graphical representation we prove clustering in 1D and 2D and coexistence in higher dimensions following the same approach as for the voter model interacting particle system.
ContributorsTaylor, Nicole Robyn (Co-author) / Lanchier, Nicolas (Co-author, Thesis director) / Smith, Hal (Committee member) / Hurlbert, Glenn (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2013-05
ContributorsBreeden, Katherine (Performer) / German, Lindsey (Performer) / Novak, Gail (Pianist) (Performer) / ASU Library. Music Library (Publisher)
Created2018-04-13
Description
ABSTRACT Many musicians, both amateur and professional alike, are continuously seeking to expand and explore their performance literature and repertory. Introducing new works into the standard repertory is an exciting endeavor for any active musician. Establishing connections, commissioning new works, and collaborating on performances can all work together toward the acceptance and success of a composer's music within an instrument community. For the flute, one such composer is Daniel Dorff (b. 1956). Dorff, a Philadelphia-based composer, has written for symphony orchestra, clarinet, contrabassoon, and others; however, his award-winning works for flute and piccolo are earning him much recognition. He has written works for such illustrious flutists as Mimi Stillman, Walfrid Kujala, and Gary Schocker; his flute works have been recorded by Laurel Zucker, Pamela Youngblood and Lois Bliss Herbine; and his pieces have been performed and premiered at each of the National Flute Association Conventions from 2004 to 2009. Despite this success, little has been written about Dorff's life, compositional style, and contributions to the flute repertory. In order to further promote the flute works of Daniel Dorff, the primary focus of this study is the creation of a compact disc recording of Dorff's most prominent works for flute: April Whirlwind, 9 Walks Down 7th Avenue, both for flute and piano, and Nocturne Caprice for solo flute. In support of this recording, the study also provides biographical information regarding Daniel Dorff, discusses his compositional methods and ideology, and presents background information, description, and performance notes for each piece. Interviews with Daniel Dorff regarding biographical and compositional details serve as the primary source for this document. Suggestions for the performance of the three flute works were gathered through interviews with prominent flutists who have studied and performed Dorff's pieces. Additional performance suggestions for Nocturne Caprice were gathered through a coaching session between the author and the composer. This project is meant to promote the flute works of Daniel Dorff and to help establish their role in the standard flute repertory.
ContributorsRich, Angela Marie (Contributor) / Novak, Gail (Pianist) (Performer) / Buck, Elizabeth Y (Thesis advisor) / Hill, Gary W. (Committee member) / Holbrook, Amy (Committee member) / Schuring, Martin (Committee member) / Arizona State University (Publisher)
Created2010