Matching Items (30)
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
In a 2004 paper, John Nagy raised the possibility of the existence of a hypertumor \emph{i.e.}, a focus of aggressively reproducing parenchyma cells that invade part or all of a tumor. His model used a system of nonlinear ordinary differential equations to find a suitable set of conditions for which these hypertumors exist. Here that model is expanded by transforming it into a system of nonlinear partial differential equations with diffusion, advection, and a free boundary condition to represent a radially symmetric tumor growth. Two strains of parenchymal cells are incorporated; one forming almost the entirety of the tumor while the much more aggressive strain
appears in a smaller region inside of the tumor. Simulations show that if the aggressive strain focuses its efforts on proliferating and does not contribute to angiogenesis signaling when in a hypoxic state, a hypertumor will form. More importantly, this resultant aggressive tumor is paradoxically prone to extinction and hypothesize is the cause of necrosis in many vascularized tumors.
appears in a smaller region inside of the tumor. Simulations show that if the aggressive strain focuses its efforts on proliferating and does not contribute to angiogenesis signaling when in a hypoxic state, a hypertumor will form. More importantly, this resultant aggressive tumor is paradoxically prone to extinction and hypothesize is the cause of necrosis in many vascularized tumors.
ContributorsAlvarez, Roberto L (Author) / Milner, Fabio A (Thesis advisor) / Nagy, John D. (Committee member) / Kuang, Yang (Committee member) / Thieme, Horst (Committee member) / Mahalov, Alex (Committee member) / Smith, Hal (Committee member) / Arizona State University (Publisher)
Created2014
Description
Persistence theory provides a mathematically rigorous answer to the question of population survival by establishing an initial-condition- independent positive lower bound for the long-term value of the population size. This study focuses on the persistence of discrete semiflows in infinite-dimensional state spaces that model the year-to-year dynamics of structured populations. The map which encapsulates the population development from one year to the next is approximated at the origin (the extinction state) by a linear or homogeneous map. The (cone) spectral radius of this approximating map is the threshold between extinction and persistence. General persistence results are applied to three particular models: a size-structured plant population model, a diffusion model (with both Neumann and Dirichlet boundary conditions) for a dispersing population of males and females that only mate and reproduce once during a very short season, and a rank-structured model for a population of males and females.
ContributorsJin, Wen (Author) / Thieme, Horst (Thesis advisor) / Milner, Fabio (Committee member) / Quigg, John (Committee member) / Smith, Hal (Committee member) / Spielberg, John (Committee member) / Arizona State University (Publisher)
Created2014
Description
In 1968, phycologist M.R. Droop published his famous discovery on the functional relationship between growth rate and internal nutrient status of algae in chemostat culture. The simple notion that growth is directly dependent on intracellular nutrient concentration is useful for understanding the dynamics in many ecological systems. The cell quota in particular lends itself to ecological stoichiometry, which is a powerful framework for mathematical ecology. Three models are developed based on the cell quota principal in order to demonstrate its applications beyond chemostat culture.
First, a data-driven model is derived for neutral lipid synthesis in green microalgae with respect to nitrogen limitation. This model synthesizes several established frameworks in phycology and ecological stoichiometry. The model demonstrates how the cell quota is a useful abstraction for understanding the metabolic shift to neutral lipid production that is observed in certain oleaginous species.
Next a producer-grazer model is developed based on the cell quota model and nutrient recycling. The model incorporates a novel feedback loop to account for animal toxicity due to accumulation of nitrogen waste. The model exhibits rich, complex dynamics which leave several open mathematical questions.
Lastly, disease dynamics in vivo are in many ways analogous to those of an ecosystem, giving natural extensions of the cell quota concept to disease modeling. Prostate cancer can be modeled within this framework, with androgen the limiting nutrient and the prostate and cancer cells as competing species. Here the cell quota model provides a useful abstraction for the dependence of cellular proliferation and apoptosis on androgen and the androgen receptor. Androgen ablation therapy is often used for patients in biochemical recurrence or late-stage disease progression and is in general initially effective. However, for many patients the cancer eventually develops resistance months to years after treatment begins. Understanding how and predicting when hormone therapy facilitates evolution of resistant phenotypes has immediate implications for treatment. Cell quota models for prostate cancer can be useful tools for this purpose and motivate applications to other diseases.
