Matching Items (43)
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
Extraordinary medical advances have led to significant reductions in the burden of infectious diseases in humans. However, infectious diseases still account for more than 13 million annual deaths. This large burden is partly due to some pathogens having found suitable conditions to emerge and spread in denser and more connected host populations, and others having evolved to escape the pressures imposed by the rampant use of antimicrobials. It is then critical to improve our understanding of how diseases spread in these modern landscapes, characterized by new host population structures and socio-economic environments, as well as containment measures such as the deployment of drugs. Thus, the motivation of this dissertation is two-fold. First, we study, using both data-driven and modeling approaches, the the spread of infectious diseases in urban areas. As a case study, we use confirmed-cases data on sexually transmitted diseases (STDs) in the United States to assess the conduciveness of population size of urban areas and their socio-economic characteristics as predictors of STD incidence. We find that the scaling of STD incidence in cities is superlinear, and that the percent of African-Americans residing in cities largely determines these statistical patterns. Since disparities in access to health care are often exacerbated in urban areas, within this project we also develop two modeling frameworks to study the effect of health care disparities on epidemic outcomes. Discrepant results between the two approaches indicate that knowledge of the shape of the recovery period distribution, not just its mean and variance, is key for assessing the epidemiological impact of inequalities. The second project proposes to study, from a modeling perspective, the spread of drug resistance in human populations featuring vital dynamics, stochasticity and contact structure. We derive effective treatment regimes that minimize both the overall disease burden and the spread of resistance. Additionally, targeted treatment in structured host populations may lead to higher levels of drug resistance, and if drug-resistant strains are compensated, they can spread widely even when the wild-type strain is below its epidemic threshold.
ContributorsPatterson-Lomba, Oscar (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Towers, Sherry (Thesis advisor) / Chowell-Puente, Gerardo (Committee member) / Arizona State University (Publisher)
Created2014
Description
With the projected population growth, the need to produce higher agricultural yield to meet projected demand is hindered by water scarcity. Out of many the approaches that could be implemented to meet the water gap, intensification of agriculture through adoption of advanced agricultural irrigation techniques is the focus for this research. Current high water consumption by agricultural sector in Arizona is due to historical dominance in the state economy and established water rights. Efficiency gained in agricultural water use in Arizona has the most potential to reduce the overall water consumption. This research studies the agricultural sector and water management of several counties in Arizona (Maricopa, Pinal, and Yuma). Several research approaches are employed: modeling of agricultural technology adoption using replicator dynamics, interview with water managers and farmers, and Arizona water management law and history review. Using systems thinking, the components of the local farming environment are documented through socio-ecological system/robustness lenses. The replicator dynamics model is employed to evaluate possible conditions in which water efficient agricultural irrigation systems proliferate. The evaluation of conditions that promote the shift towards advanced irrigation technology is conducted through a combination of literature review, interview data, and model analysis. Systematic shift from the currently dominant flood irrigation toward a more water efficient irrigation technologies could be attributed to the followings: the increase in advanced irrigation technology yield efficiency; the reduction of advanced irrigation technology implementation and maintenance cost; the change in growing higher value crop; and the change in growing/harvesting time where there is less competition from other states. Insights learned will further the knowledge useful for this arid state's agricultural policy decision making that will both adhere to the water management goals and meet the projected food production and demand gap.
ContributorsBudiyanto, Yoshi (Author) / Muneepeerakul, Rachata (Thesis advisor) / Smith, Karen (Committee member) / Abbott, Joshua (Committee member) / Arizona State University (Publisher)
Created2014
Description
This dissertation consists of three substantive chapters. The first substantive chapter investigates the premature harvesting problem in fisheries. Traditionally, yield-per-recruit analysis has been used to both assess and address the premature harvesting of fish stocks. However, the fact that fish size often affects the unit price suggests that this approach may be inadequate. In this chapter, I first synthesize the conventional yield-per-recruit analysis, and then extend this conventional approach by incorporating a size-price function for a revenue-per-recruit analysis. An optimal control approach is then used to derive a general bioeconomic solution for the optimal harvesting of a short-lived single cohort. This approach prevents economically premature harvesting and provides an "optimal economic yield". By comparing the yield- and revenue-per-recruit management strategies with the bioeconomic management strategy, I am able to test the economic efficiency of the conventional yield-per-recruit approach. This is illustrated with a numerical study. It shows that a bioeconomic strategy can significantly improve economic welfare compared with the yield-per-recruit strategy, particularly in the face of high natural mortality. Nevertheless, I find that harvesting on a revenue-per-recruit basis improves management policy and can generate a rent that is close to that from bioeconomic analysis, in particular when the natural mortality is relatively low.
