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- All Subjects: Mathematics
- Creators: School of Mathematical and Statistical Sciences
- Creators: Kang, Yun
Description
Mathematical modeling of infectious diseases can help public health officials to make decisions related to the mitigation of epidemic outbreaks. However, over or under estimations of the morbidity of any infectious disease can be problematic. Therefore, public health officials can always make use of better models to study the potential implication of their decisions and strategies prior to their implementation. Previous work focuses on the mechanisms underlying the different epidemic waves observed in Mexico during the novel swine origin influenza H1N1 pandemic of 2009 and showed extensions of classical models in epidemiology by adding temporal variations in different parameters that are likely to change during the time course of an epidemic, such as, the influence of media, social distancing, school closures, and how vaccination policies may affect different aspects of the dynamics of an epidemic. This current work further examines the influence of different factors considering the randomness of events by adding stochastic processes to meta-population models. I present three different approaches to compare different stochastic methods by considering discrete and continuous time. For the continuous time stochastic modeling approach I consider the continuous-time Markov chain process using forward Kolmogorov equations, for the discrete time stochastic modeling I consider stochastic differential equations using Wiener's increment and Poisson point increments, and also I consider the discrete-time Markov chain process. These first two stochastic modeling approaches will be presented in a one city and two city epidemic models using, as a base, our deterministic model. The last one will be discussed briefly on a one city SIS and SIR-type model.
ContributorsCruz-Aponte, Maytee (Author) / Wirkus, Stephen A. (Thesis advisor) / Castillo-Chavez, Carlos (Thesis advisor) / Camacho, Erika T. (Committee member) / Kang, Yun (Committee member) / Arizona State University (Publisher)
Created2014
Description
There has been important progress in understanding ecological dynamics through the development of the theory of ecological stoichiometry. This fast growing theory provides new constraints and mechanisms that can be formulated into mathematical models. Stoichiometric models incorporate the effects of both food quantity and food quality into a single framework that produce rich dynamics. While the effects of nutrient deficiency on consumer growth are well understood, recent discoveries in ecological stoichiometry suggest that consumer dynamics are not only affected by insufficient food nutrient content (low phosphorus (P): carbon (C) ratio) but also by excess food nutrient content (high P:C). This phenomenon, known as the stoichiometric knife edge, in which animal growth is reduced not only by food with low P content but also by food with high P content, needs to be incorporated into mathematical models. Here we present Lotka-Volterra type models to investigate the growth response of Daphnia to algae of varying P:C ratios. Using a nonsmooth system of two ordinary differential equations (ODEs), we formulate the first model to incorporate the phenomenon of the stoichiometric knife edge. We then extend this stoichiometric model by mechanistically deriving and tracking free P in the environment. This resulting full knife edge model is a nonsmooth system of three ODEs. Bifurcation analysis and numerical simulations of the full model, that explicitly tracks phosphorus, leads to quantitatively different predictions than previous models that neglect to track free nutrients. The full model shows that the grazer population is sensitive to excess nutrient concentrations as a dynamical free nutrient pool induces extreme grazer population density changes. These modeling efforts provide insight on the effects of excess nutrient content on grazer dynamics and deepen our understanding of the effects of stoichiometry on the mechanisms governing population dynamics and the interactions between trophic levels.
ContributorsPeace, Angela (Author) / Kuang, Yang (Thesis advisor) / Elser, James J (Committee member) / Baer, Steven (Committee member) / Tang, Wenbo (Committee member) / Kang, Yun (Committee member) / Arizona State University (Publisher)
Created2014
Description
In 1968, phycologist M.R. Droop published his famous discovery on the functional relationship between growth rate and internal nutrient status of algae in chemostat culture. The simple notion that growth is directly dependent on intracellular nutrient concentration is useful for understanding the dynamics in many ecological systems. The cell quota in particular lends itself to ecological stoichiometry, which is a powerful framework for mathematical ecology. Three models are developed based on the cell quota principal in order to demonstrate its applications beyond chemostat culture.
First, a data-driven model is derived for neutral lipid synthesis in green microalgae with respect to nitrogen limitation. This model synthesizes several established frameworks in phycology and ecological stoichiometry. The model demonstrates how the cell quota is a useful abstraction for understanding the metabolic shift to neutral lipid production that is observed in certain oleaginous species.
