Matching Items (115)
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Description
Rabies is an infectious viral disease. It is usually fatal if a victim reaches the rabid stage, which starts after the appearance of disease symptoms. The disease virus attacks the central nervous system, and then it migrates from peripheral nerves to the spinal cord and brain. At the time when

Rabies is an infectious viral disease. It is usually fatal if a victim reaches the rabid stage, which starts after the appearance of disease symptoms. The disease virus attacks the central nervous system, and then it migrates from peripheral nerves to the spinal cord and brain. At the time when the rabies virus reaches the brain, the incubation period is over and the symptoms of clinical disease appear on the victim. From the brain, the virus travels via nerves to the salivary glands and saliva.

A mathematical model is developed for the spread of rabies in a spatially distributed fox population to model the spread of the rabies epizootic through middle Europe that occurred in the second half of the 20th century. The model considers both territorial and wandering rabid foxes and includes a latent period for the infection. Since the model assumes these two kinds of rabid foxes, it is a system of both partial differential and integral equations (with integration

over space and, occasionally, also over time). To study the spreading speeds of the rabies epidemic, the model is reduced to a scalar Volterra-Hammerstein integral equation, and space-time Laplace transform of the integral equation is used to derive implicit formulas for the spreading speed. The spreading speeds are discussed and implicit formulas are given for latent periods of fixed length, exponentially distributed length, Gamma distributed length, and log-normally distributed length. A number of analytic and numerical results are shown pertaining to the spreading speeds.

Further, a numerical algorithm is described for the simulation

of the spread of rabies in a spatially distributed fox population on a bounded domain with Dirichlet boundary conditions. I propose the following methods for the numerical approximation of solutions. The partial differential and integral equations are discretized in the space variable by central differences of second order and by

the composite trapezoidal rule. Next, the ordinary or delay differential equations that are obtained this way are discretized in time by explicit

continuous Runge-Kutta methods of fourth order for ordinary and delay differential systems. My particular interest

is in how the partition of rabid foxes into

territorial and diffusing rabid foxes influences

the spreading speed, a question that can be answered by purely analytic means only for small basic reproduction numbers. I will restrict the numerical analysis

to latent periods of fixed length and to exponentially

distributed latent periods.

The results of the numerical calculations

are compared for latent periods

of fixed and exponentially distributed length

and for various proportions of territorial

and wandering rabid foxes.

The speeds of spread observed in the

simulations are compared

to spreading speeds obtained by numerically solving the analytic formulas

and to observed speeds of epizootic frontlines

in the European rabies outbreak 1940 to 1980.
ContributorsAlanazi, Khalaf Matar (Author) / Thieme, Horst R. (Thesis advisor) / Jackiewicz, Zdzislaw (Committee member) / Baer, Steven (Committee member) / Gardner, Carl (Committee member) / Kuang, Yang (Committee member) / Smith, Hal (Committee member) / Arizona State University (Publisher)
Created2018
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Description
Anthropogenic land use has irrevocably transformed the natural systems on which humankind relies. Understanding where, why, and how social and economic processes drive globally-important land-use changes, from deforestation to urbanization, has advanced substantially. Illicit and clandestine activities--behavior that is intentionally secret because it breaks formal laws or violates informal norms--are

