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Diseases have been part of human life for generations and evolve within the population, sometimes dying out while other times becoming endemic or the cause of recurrent outbreaks. The long term influence of a disease stems from different dynamics within or between pathogen-host, that have been analyzed and studied by many researchers using mathematical models. Co-infection with different pathogens is common, yet little is known about how infection with one pathogen affects the host's immunological response to another. Moreover, no work has been found in the literature that considers the variability of the host immune health or that examines a disease at the population level and its corresponding interconnectedness with the host immune system. Knowing that the spread of the disease in the population starts at the individual level, this thesis explores how variability in immune system response within an endemic environment affects an individual's vulnerability, and how prone it is to co-infections. Immunology-based models of Malaria and Tuberculosis (TB) are constructed by extending and modifying existing mathematical models in the literature. The two are then combined to give a single nine-variable model of co-infection with Malaria and TB. Because these models are difficult to gain any insight analytically due to the large number of parameters, a phenomenological model of co-infection is proposed with subsystems corresponding to the individual immunology-based model of a single infection. Within this phenomenological model, the variability of the host immune health is also incorporated through three different pathogen response curves using nonlinear bounded Michaelis-Menten functions that describe the level or state of immune system (healthy, moderate and severely compromised). The immunology-based models of Malaria and TB give numerical results that agree with the biological observations. The Malaria--TB co-infection model gives reasonable results and these suggest that the order in which the two diseases are introduced have an impact on the behavior of both. The subsystems of the phenomenological models that correspond to a single infection (either of Malaria or TB) mimic much of the observed behavior of the immunology-based counterpart and can demonstrate different behavior depending on the chosen pathogen response curve. In addition, varying some of the parameters and initial conditions in the phenomenological model yields a range of topologically different mathematical behaviors, which suggests that this behavior may be able to be observed in the immunology-based models as well. The phenomenological models clearly replicate the qualitative behavior of primary and secondary infection as well as co-infection. The mathematical solutions of the models correspond to the fundamental states described by immunologists: virgin state, immune state and tolerance state. The phenomenological model of co-infection also demonstrates a range of parameter values and initial conditions in which the introduction of a second disease causes both diseases to grow without bound even though those same parameters and initial conditions did not yield unbounded growth in the corresponding subsystems. This results applies to all three states of the host immune system. In terms of the immunology-based system, this would suggest the following: there may be parameter values and initial conditions in which a person can clear Malaria or TB (separately) from their system but in which the presence of both can result in the person dying of one of the diseases. Finally, this thesis studies links between epidemiology (population level) and immunology in an effort to assess the impact of pathogen's spread within the population on the immune response of individuals. Models of Malaria and TB are proposed that incorporate the immune system of the host into a mathematical model of an epidemic at the population level.
ContributorsSoho, Edmé L (Author) / Wirkus, Stephen (Thesis advisor) / Castillo-Chavez, Carlos (Thesis advisor) / Chowell-Puente, Gerardo (Committee member) / Arizona State University (Publisher)
Created2011
Description
Over the past century in the southwestern United States human actions have altered hydrological processes that shape riparian ecosystems. One change, release of treated wastewater into waterways, has created perennial base flows and increased nutrient availability in ephemeral or intermittent channels. While there are benefits to utilizing treated wastewater for environmental flows, there are numerous unresolved ecohydrological issues regarding the efficacy of effluent to sustain groundwater-dependent riparian ecosystems. This research examined how nutrient-rich effluent, released into waterways with varying depths to groundwater, influences riparian plant community development. Statewide analysis of spatial and temporal patterns of effluent generation and release revealed that hydrogeomorphic setting significantly influences downstream riparian response. Approximately 70% of effluent released is into deep groundwater systems, which produced the lowest riparian development. A greenhouse study assessed how varying concentrations of nitrogen and phosphorus, emulating levels in effluent, influenced plant community response. With increasing nitrogen concentrations, vegetation emerging from riparian seed banks had greater biomass, reduced species richness, and greater abundance of nitrophilic species. The effluent-dominated Santa Cruz River in southern Arizona, with a shallow groundwater upper reach and deep groundwater lower reach, served as a study river while the San Pedro River provided a control. Analysis revealed that woody species richness and composition were similar between the two systems. Hydric pioneers (Populus fremontii, Salix gooddingii) were dominant at perennial sites on both rivers. Nitrophilic species (Conium maculatum, Polygonum lapathifolium) dominated herbaceous plant communities and plant heights were greatest in effluent-dominated reaches. Riparian vegetation declined with increasing downstream distance in the upper Santa Cruz, while patterns in the lower Santa Cruz were confounded by additional downstream agricultural input and a channelized floodplain. There were distinct longitudinal and lateral shifts toward more xeric species with increasing downstream distance and increasing lateral distance from the low-flow channel. Patterns in the upper and lower Santa Cruz reaches indicate that water availability drives riparian vegetation outcomes below treatment facilities. Ultimately, this research informs decision processes and increases adaptive capacity for water resources policy and management through the integration of ecological data in decision frameworks regarding the release of effluent for environmental flows.