The second substantive chapter explores the conservation potential of a whale permit market under bounded economic uncertainty. Pro- and anti-whaling stakeholders are concerned about a recently proposed, "cap and trade" system for managing the global harvest of whales. Supporters argue that such an approach represents a novel solution to the current gridlock in international whale management. In addition to ethical objections, opponents worry that uncertainty about demand for whale-based products and the environmental benefits of conservation may make it difficult to predict the outcome of a whale share market. In this study, I use population and economic data for minke whales to examine the potential ecological consequences of the establishment of a whale permit market in Norway under bounded but significant economic uncertainty. A bioeconomic model is developed to evaluate the influence of economic uncertainties associated with pro- and anti- whaling demands on long-run steady state whale population size, harvest, and potential allocation. The results indicate that these economic uncertainties, in particular on the conservation demand side, play an important role in determining the steady state ecological outcome of a whale share market. A key finding is that while a whale share market has the potential to yield a wide range of allocations between conservation and whaling interests - outcomes in which conservationists effectively "buy out" the whaling industry seem most likely.
The third substantive chapter examines the sea lice externality between farmed fisheries and wild fisheries. A central issue in the debate over the effect of fish farming on the wild fisheries is the nature of sea lice population dynamics and the wild juvenile mortality rate induced by sea lice infection. This study develops a bioeconomic model that integrates sea lice population dynamics, fish population dynamics, aquaculture and wild capture salmon fisheries in an optimal control framework. It provides a tool to investigate sea lice control policy from the standpoint both of private aquaculture producers and wild fishery managers by considering the sea lice infection externality between farmed and wild fisheries. Numerical results suggest that the state trajectory paths may be quite different under different management regimes, but approach the same steady state. Although the difference in economic benefits is not significant in the particular case considered due to the low value of the wild fishery, I investigate the possibility of levying a tax on aquaculture production for correcting the sea lice externality generated by fish farms.
The second substantive chapter explores the conservation potential of a whale permit market under bounded economic uncertainty. Pro- and anti-whaling stakeholders are concerned about a recently proposed, "cap and trade" system for managing the global harvest of whales. Supporters argue that such an approach represents a novel solution to the current gridlock in international whale management. In addition to ethical objections, opponents worry that uncertainty about demand for whale-based products and the environmental benefits of conservation may make it difficult to predict the outcome of a whale share market. In this study, I use population and economic data for minke whales to examine the potential ecological consequences of the establishment of a whale permit market in Norway under bounded but significant economic uncertainty. A bioeconomic model is developed to evaluate the influence of economic uncertainties associated with pro- and anti- whaling demands on long-run steady state whale population size, harvest, and potential allocation. The results indicate that these economic uncertainties, in particular on the conservation demand side, play an important role in determining the steady state ecological outcome of a whale share market. A key finding is that while a whale share market has the potential to yield a wide range of allocations between conservation and whaling interests - outcomes in which conservationists effectively "buy out" the whaling industry seem most likely.
The third substantive chapter examines the sea lice externality between farmed fisheries and wild fisheries. A central issue in the debate over the effect of fish farming on the wild fisheries is the nature of sea lice population dynamics and the wild juvenile mortality rate induced by sea lice infection. This study develops a bioeconomic model that integrates sea lice population dynamics, fish population dynamics, aquaculture and wild capture salmon fisheries in an optimal control framework. It provides a tool to investigate sea lice control policy from the standpoint both of private aquaculture producers and wild fishery managers by considering the sea lice infection externality between farmed and wild fisheries. Numerical results suggest that the state trajectory paths may be quite different under different management regimes, but approach the same steady state. Although the difference in economic benefits is not significant in the particular case considered due to the low value of the wild fishery, I investigate the possibility of levying a tax on aquaculture production for correcting the sea lice externality generated by fish farms.
ContributorsHuang, Biao (Author) / Abbott, Joshua K (Thesis advisor) / Perrings, Charles (Thesis advisor) / Gerber, Leah R. (Committee member) / Muneepeerakul, Rachata (Committee member) / Schoon, Michael (Committee member) / Arizona State University (Publisher)
Created2014
Description
Sustainability requires developing the capacity to manage difficult tradeoffs to advance human livelihoods now and in the future. Decision-makers are recognizing the ecosystem services approach as a useful framework for evaluating tradeoffs associated with environmental change to advance decision-making towards holistic solutions. In this dissertation I conduct an ecosystem services assessment on the Yongding River Ecological Corridor in Beijing, China. I developed a `10-step approach' to evaluate multiple ecosystem services for public policy. I use the 10-step approach to evaluate five ecosystem services for management from the Yongding Corridor. The Beijing government created lakes and wetlands for five services (human benefits): (1) water storage (groundwater recharge), (2) local climate regulation (cooling), (3) water purification (water quality), (4) dust control (air quality), and (5) landscape aesthetics (leisure, recreation, and economic development).