Anthropogenic land use has irrevocably transformed the natural systems on which humankind relies. Understanding where, why, and how social and economic processes drive globally-important land-use changes, from deforestation to urbanization, has advanced substantially. Illicit and clandestine activities--behavior that is intentionally secret because it breaks formal laws or violates informal norms--are poorly understood, however, despite the recognition of their significant role in land change. This dissertation fills this lacuna by studying illicit and clandestine activity and quantifying its influence on land-use patterns through examining informal urbanization in Mexico City and deforestation Central America. The first chapter introduces the topic, presenting a framework to examine illicit transactions in land systems. The second chapter uses data from interviews with actors involved with land development in Mexico City, demonstrating how economic and political payoffs explain the persistence of four types of informal urban expansion. The third chapter examines how electoral politics influence informal urban expansion and land titling in Mexico City using panel regression. Results show land title distribution increases just before elections, and more titles are extended to loyal voters of the dominant party in power. Urban expansion increases with electoral competition in local elections for borough chiefs and legislators. The fourth chapter tests and confirms the hypothesis that narcotrafficking has a causal effect on forest loss in Central America from 2001-2016 using two proxies of narcoactivity: drug seizures and events from media reports. The fifth chapter explores the spatial signature and pattern of informal urban development. It uses a typology of urban informality identified in chapter two to hypothesize and demonstrate distinct urban expansion patterns from satellite imagery. The sixth and final chapter summarizes the role of illicit and clandestine activity in shaping deforestation and urban expansion through illegal economies, electoral politics, and other informal transactions. Measures of illicit and clandestine activity should--and could--be incorporated into land change models to account for a wider range of relevant causes. This dissertation shines a new light on the previously hidden processes behind ever-easier to detect land-use patterns as earth observing satellites increase spatial and temporal resolution.
ContributorsTellman, Elizabeth (Author) / Turner II, Billie L (Thesis advisor) / Eakin, Hallie (Thesis advisor) / Janssen, Marco (Committee member) / Alba, Felipe de (Committee member) / Jain, Meha (Committee member) / Arizona State University (Publisher)
Created2019
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Description
Ideas from coding theory are employed to theoretically demonstrate the engineering of mutation-tolerant genes, genes that can sustain up to some arbitrarily chosen number of mutations and still express the originally intended protein. Attention is restricted to tolerating substitution mutations. Future advances in genomic engineering will make possible the ability

Ideas from coding theory are employed to theoretically demonstrate the engineering of mutation-tolerant genes, genes that can sustain up to some arbitrarily chosen number of mutations and still express the originally intended protein. Attention is restricted to tolerating substitution mutations. Future advances in genomic engineering will make possible the ability to synthesize entire genomes from scratch. This presents an opportunity to embed desirable capabilities like mutation-tolerance, which will be useful in preventing cell deaths in organisms intended for research or industrial applications in highly mutagenic environments. In the extreme case, mutation-tolerant genes (mutols) can make organisms resistant to retroviral infections.

An algebraic representation of the nucleotide bases is developed. This algebraic representation makes it possible to convert nucleotide sequences into algebraic sequences, apply mathematical ideas and convert results back into nucleotide terms. Using the algebra developed, a mapping is found from the naturally-occurring codons to an alternative set of codons which makes genes constructed from them mutation-tolerant, provided no more than one substitution mutation occurs per codon. The ideas discussed naturally extend to finding codons that can tolerate t arbitrarily chosen number of mutations per codon. Finally, random substitution events are simulated in both a wild-type green fluorescent protein (GFP) gene and its mutol variant and the amino acid sequence expressed from each post-mutation is compared with the amino acid sequence pre-mutation.

This work assumes the existence of synthetic protein-assembling entities that function like tRNAs but can read k nucleotides at a time, with k greater than or equal to 5. The realization of this assumption is presented as a challenge to the research community.
ContributorsAmpofo, Prince Kwame (Author) / Tian, Xiaojun (Thesis advisor) / Kiani, Samira (Committee member) / Kuang, Yang (Committee member) / Arizona State University (Publisher)
Created2019
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Description
Cancer is a major health problem in the world today and is expected to become an even larger one in the future. Although cancer therapy has improved for many cancers in the last several decades, there is much room for further improvement. Mathematical modeling has the advantage of being able

Cancer is a major health problem in the world today and is expected to become an even larger one in the future. Although cancer therapy has improved for many cancers in the last several decades, there is much room for further improvement. Mathematical modeling has the advantage of being able to test many theoretical therapies without having to perform clinical trials and experiments. Mathematical oncology will continue to be an important tool in the future regarding cancer therapies and management.

This dissertation is structured as a growing tumor. Chapters 2 and 3 consider spheroid models. These models are adept at describing 'early-time' tumors, before the tumor needs to co-opt blood vessels to continue sustained growth. I consider two partial differential equation (PDE) models for spheroid growth of glioblastoma. I compare these models to in vitro experimental data for glioblastoma tumor cell lines and other proposed models. Further, I investigate the conditions under which traveling wave solutions exist and confirm numerically.

As a tumor grows, it can no longer be approximated by a spheroid, and it becomes necessary to use in vivo data and more sophisticated modeling to model the growth and diffusion. In Chapter 4, I explore experimental data and computational models for describing growth and diffusion of glioblastoma in murine brains. I discuss not only how the data was obtained, but how the 3D brain geometry is created from Magnetic Resonance (MR) images. A 3D finite-difference code is used to model tumor growth using a basic reaction-diffusion equation. I formulate and test hypotheses as to why there are large differences between the final tumor sizes between the mice.