First, a data-driven model is derived for neutral lipid synthesis in green microalgae with respect to nitrogen limitation. This model synthesizes several established frameworks in phycology and ecological stoichiometry. The model demonstrates how the cell quota is a useful abstraction for understanding the metabolic shift to neutral lipid production that is observed in certain oleaginous species.
Next a producer-grazer model is developed based on the cell quota model and nutrient recycling. The model incorporates a novel feedback loop to account for animal toxicity due to accumulation of nitrogen waste. The model exhibits rich, complex dynamics which leave several open mathematical questions.
Lastly, disease dynamics in vivo are in many ways analogous to those of an ecosystem, giving natural extensions of the cell quota concept to disease modeling. Prostate cancer can be modeled within this framework, with androgen the limiting nutrient and the prostate and cancer cells as competing species. Here the cell quota model provides a useful abstraction for the dependence of cellular proliferation and apoptosis on androgen and the androgen receptor. Androgen ablation therapy is often used for patients in biochemical recurrence or late-stage disease progression and is in general initially effective. However, for many patients the cancer eventually develops resistance months to years after treatment begins. Understanding how and predicting when hormone therapy facilitates evolution of resistant phenotypes has immediate implications for treatment. Cell quota models for prostate cancer can be useful tools for this purpose and motivate applications to other diseases.
ContributorsPacker, Aaron (Author) / Kuang, Yang (Thesis advisor) / Nagy, John (Committee member) / Smith, Hal (Committee member) / Kostelich, Eric (Committee member) / Kang, Yun (Committee member) / Arizona State University (Publisher)
Created2014
Description
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
Affect is a domain of psychology that includes attitudes, emotions, interests, and values. My own affect influenced the choice of topics for my dissertation. After examining asteroid interiors and the Moon’s thermal evolution, I discuss the role of affect in online science education. I begin with asteroids, which are collections of smaller objects held together by gravity and possibly cohesion. These “rubble-pile” objects may experience the Brazil Nut Effect (BNE). When a collection of particles of similar densities, but of different sizes, is shaken, smaller particles will move parallel to the local gravity vector while larger objects will do the opposite. Thus, when asteroids are shaken by impacts, they may experience the BNE as possibly evidenced by large boulders seen on their surfaces. I found while the BNE is plausible on asteroids, it is confined to only the outer layers. The Moon, which formed with a Lunar Magma Ocean (LMO), is the next topic of this work. The LMO is due to the Moon forming rapidly after a giant impact between the proto-Earth and another planetary body. The first 80% of the LMO solidified rapidly at which point a floatation crust formed and slowed solidification of the remaining LMO. Impact bombardment during this cooling process, while an important component, has not been studied in detail. Impacts considered here are from debris generated during the formation of the Moon. I developed a thermal model that incorporates impacts and find that impacts may have either expedited or delayed LMO solidification. Finally, I return to affect to consider the differences in attitudes towards science between students enrolled in fully-online degree programs and those enrolled in traditional, in-person degree programs. I analyzed pre- and post-course survey data from the online astrobiology course Habitable Worlds. Unlike their traditional program counterparts, students enrolled in online programs started the course with better attitudes towards science and also further changed towards more positive attitudes during the course. Along with important conclusions in three research fields, this work aims to demonstrate the importance of affect in both scientific research and science education.
ContributorsDingatantrige Perera, Jude Viranga (Author) / Asphaug, Erik (Thesis advisor) / Semken, Steven (Thesis advisor) / Anbar, Ariel (Committee member) / Elkins-Tanton, Linda T. (Committee member) / Robinson, Mark (Committee member) / Arizona State University (Publisher)
Created2017
Description
Impact cratering and volcanism are two fundamental processes that alter the surfaces of the terrestrial planets. Though well studied through laboratory experiments and terrestrial analogs, many questions remain regarding how these processes operate across the Solar System. Little is known about the formation of large impact basins (>300 km in diameter) and the degree to which they modify planetary surfaces. On the Moon, large impact basins dominate the terrain and are relatively well preserved. Because the lunar geologic timescale is largely derived from basin stratigraphic relations, it is crucial that we are able to identify and characterize materials emplaced as a result of the formation of the basins, such as light plains. Using high-resolution images under consistent illumination conditions and topography from the Lunar Reconnaissance Orbiter Camera (LROC), a new global map of light plains is presented at an unprecedented scale, revealing critical details of lunar stratigraphy and providing insight into the erosive power of large impacts. This work demonstrates that large basins significantly alter the lunar surface out to at least 4 radii from the rim, two times farther than previously thought. Further, the effect of pre-existing topography on the degradation of impact craters is unclear, despite their use in the age dating of surfaces. Crater measurements made over large regions of consistent coverage using LROC images and slopes derived from LROC topography show that pre-existing topography affects crater abundances and absolute model ages for craters up to at least 4 km in diameter.