The Yongding Corridor is meeting the final ecosystem service levels for landscape aesthetics, but the new ecosystems are falling short on meeting final ecosystem service levels for water storage, local climate regulation, water purification, and dust control. I used biophysical models (process-based and empirically-based), field data (biophysical and visitor surveys), and government datasets to create ecological production functions (i.e., regression models). I used the ecological production functions to evaluate how marginal changes in the ecosystems could impact final ecosystem service outcomes. I evaluate potential tradeoffs considering stakeholder needs to recommend synergistic actions for addressing priorities while reducing service shortfalls.
The Yongding Corridor is meeting the final ecosystem service levels for landscape aesthetics, but the new ecosystems are falling short on meeting final ecosystem service levels for water storage, local climate regulation, water purification, and dust control. I used biophysical models (process-based and empirically-based), field data (biophysical and visitor surveys), and government datasets to create ecological production functions (i.e., regression models). I used the ecological production functions to evaluate how marginal changes in the ecosystems could impact final ecosystem service outcomes. I evaluate potential tradeoffs considering stakeholder needs to recommend synergistic actions for addressing priorities while reducing service shortfalls.
ContributorsWong, Christina P (Author) / Kinzig, Ann P (Thesis advisor) / Lee, Kai N. (Committee member) / Muneepeerakul, Rachata (Committee member) / Ouyang, Zhiyun (Committee member) / Vivoni, Enrique (Committee member) / Arizona State University (Publisher)
Created2014
Description
Urban scaling analysis has introduced a new scientific paradigm to the study of cities. With it, the notions of size, heterogeneity and structure have taken a leading role. These notions are assumed to be behind the causes for why cities differ from one another, sometimes wildly. However, the mechanisms by which size, heterogeneity and structure shape the general statistical patterns that describe urban economic output are still unclear. Given the rapid rate of urbanization around the globe, we need precise and formal mathematical understandings of these matters. In this context, I perform in this dissertation probabilistic, distributional and computational explorations of (i) how the broadness, or narrowness, of the distribution of individual productivities within cities determines what and how we measure urban systemic output, (ii) how urban scaling may be expressed as a statistical statement when urban metrics display strong stochasticity, (iii) how the processes of aggregation constrain the variability of total urban output, and (iv) how the structure of urban skills diversification within cities induces a multiplicative process in the production of urban output.
ContributorsGómez-Liévano, Andrés (Author) / Lobo, Jose (Thesis advisor) / Muneepeerakul, Rachata (Thesis advisor) / Bettencourt, Luis M. A. (Committee member) / Chowell-Puente, Gerardo (Committee member) / Arizona State University (Publisher)
Created2014
Description
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
Yersinia enterocolitica is a major foodborne pathogen found worldwide that causes approximately 87,000 human cases and approximately 1,100 hospitalizations per year in the United States. Y. enterocolitica is a very unique pathogen with the domesticated pig acting as the main animal reservoir for pathogenic bio/serotypes, and as the primary source of human infection. Similar to other gastrointestinal infections, Yersinia enterocolitica is known to trigger autoimmune responses in humans. The most frequent complication associated with Y. enterocolitica is reactive arthritis - an aseptic, asymmetrical inflammation in the peripheral and axial joints, most frequently occurring as an autoimmune response in patients with the HLA-B27 histocompatability antigen. As a foodborne illness it may prove to be a reasonable explanation for some of the cases of arthritis observed in past populations that are considered to be of unknown etiology. The goal of this dissertation project was to study the relationship between the foodborne illness -Y. enterocolitica, and the incidence of arthritis in individuals with and without contact with the domesticated pig.