Once a tumor has reached a detectable size, it is diagnosed, and treatment begins. Chapter 5 considers modeling the treatment of prostate cancer. I consider a joint model with hormonal therapy as well as immunotherapy. I consider a timing study to determine whether changing the vaccine timing has any effect on the outcome of the patient. In addition, I perform basic analysis on the six-dimensional ordinary differential equation (ODE). I also consider the limiting case, and perform a full global analysis.
ContributorsRutter, Erica Marie (Author) / Kuang, Yang (Thesis advisor) / Kostelich, Eric J (Thesis advisor) / Frakes, David (Committee member) / Gardner, Carl (Committee member) / Jackiewicz, Zdzislaw (Committee member) / Arizona State University (Publisher)
Created2016
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Description
This dissertation examines the various factors and processes that have been proposed as explanations for the spread of agriculture in the west Mediterranean. The expansion of the Neolithic in the west Mediterranean (the Impresso-Cardial Neolithic) is characterized by a rapid spread of agricultural subsistence and material culture from the southern

This dissertation examines the various factors and processes that have been proposed as explanations for the spread of agriculture in the west Mediterranean. The expansion of the Neolithic in the west Mediterranean (the Impresso-Cardial Neolithic) is characterized by a rapid spread of agricultural subsistence and material culture from the southern portion of the Italian peninsula to the western coast of the Iberian peninsula. To address this unique case, four conceptual models of Neolithic spread have been proposed: the Wave of Advance, the Capillary Spread Model, the Maritime Pioneer Colonization Model and the Dual Model. An agent-based model, the Cardial Spread Model, was built to simulate each conceptual spread model in a spatially explicit environment for comparison with evidence from the archaeological record. Chronological information detailing the arrival of the Neolithic was used to create a map of the initial arrival of the Neolithic (a chronosurface) throughout the study area. The results of each conceptual spread model were then compared to the chronosurface in order to evaluate the relative performance of each conceptual model of spread. These experiments suggest that both the Dual and Maritime Pioneer Colonization models best fit the available chronological and spatial distribution of the Impresso-Cardial Neolithic.

For the purpose of informing agent movement and improving the fit of the conceptual spread models, a variety of paleoenvironmental maps were tested within the Cardial Spread Model. The outcome of these experiments suggests that topographic slope was an important factor in settlement location and that rivers were important vectors of transportation for early Neolithic migration. This research demonstrates the application of techniques rare to archaeological analysis, agent-based modeling and the inclusion of paleoenvironmental information, and provides a valuable tool that future researchers can utilize to further evaluate and fabricate new models of Neolithic expansion.
ContributorsBergin, Sean M (Author) / Barton, Michael (Thesis advisor) / Janssen, Marco (Committee member) / Coudart, Anick (Committee member) / Arizona State University (Publisher)
Created2016
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Description
In recent decades, marine ecologists have conducted extensive field work and experiments to understand the interactions between bacteria and bacteriophage (phage) in marine environments. This dissertation provides a detailed rigorous framework for gaining deeper insight into these interactions. Specific features of the dissertation include the design of a new deterministic

In recent decades, marine ecologists have conducted extensive field work and experiments to understand the interactions between bacteria and bacteriophage (phage) in marine environments. This dissertation provides a detailed rigorous framework for gaining deeper insight into these interactions. Specific features of the dissertation include the design of a new deterministic Lotka-Volterra model with n + 1 bacteria, n
+ 1 phage, with explicit nutrient, where the jth phage strain infects the first j bacterial strains, a perfectly nested infection network (NIN). This system is subject to trade-off conditions on the life-history traits of both bacteria and phage given in an earlier study Jover et al. (2013). Sufficient conditions are provided to show that a bacteria-phage community of arbitrary size with NIN can arise through the succession of permanent subcommunities, by the successive addition of one new population. Using uniform persistence theory, this entire community is shown to be permanent (uniformly persistent), meaning that all populations ultimately survive.

It is shown that a modified version of the original NIN Lotka-Volterra model with implicit nutrient considered by Jover et al. (2013) is permanent. A new one-to-one infection network (OIN) is also considered where each bacterium is infected by only one phage, and that phage infects only that bacterium. This model does not use the trade-offs on phage infection range, and bacterium resistance to phage. The OIN model is shown to be permanent, and using Lyapunov function theory, coupled with LaSalle’s Invariance Principle, the unique coexistence equilibrium associated with the NIN is globally asymptotically stable provided that the inter- and intra-specific bacterial competition coefficients are equal across all bacteria.

