Matching Items (48)
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
Olfaction is an important sensory modality for behavior since odors inform animals of the presence of food, potential mates, and predators. The fruit fly, Drosophila melanogaster, is a favorable model organism for the investigation of the biophysical mechanisms that contribute to olfaction because its olfactory system is anatomically similar to but simpler than that of vertebrates. In the Drosophila olfactory system, sensory transduction takes place in olfactory receptor neurons housed in the antennae and maxillary palps on the front of the head. The first stage of olfactory processing resides in the antennal lobe, where the structural unit is the glomerulus. There are at least three classes of neurons in the antennal lobe - excitatory projection neurons, excitatory local neurons, and inhibitory local neurons. The arborizations of the local neurons are confined to the antennal lobe, and output from the antennal lobe is carried by projection neurons to higher regions of the brain. Different views exist of how circuits of the Drosophila antennal lobe translate input from the olfactory receptor neurons into projection neuron output. We construct a conductance based neuronal network model of the Drosophila antennal lobe with the aim of understanding possible mechanisms within the antennal lobe that account for the variety of projection neuron activity observed in experimental data. We explore possible outputs obtained from olfactory receptor neuron input that mimic experimental recordings under different connectivity paradigms. First, we develop realistic minimal cell models for the excitatory local neurons, inhibitory local neurons, and projections neurons based on experimental data for Drosophila channel kinetics, and explore the firing characteristics and mathematical structure of these models. We then investigate possible interglomerular and intraglomerular connectivity patterns in the Drosophila antennal lobe, where olfactory receptor neuron input to the antennal lobe is modeled with Poisson spike trains, and synaptic connections within the antennal lobe are mediated by chemical synapses and gap junctions as described in the Drosophila antennal lobe literature. Our simulation results show that inhibitory local neurons spread inhibition among all glomeruli, where projection neuron responses are decreased relatively uniformly for connections of synaptic strengths that are homogeneous. Also, in the case of homogeneous excitatory synaptic connections, the excitatory local neuron network facilitates odor detection in the presence of weak stimuli. Excitatory local neurons can spread excitation from projection neurons that receive more input from olfactory receptor neurons to projection neurons that receive less input from olfactory receptor neurons. For the parameter values for the network models associated with these results, eLNs decrease the ability of the network to discriminate among single odors.
ContributorsLuli, Dori (Author) / Crook, Sharon (Thesis advisor) / Baer, Steven (Committee member) / Castillo-Chavez, Carlos (Committee member) / Smith, Brian (Committee member) / Arizona State University (Publisher)
Created2013
Description
A general continuum model for simulating the flow of ions in the salt baths that surround and fill excitable neurons is developed and presented. The ion densities and electric potential are computed using the drift-diffusion equations. In addition, a detailed model is given for handling the electrical dynamics on interior membrane boundaries, including a model for ion channels in the membranes that facilitate the transfer of ions in and out of cells. The model is applied to the triad synapse found in the outer plexiform layer of the retina in most species. Experimental evidence suggests the existence of a negative feedback pathway between horizontal cells and cone photoreceptors that modulates the flow of calcium ions into the synaptic terminals of cones. However, the underlying mechanism for this feedback is controversial and there are currently three competing hypotheses: the ephaptic hypothesis, the pH hypothesis and the GABA hypothesis. The goal of this work is to test some features of the ephaptic hypothesis using detailed simulations that employ rigorous numerical methods. The model is first applied in a simple rectangular geometry to demonstrate the effects of feedback for different extracellular gap widths. The model is then applied to a more complex and realistic geometry to demonstrate the existence of strictly electrical feedback, as predicted by the ephaptic hypothesis. Lastly, the effects of electrical feedback in regards to the behavior of the bipolar cell membrane potential is explored. Figures for the ion densities and electric potential are presented to verify key features of the model. The computed steady state IV curves for several cases are presented, which can be compared to experimental data. The results provide convincing evidence in favor of the ephaptic hypothesis since the existence of feedback that is strictly electrical in nature is shown, without any dependence on pH effects or chemical transmitters.