ContributorsBrown, Starletta (Author) / Hurtado, Ana M (Thesis advisor) / Chowell-Puente, Gerardo (Committee member) / Hill, Kim (Committee member) / Arizona State University (Publisher)
Created2015
Description
Perceptions of climate variability and change reflect local concerns and the actual impacts of climate phenomena on people's lives. Perceptions are the bases of people's decisions to act, and they determine what adaptive measures will be taken. But perceptions of climate may not always be aligned with scientific observations because they are influenced by socio-economic and ecological variables. To find sustainability solutions to climate-change challenges, researchers and policy makers need to understand people's perceptions so that they can account for likely responses. Being able to anticipate responses will increase decision-makers' capacities to create policies that support effective adaptation strategies. I analyzed Mexican maize farmers' perceptions of drought variability as a proxy for their perceptions of climate variability and change. I identified the factors that contribute to the perception of changing drought frequency among farmers in the states of Chiapas, Mexico, and Sinaloa. I conducted Chi-square tests and Logit regression analyses using data from a survey of 1092 maize-producing households in the three states. Results showed that indigenous identity, receipt of credits or loans, and maize-type planted were the variables that most strongly influenced perceptions of drought frequency. The results suggest that climate-adaptation policy will need to consider the social and institutional contexts of farmers' decision-making, as well as the agronomic options for smallholders in each state.
ContributorsRodríguez, Natalia (Author) / Eakin, Hallie (Thesis advisor) / Muneepeerakul, Rachata (Thesis advisor) / Manuel-Navarrete, David (Committee member) / Arizona State University (Publisher)
Created2015
Description
Background: While research has quantified the mortality burden of the 1957 H2N2 influenza pandemic in the United States, little is known about how the virus spread locally in Arizona, an area where the dry climate was promoted as reducing respiratory illness transmission yet tuberculosis prevalence was high.
Methods: Using archival death certificates from 1954 to 1961, this study quantified the age-specific seasonal patterns, excess-mortality rates, and transmissibility patterns of the 1957 pandemic in Maricopa County, Arizona. By applying cyclical Serfling linear regression models to weekly mortality rates, the excess-mortality rates due to respiratory and all-causes were estimated for each age group during the pandemic period. The reproduction number was quantified from weekly data using a simple growth rate method and generation intervals of 3 and 4 days. Local newspaper articles from The Arizona Republic were analyzed from 1957-1958.
Results: Excess-mortality rates varied between waves, age groups, and causes of death, but overall remained low. From October 1959-June 1960, the most severe wave of the pandemic, the absolute excess-mortality rate based on respiratory deaths per 10,000 population was 17.85 in the elderly (≥65 years). All other age groups had extremely low excess-mortality and the typical U-shaped age-pattern was absent. However, relative risk was greatest (3.61) among children and young adolescents (5-14 years) from October 1957-March 1958, based on incidence rates of respiratory deaths. Transmissibility was greatest during the same 1957-1958 period, when the mean reproduction number was 1.08-1.11, assuming 3 or 4 day generation intervals and exponential or fixed distributions.
Conclusions: Maricopa County largely avoided pandemic influenza from 1957-1961. Understanding this historical pandemic and the absence of high excess-mortality rates and transmissibility in Maricopa County may help public health officials prepare for and mitigate future outbreaks of influenza.
Methods: Using archival death certificates from 1954 to 1961, this study quantified the age-specific seasonal patterns, excess-mortality rates, and transmissibility patterns of the 1957 pandemic in Maricopa County, Arizona. By applying cyclical Serfling linear regression models to weekly mortality rates, the excess-mortality rates due to respiratory and all-causes were estimated for each age group during the pandemic period. The reproduction number was quantified from weekly data using a simple growth rate method and generation intervals of 3 and 4 days. Local newspaper articles from The Arizona Republic were analyzed from 1957-1958.
Results: Excess-mortality rates varied between waves, age groups, and causes of death, but overall remained low. From October 1959-June 1960, the most severe wave of the pandemic, the absolute excess-mortality rate based on respiratory deaths per 10,000 population was 17.85 in the elderly (≥65 years). All other age groups had extremely low excess-mortality and the typical U-shaped age-pattern was absent. However, relative risk was greatest (3.61) among children and young adolescents (5-14 years) from October 1957-March 1958, based on incidence rates of respiratory deaths. Transmissibility was greatest during the same 1957-1958 period, when the mean reproduction number was 1.08-1.11, assuming 3 or 4 day generation intervals and exponential or fixed distributions.
Conclusions: Maricopa County largely avoided pandemic influenza from 1957-1961. Understanding this historical pandemic and the absence of high excess-mortality rates and transmissibility in Maricopa County may help public health officials prepare for and mitigate future outbreaks of influenza.
ContributorsCobos, April J (Author) / Jehn, Megan (Thesis director) / Chowell-Puente, Gerardo (Committee member) / Barrett, The Honors College (Contributor) / School of Human Evolution and Social Change (Contributor) / School of Life Sciences (Contributor)
Created2015-05