Next a producer-grazer model is developed based on the cell quota model and nutrient recycling. The model incorporates a novel feedback loop to account for animal toxicity due to accumulation of nitrogen waste. The model exhibits rich, complex dynamics which leave several open mathematical questions.
Lastly, disease dynamics in vivo are in many ways analogous to those of an ecosystem, giving natural extensions of the cell quota concept to disease modeling. Prostate cancer can be modeled within this framework, with androgen the limiting nutrient and the prostate and cancer cells as competing species. Here the cell quota model provides a useful abstraction for the dependence of cellular proliferation and apoptosis on androgen and the androgen receptor. Androgen ablation therapy is often used for patients in biochemical recurrence or late-stage disease progression and is in general initially effective. However, for many patients the cancer eventually develops resistance months to years after treatment begins. Understanding how and predicting when hormone therapy facilitates evolution of resistant phenotypes has immediate implications for treatment. Cell quota models for prostate cancer can be useful tools for this purpose and motivate applications to other diseases.
First, a data-driven model is derived for neutral lipid synthesis in green microalgae with respect to nitrogen limitation. This model synthesizes several established frameworks in phycology and ecological stoichiometry. The model demonstrates how the cell quota is a useful abstraction for understanding the metabolic shift to neutral lipid production that is observed in certain oleaginous species.
Next a producer-grazer model is developed based on the cell quota model and nutrient recycling. The model incorporates a novel feedback loop to account for animal toxicity due to accumulation of nitrogen waste. The model exhibits rich, complex dynamics which leave several open mathematical questions.
Lastly, disease dynamics in vivo are in many ways analogous to those of an ecosystem, giving natural extensions of the cell quota concept to disease modeling. Prostate cancer can be modeled within this framework, with androgen the limiting nutrient and the prostate and cancer cells as competing species. Here the cell quota model provides a useful abstraction for the dependence of cellular proliferation and apoptosis on androgen and the androgen receptor. Androgen ablation therapy is often used for patients in biochemical recurrence or late-stage disease progression and is in general initially effective. However, for many patients the cancer eventually develops resistance months to years after treatment begins. Understanding how and predicting when hormone therapy facilitates evolution of resistant phenotypes has immediate implications for treatment. Cell quota models for prostate cancer can be useful tools for this purpose and motivate applications to other diseases.
ContributorsPacker, Aaron (Author) / Kuang, Yang (Thesis advisor) / Nagy, John (Committee member) / Smith, Hal (Committee member) / Kostelich, Eric (Committee member) / Kang, Yun (Committee member) / Arizona State University (Publisher)
Created2014
Description
Presented is a study on the chemotaxis reaction process and its relation with flow topology. The effect of coherent structures in turbulent flows is characterized by studying nutrient uptake and the advantage that is received from motile bacteria over other non-motile bacteria. Variability is found to be dependent on the initial location of scalar impurity and can be tied to Lagrangian coherent structures through recent advances in the identification of finite-time transport barriers. Advantage is relatively small for initial nutrient found within high stretching regions of the flow, and nutrient within elliptic structures provide the greatest advantage for motile species. How the flow field and the relevant flow topology lead to such a relation is analyzed.
ContributorsJones, Kimberly (Author) / Tang, Wenbo (Thesis advisor) / Kang, Yun (Committee member) / Jones, Donald (Committee member) / Arizona State University (Publisher)
Created2015
Description
A semi-implicit, fourth-order time-filtered leapfrog numerical scheme is investigated for accuracy and stability, and applied to several test cases, including one-dimensional advection and diffusion, the anelastic equations to simulate the Kelvin-Helmholtz instability, and the global shallow water spectral model to simulate the nonlinear evolution of twin tropical cyclones. The leapfrog scheme leads to computational modes in the solutions to highly nonlinear systems, and time-filters are often used to damp these modes. The proposed filter damps the computational modes without appreciably degrading the physical mode. Its performance in these metrics is superior to the second-order time-filtered leapfrog scheme developed by Robert and Asselin.