ContributorsWhite, Margaret Susan (Author) / Stromberg, Juliet C. (Thesis advisor) / Fisher, Stuart G. (Committee member) / White, Dave (Committee member) / Holway, James (Committee member) / Wu, Jianguo (Committee member) / Arizona State University (Publisher)
Created2011
Description
Driven by concern over environmental, economic and social problems, small, place based communities are engaging in processes of transition to become more sustainable. These communities may be viewed as innovative front runners of a transition to a more sustainable society in general, each one, an experiment in social transformation. These experiments present learning opportunities to build robust theories of community transition and to create specific, actionable knowledge to improve, replicate, and accelerate transitions in real communities. Yet to date, there is very little empirical research into the community transition phenomenon. This thesis empirically develops an analytical framework and method for the purpose of researching community transition processes, the ultimate goal of which is to arrive at a practice of evidence based transitions. A multiple case study approach was used to investigate three community transitions while simultaneously developing the framework and method in an iterative fashion. The case studies selected were Ashton Hayes, a small English village, BedZED, an urban housing complex in London, and Forres, a small Scottish town. Each community was visited and data collected by interview and document analysis. The research design brings together elements of process tracing, transformative planning and governance, sustainability assessment, transition path analysis and transition management within a multiple case study envelope. While some preliminary insights are gained into community transitions based on the three cases the main contribution of this thesis is in the creation of the research framework and method. The general framework and method developed has potential for standardizing and synthesizing research of community transition processes leading to both theoretical and practical knowledge that allows sustainability transition to be approached with confidence and not just hope.
ContributorsForrest, Nigel (Author) / Wiek, Arnim (Thesis advisor) / Golub, Aaron (Thesis advisor) / Redman, Charles (Committee member) / White, Dave (Committee member) / Arizona State University (Publisher)
Created2011
Description
The sacred San Francisco Peaks in northern Arizona have been at the center of a series of land development controversies since the 1800s. Most recently, a controversy arose over a proposal by the ski area on the Peaks to use 100% reclaimed water to make artificial snow. The current state of the San Francisco Peaks controversy would benefit from a decision-making process that holds sustainability policy at its core. The first step towards a new sustainability-focused deliberative process regarding a complex issue like the San Francisco Peaks controversy requires understanding the issue's origins and the perspectives of the people involved in the issue. My thesis provides an historical analysis of the controversy and examines some of the laws and participatory mechanisms that have shaped the decision-making procedures and power structures from the 19th century to the early 21st century.
ContributorsMahoney, Maren (Author) / Hirt, Paul W. (Thesis advisor) / Tsosie, Rebecca (Committee member) / White, Dave (Committee member) / Arizona State University (Publisher)
Created2011
Description
Despite similar climate, ecosystem, and population size, the cities of Hermosillo, Mexico and Mesa, USA manage their water very differently. Mesa has a stable and resilient system organized around state and federal regulations. Hermosillo, after rapidly industrializing, has not been able to cope with climate change and long-term drought conditions. Water distribution statistics, stakeholders, policy structure, and government organization were combined in an organizational framework to compare the practices of the two cities. These inputs were weighed against the outcomes and the sustainability of each system. While Mesa is part of a massive metropolitan area, Hermosillo is still developing into a metropolitan center and does not have access to the same infrastructure and resources. In Hermosillo local needs are frequently discounted in favor of broad political goals.