ContributorsJones, Jeremiah (Author) / Gardner, Carl (Committee member) / Baer, Steven (Committee member) / Crook, Sharon (Committee member) / Kostelich, Eric (Committee member) / Ringhofer, Christian (Committee member) / Arizona State University (Publisher)
Created2013
Description
Dendrites are the structures of a neuron specialized to receive input signals and to provide the substrate for the formation of synaptic contacts with other cells. The goal of this work is to study the activity-dependent mechanisms underlying dendritic growth in a single-cell model. For this, the individually identifiable adult motoneuron, MN5, in Drosophila melanogaster was used. This dissertation presents the following results. First, the natural variability of morphological parameters of the MN5 dendritic tree in control flies is not larger than 15%, making MN5 a suitable model for quantitative morphological analysis. Second, three-dimensional topological analyses reveals that different parts of the MN5 dendritic tree innervate spatially separated areas (termed "isoneuronal tiling"). Third, genetic manipulation of the MN5 excitability reveals that both increased and decreased activity lead to dendritic overgrowth; whereas decreased excitability promoted branch elongation, increased excitability enhanced dendritic branching. Next, testing the activity-regulated transcription factor AP-1 for its role in MN5 dendritic development reveals that neural activity enhanced AP-1 transcriptional activity, and that AP-1 expression lead to opposite dendrite fates depending on its expression timing during development. Whereas overexpression of AP-1 at early stages results in loss of dendrites, AP-1 overexpression after the expression of acetylcholine receptors and the formation of all primary dendrites in MN5 causes overgrowth. Fourth, MN5 has been used to examine dendritic development resulting from the expression of the human gene MeCP2, a transcriptional regulator involved in the neurodevelopmental disease Rett syndrome. Targeted expression of full-length human MeCP2 in MN5 causes impaired dendritic growth, showing for the first time the cellular consequences of MeCP2 expression in Drosophila neurons. This dendritic phenotype requires the methyl-binding domain of MeCP2 and the chromatin remodeling protein Osa. In summary, this work has fully established MN5 as a single-neuron model to study mechanisms underlying dendrite development, maintenance and degeneration, and to test the behavioral consequences resulting from dendritic growth misregulation. Furthermore, this thesis provides quantitative description of isoneuronal tiling of a central neuron, offers novel insight into activity- and AP-1 dependent developmental plasticity, and finally, it establishes Drosophila MN5 as a model to study some specific aspects of human diseases.
ContributorsVonhoff, Fernando Jaime (Author) / Duch, Carsten J (Thesis advisor) / Smith, Brian H. (Committee member) / Vu, Eric (Committee member) / Crook, Sharon (Committee member) / Arizona State University (Publisher)
Created2012
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
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
Description
Tremendous phenotypic variation exists across people with Turner syndrome (45,X). This variation likely stems from differential dosage of genes on the X chromosome. X-inactivation is the process whereby all X chromosomes in excess of one are silenced. However, about 15% of the genes on the silenced X chromosome escape this inactivation and are candidates for affecting phenotype in people with Turner syndrome. In this study we take an evolutionary approach to rank candidate genes that may contribute to phenotypic variation among people with Turner Syndrome. We incorporate analysis of patterns of DNA methylation from 46,XX and 45,X individuals, and estimates of variable X-inactivation status across 46,XX individuals, with patterns of gene expression conservation on the X chromosomes across five tissues and ten species. We find that genes that escape XCI are possible candidate genes for Turner syndrome phenotype, indicated by the constant levels of expression in escape genes and inactivated genes. Variation in these genes is expected to affect phenotype when dosage is altered from typical levels.
ContributorsSchaffer, Kara Nina (Author) / Wilson Sayres, Melissa (Thesis director) / Crook, Sharon (Committee member) / Narang, Pooja (Committee member) / School of Molecular Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2015-12
Description
Electrical stimulation can be used to activate peripheral nerve fibers to restore sensation to individuals with amputation and the technique is also being investigated as a means of treating a wide range of diseases. Longitudinal intrafascicular electrodes (LIFEs) are one of several types of electrodes that have been used to activate peripheral nerves. LIFEs can be used to activate small groups of fibers within a peripheral nerve fascicle, but the degree of their selectivity is uncertain. To investigate the effects of intrafascicular stimulation on nerve fiber activation, a mathematical, conductance-based model of an axon drawn from the literature was implemented and used to simulate the firing response of sensory nerve fibers in the presence of an applied monopolar electric field. Several axons were simulated to represent axons of different size, conductivity, spatial composition and location with respect to the electrode. Electric field profiles produced by pulses of different pulse widths and pulse amplitudes were created. Each fiber was placed within each resulting electric field and the firing threshold was determined. The effects of changes in pulse width, pulse amplitude, and distance on firing patterns were shown; all of these results were consistent with published experimental findings. The models showed lower firing threshold for smaller fibers than larger fibers and for fibers that were farther from the stimulating electrode than those that were closer. Firing threshold was also lower for stimuli of greater pulse width. Analysis of axon recruitment upon increases in pulse amplitude showed that the effects of fiber distance may be more pronounced than the effects of fiber size. This model can serve as a basis for further development to more accurately represent the effects of LIFEs and eventually may assist in the design of stimulation paradigms and waveforms to improve selectivity of axon activation when using LIFEs.