ContributorsBurke, Lee Matthew Moore (Author) / Moustaoui, Mohamed (Thesis director) / Kostelich, Eric (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Mechanical and Aerospace Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Honey bees (Apis mellifera) are responsible for pollinating nearly 80\% of all pollinated plants, meaning humans depend on honey bees to pollinate many staple crops. The success or failure of a colony is vital to global food production. There are various complex factors that can contribute to a colony's failure, including pesticides. Neonicotoids are a popular pesticide that have been used in recent times. In this study we concern ourselves with pesticides and its impact on honey bee colonies. Previous investigations that we draw significant inspiration from include Khoury et Al's \emph{A Quantitative Model of Honey Bee Colony Population Dynamics}, Henry et Al's \emph{A Common Pesticide Decreases Foraging Success and Survival in Honey Bees}, and Brown's \emph{ Mathematical Models of Honey Bee Populations: Rapid Population Decline}. In this project we extend a mathematical model to investigate the impact of pesticides on a honey bee colony, with birth rates and death rates being dependent on pesticides, and we see how these death rates influence the growth of a colony. Our studies have found an equilibrium point that depends on pesticides. Trace amounts of pesticide are detrimental as they not only affect death rates, but birth rates as well.
ContributorsSalinas, Armando (Author) / Vaz, Paul (Thesis director) / Jones, Donald (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / School of International Letters and Cultures (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
A Guide to Financial Mathematics is a comprehensive and easy-to-use study guide for students studying for the one of the first actuarial exams, Exam FM. While there are many resources available to students to study for these exams, this study is free to the students and offers an approach to the material similar to that of which is presented in class at ASU. The guide is available to students and professors in the new Actuarial Science degree program offered by ASU. There are twelve chapters, including financial calculator tips, detailed notes, examples, and practice exercises. Included at the end of the guide is a list of referenced material.
ContributorsDougher, Caroline Marie (Author) / Milovanovic, Jelena (Thesis director) / Boggess, May (Committee member) / Barrett, The Honors College (Contributor) / Department of Information Systems (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2015-05
Description
Covering subsequences with sets of permutations arises in many applications, including event-sequence testing. Given a set of subsequences to cover, one is often interested in knowing the fewest number of permutations required to cover each subsequence, and in finding an explicit construction of such a set of permutations that has size close to or equal to the minimum possible. The construction of such permutation coverings has proven to be computationally difficult. While many examples for permutations of small length have been found, and strong asymptotic behavior is known, there are few explicit constructions for permutations of intermediate lengths. Most of these are generated from scratch using greedy algorithms. We explore a different approach here. Starting with a set of permutations with the desired coverage properties, we compute local changes to individual permutations that retain the total coverage of the set. By choosing these local changes so as to make one permutation less "essential" in maintaining the coverage of the set, our method attempts to make a permutation completely non-essential, so it can be removed without sacrificing total coverage. We develop a post-optimization method to do this and present results on sequence covering arrays and other types of permutation covering problems demonstrating that it is surprisingly effective.
ContributorsMurray, Patrick Charles (Author) / Colbourn, Charles (Thesis director) / Czygrinow, Andrzej (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Department of Physics (Contributor)
Created2014-12
Description
Deconvolution of noisy data is an ill-posed problem, and requires some form of regularization to stabilize its solution. Tikhonov regularization is the most common method used, but it depends on the choice of a regularization parameter λ which must generally be estimated using one of several common methods. These methods can be computationally intensive, so I consider their behavior when only a portion of the sampled data is used. I show that the results of these methods converge as the sampling resolution increases, and use this to suggest a method of downsampling to estimate λ. I then present numerical results showing that this method can be feasible, and propose future avenues of inquiry.
ContributorsHansen, Jakob Kristian (Author) / Renaut, Rosemary (Thesis director) / Cochran, Douglas (Committee member) / Barrett, The Honors College (Contributor) / School of Music (Contributor) / Economics Program in CLAS (Contributor) / School of Mathematical and Statistical Sciences (Contributor)
Created2015-05
Description
The purpose of this thesis is to examine the events surrounding the creation of the oboe and its rapid spread throughout Europe during the mid to late seventeenth century. The first section describes similar instruments that existed for thousands of years before the invention of the oboe. The following sections examine reasons and methods for the oboe's invention, as well as possible causes of its migration from its starting place in France to other European countries, as well as many other places around the world. I conclude that the oboe was invented to suit the needs of composers in the court of Louis XIV, and that it was brought to other countries by French performers who left France for many reasons, including to escape from the authority of composer Jean-Baptiste Lully and in some cases to promote French culture in other countries.
ContributorsCook, Mary Katherine (Author) / Schuring, Martin (Thesis director) / Micklich, Albie (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of Music (Contributor)
Created2015-05