ContributorsMoe, Rud Lamb (Author) / Chhetri, Netra (Thesis director) / White, Dave (Committee member) / Robles-Morua, Agustin (Committee member) / Barrett, The Honors College (Contributor) / School of Earth and Space Exploration (Contributor) / School of Sustainability (Contributor) / School of Geographical Sciences and Urban Planning (Contributor)
Created2013-05
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
Solution methods for certain linear and nonlinear evolution equations are presented in this dissertation. Emphasis is placed mainly on the analytical treatment of nonautonomous differential equations, which are challenging to solve despite the existent numerical and symbolic computational software programs available. Ideas from the transformation theory are adopted allowing one to solve the problems under consideration from a non-traditional perspective. First, the Cauchy initial value problem is considered for a class of nonautonomous and inhomogeneous linear diffusion-type equation on the entire real line. Explicit transformations are used to reduce the equations under study to their corresponding standard forms emphasizing on natural relations with certain Riccati(and/or Ermakov)-type systems. These relations give solvability results for the Cauchy problem of the parabolic equation considered. The superposition principle allows to solve formally this problem from an unconventional point of view. An eigenfunction expansion approach is also considered for this general evolution equation. Examples considered to corroborate the efficacy of the proposed solution methods include the Fokker-Planck equation, the Black-Scholes model and the one-factor Gaussian Hull-White model. The results obtained in the first part are used to solve the Cauchy initial value problem for certain inhomogeneous Burgers-type equation. The connection between linear (the Diffusion-type) and nonlinear (Burgers-type) parabolic equations is stress in order to establish a strong commutative relation. Traveling wave solutions of a nonautonomous Burgers equation are also investigated. Finally, it is constructed explicitly the minimum-uncertainty squeezed states for quantum harmonic oscillators. They are derived by the action of corresponding maximal kinematical invariance group on the standard ground state solution. It is shown that the product of the variances attains the required minimum value only at the instances that one variance is a minimum and the other is a maximum, when the squeezing of one of the variances occurs. Such explicit construction is possible due to the relation between the diffusion-type equation studied in the first part and the time-dependent Schrodinger equation. A modication of the radiation field operators for squeezed photons in a perfect cavity is also suggested with the help of a nonstandard solution of Heisenberg's equation of motion.
ContributorsVega-Guzmán, José Manuel, 1982- (Author) / Sulov, Sergei K (Thesis advisor) / Castillo-Chavez, Carlos (Thesis advisor) / Platte, Rodrigo (Committee member) / Chowell-Puente, Gerardo (Committee member) / Arizona State University (Publisher)
Created2013
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
In vertebrate outer retina, changes in the membrane potential of horizontal cells affect the calcium influx and glutamate release of cone photoreceptors via a negative feedback. This feedback has a number of important physiological consequences. One is called background-induced flicker enhancement (BIFE) in which the onset of dim background enhances the center flicker response of horizontal cells. The underlying mechanism for the feedback is still unclear but competing hypotheses have been proposed. One is the GABA hypothesis, which states that the feedback is mediated by gamma-aminobutyric acid (GABA), an inhibitory neurotransmitter released from horizontal cells. Another is the ephaptic hypothesis, which contends that the feedback is non-GABAergic and is achieved through the modulation of electrical potential in the intersynaptic cleft between cones and horizontal cells. In this study, a continuum spine model of the cone-horizontal cell synaptic circuitry is formulated. This model, a partial differential equation system, incorporates both the GABA and ephaptic feedback mechanisms. Simulation results, in comparison with experiments, indicate that the ephaptic mechanism is necessary in order for the model to capture the major spatial and temporal dynamics of the BIFE effect. In addition, simulations indicate that the GABA mechanism may play some minor modulation role.
ContributorsChang, Shaojie (Author) / Baer, Steven M. (Thesis advisor) / Gardner, Carl L (Thesis advisor) / Crook, Sharon M (Committee member) / Kuang, Yang (Committee member) / Ringhofer, Christian (Committee member) / Arizona State University (Publisher)
Created2012
Description
Mortality of 1918 influenza virus was high, partly due to bacteria coinfections. We characterize pandemic mortality in Arizona, which had high prevalence of tuberculosis. We applied regressions to over 35,000 data points to estimate the basic reproduction number and excess mortality. Age-specific mortality curves show elevated mortality for all age groups, especially the young, and senior sparing effects. The low value for reproduction number indicates that transmissibility was moderately low.
ContributorsJenner, Melinda Eva (Author) / Chowell-Puente, Gerardo (Thesis director) / Kostelich, Eric (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of Life Sciences (Contributor)
Created2015-05