Finally, the OIN model is extended to a “Kill the Winner” (KtW) Lotka-Volterra model

of marine communities consisting of bacteria, phage, and zooplankton. The zooplankton

acts as a super bacteriophage, which infects all bacteria. This model is shown to be permanent.
ContributorsKorytowski, Daniel (Author) / Smith, Hal (Thesis advisor) / Gumel, Abba (Committee member) / Kuang, Yang (Committee member) / Gardner, Carl (Committee member) / Thieme, Horst (Committee member) / Arizona State University (Publisher)
Created2016
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Description
The closer integration of the world economy has yielded many positive benefits including the worldwide diffusion of innovative technologies and efficiency gains following the widening of international markets. However, closer integration also has negative consequences. Specifically, I focus on the ecology and economics of the spread of species

The closer integration of the world economy has yielded many positive benefits including the worldwide diffusion of innovative technologies and efficiency gains following the widening of international markets. However, closer integration also has negative consequences. Specifically, I focus on the ecology and economics of the spread of species and pathogens. I approach the problem using theoretical and applied models in ecology and economics. First, I use a multi-species theoretical network model to evaluate the ability of dispersal to maintain system-level biodiversity and productivity. I then extend this analysis to consider the effects of dispersal in a coupled social-ecological system where people derive benefits from species. Finally, I estimate an empirical model of the foot and mouth disease risks of trade. By combining outbreak and trade data I estimate the disease risks associated with the international trade in live animals while controlling for the biosecurity measures in place in importing countries and the presence of wild reservoirs. I find that the risks associated with the spread and dispersal of species may be positive or negative, but that this relationship depends on the ecological and economic components of the system and the interactions between them.
ContributorsShanafelt, David William (Author) / Perrings, Charles (Thesis advisor) / Fenichel, Eli (Committee member) / Richards, Timorthy (Committee member) / Janssen, Marco (Committee member) / Collins, James (Committee member) / Arizona State University (Publisher)
Created2016
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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

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
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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 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.
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
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Description
The coordination of group behavior in the social insects is representative of a broader phenomenon in nature, emergent biological complexity. In such systems, it is believed that large-scale patterns result from the interaction of relatively simple subunits. This dissertation involved the study of one such system: the social foraging of

The coordination of group behavior in the social insects is representative of a broader phenomenon in nature, emergent biological complexity. In such systems, it is believed that large-scale patterns result from the interaction of relatively simple subunits. This dissertation involved the study of one such system: the social foraging of the ant Temnothorax rugatulus. Physically tiny with small population sizes, these cavity-dwelling ants provide a good model system to explore the mechanisms and ultimate origins of collective behavior in insect societies. My studies showed that colonies robustly exploit sugar water. Given a choice between feeders unequal in quality, colonies allocate more foragers to the better feeder. If the feeders change in quality, colonies are able to reallocate their foragers to the new location of the better feeder. These qualities of flexibility and allocation could be explained by the nature of positive feedback (tandem run recruitment) that these ants use. By observing foraging colonies with paint-marked ants, I was able to determine the `rules' that individuals follow: foragers recruit more and give up less when they find a better food source. By altering the nutritional condition of colonies, I found that these rules are flexible - attuned to the colony state. In starved colonies, individual ants are more likely to explore and recruit to food sources than in well-fed colonies. Similar to honeybees, Temmnothorax foragers appear to modulate their exploitation and recruitment behavior in response to environmental and social cues. Finally, I explored the influence of ecology (resource distribution) on the foraging success of colonies. Larger colonies showed increased consistency and a greater rate of harvest than smaller colonies, but this advantage was mediated by the distribution of resources. While patchy or rare food sources exaggerated the relative success of large colonies, regularly (or easily found) distributions leveled the playing field for smaller colonies. Social foraging in ant societies can best be understood when we view the colony as a single organism and the phenotype - group size, communication, and individual behavior - as integrated components of a homeostatic unit.
ContributorsShaffer, Zachary (Author) / Pratt, Stephen C (Thesis advisor) / Hölldobler, Bert (Committee member) / Janssen, Marco (Committee member) / Fewell, Jennifer (Committee member) / Liebig, Juergen (Committee member) / Arizona State University (Publisher)
Created2014