ContributorsSira, Alarmel (Author) / Abbas, James (Thesis director) / Crook, Sharon (Committee member) / Harrington Bioengineering Program (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
The sport of Ultimate, formerly known as Ultimate Frisbee™, spread around the world in the mid-seventies and was considered an alternative sport that embraced a more casual atmosphere than other traditional, competitive sports. Ultimate is now receiving national and international attention as a competitive sport, with broadcasts of games on networks such as ESPN. As it transitions into a mainstream sport while attempting to maintain its alternative roots, it is possible that there are contrasting opinions between those who want to bring it further into the mainstream and those who want to maintain as much as possible of the original, alternative culture. In this work, we surveyed members of the Ultimate community for their perspectives on the unique culture of Ultimate.
Because the Ultimate community considers itself to be progressive, despite its largely Caucasian makeup, one topic of exploration was the political landscape of the Ultimate community. A second unique aspect of ultimate is the system for enforcing rules used by the players on the field, known as the spirit of the game. This system replaces referees and creates an ethical dynamic both during play and within the community that is not found in other sports. The last major topic of study here is the self-perception of the players as athletes. Because Ultimate continues to maintain a reputation as an alternative sport, athletes may perceive themselves differently than in more established sports.
When asked if Ultimate players perceived the Ultimate community as accepting of athletes who are people of color (POC) or members of the lesbian, gay, bisexual, or transgender community (LGBT), the community reported being accepting of all minorities. However, acceptance of POC athletes was rated significantly lower than the acceptance of LGBT athletes. When asked about comradery, the respondents rated comradery higher within the Ultimate community than in other sports. When asked how impartial players were in Ultimate compared to other sports, players with more experience tended to report perceiving themselves as more impartial. All demographics reported being more impartial in Ultimate than in other athletics. When asked about the seriousness of Ultimate, those who had not played another sport considered Ultimate to be more serious than those who had played another sport. In addition, players with more years of Ultimate experience also considered it to be more serious than those with fewer years of experience. Overall, additional studies on Ultimate culture are needed in order to obtain more viewpoints, as there is a lack of research in this field for comparison.
Because the Ultimate community considers itself to be progressive, despite its largely Caucasian makeup, one topic of exploration was the political landscape of the Ultimate community. A second unique aspect of ultimate is the system for enforcing rules used by the players on the field, known as the spirit of the game. This system replaces referees and creates an ethical dynamic both during play and within the community that is not found in other sports. The last major topic of study here is the self-perception of the players as athletes. Because Ultimate continues to maintain a reputation as an alternative sport, athletes may perceive themselves differently than in more established sports.
When asked if Ultimate players perceived the Ultimate community as accepting of athletes who are people of color (POC) or members of the lesbian, gay, bisexual, or transgender community (LGBT), the community reported being accepting of all minorities. However, acceptance of POC athletes was rated significantly lower than the acceptance of LGBT athletes. When asked about comradery, the respondents rated comradery higher within the Ultimate community than in other sports. When asked how impartial players were in Ultimate compared to other sports, players with more experience tended to report perceiving themselves as more impartial. All demographics reported being more impartial in Ultimate than in other athletics. When asked about the seriousness of Ultimate, those who had not played another sport considered Ultimate to be more serious than those who had played another sport. In addition, players with more years of Ultimate experience also considered it to be more serious than those with fewer years of experience. Overall, additional studies on Ultimate culture are needed in order to obtain more viewpoints, as there is a lack of research in this field for comparison.
ContributorsRandall, Sean Edward (Co-author) / Furey, Michael (Co-author) / Mebane, Tyler (Co-author) / Crook, Sharon (Thesis director) / Arrowsmith, Ramon (Committee member) / Simeone, Michael (Committee member) / Mechanical and Aerospace Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05