On Mars, small volcanic edifices can provide valuable insight into the evolution of the crust and interior, but a lack of superposed craters and heavy mantling by dust make them difficult to age date. On Earth, morphometry can be used to determine the ages of cinder cone volcanoes in the absence of dated samples. Comparisons of high-resolution topography from the Context Imager (CTX) and a two-dimensional nonlinear diffusion model show that the forms observed on Mars could have been created through Earth-like processes, and with future work, it may be possible to derive an age estimate for these features in the absence of superposed craters or samples.
On Mars, small volcanic edifices can provide valuable insight into the evolution of the crust and interior, but a lack of superposed craters and heavy mantling by dust make them difficult to age date. On Earth, morphometry can be used to determine the ages of cinder cone volcanoes in the absence of dated samples. Comparisons of high-resolution topography from the Context Imager (CTX) and a two-dimensional nonlinear diffusion model show that the forms observed on Mars could have been created through Earth-like processes, and with future work, it may be possible to derive an age estimate for these features in the absence of superposed craters or samples.
ContributorsMeyer, Heather (Author) / Robinson, Mark S (Thesis advisor) / Bell, Jim (Thesis advisor) / Denevi, Brett (Committee member) / Clarke, Amanda (Committee member) / Asphaug, Erik (Committee member) / Arizona State University (Publisher)
Created2018
Description
Many planetary science missions study thermophysical properties of surfaces using infrared spectrometers and infrared cameras. Thermal inertia is a frequently derived thermophysical property that quantifies the ability for heat to exchange through planetary surfaces.
To conceptualize thermal inertia, the diffusion equation analogies are extended using a general effusivity term: the square root of a product of conductivity and capacity terms. A hypothetical thermal inductance was investigated for diurnal planetary heating. The hyperbolic heat diffusion equation was solved to derive an augmented thermal inertia. The hypothetical thermal inductance was modeled with negligible effect on Mars.
Extending spectral performance of infrared cameras was desired for colder bodies in the outer solar system where peak infrared emission is at longer wavelengths. The far-infrared response of an infrared microbolometer array with a retrofitted diamond window was determined using an OSIRIS-REx—OTES interferometer. An instrument response function of the diamond interferometer-microbolometer system shows extended peak performance from 15 µm out to 20 µm and 40% performance to at least 30 µm. The results are folded into E-THEMIS for the NASA flagship mission: Europa Clipper.
Infrared camera systems are desired for the expanding smallsat community that can inherit risk and relax performance requirements. The Thermal-camera for Exploration, Science, and Imaging Spacecraft (THESIS) was developed for the Prox-1 microsat mission. THESIS, incorporating 2001 Mars Odyssey—THEMIS experience, consists of an infrared camera, a visible camera, and an instrument computer. THESIS was planned to provide images for demonstrating autonomous proximity operations between two spacecraft, verifying deployment of the Planetary Society’s LightSail-B, and conducting remote sensing of Earth. Prox-1—THESIS was selected as the finalist for the competed University Nanosatellite Program-7 and was awarded a launch on the maiden commercial SpaceX Falcon Heavy. THESIS captures 8-12 µm IR images with 100 mm optics and RGB color images with 25 mm optics. The instrument computer was capable of instrument commanding, automatic data processing, image storage, and telemetry recording. The completed THESIS has a mass of 2.04 kg, a combined volume of 3U, and uses 7W of power. THESIS was designed, fabricated, integrated, and tested in ASU’s 100K clean lab.
To conceptualize thermal inertia, the diffusion equation analogies are extended using a general effusivity term: the square root of a product of conductivity and capacity terms. A hypothetical thermal inductance was investigated for diurnal planetary heating. The hyperbolic heat diffusion equation was solved to derive an augmented thermal inertia. The hypothetical thermal inductance was modeled with negligible effect on Mars.
Extending spectral performance of infrared cameras was desired for colder bodies in the outer solar system where peak infrared emission is at longer wavelengths. The far-infrared response of an infrared microbolometer array with a retrofitted diamond window was determined using an OSIRIS-REx—OTES interferometer. An instrument response function of the diamond interferometer-microbolometer system shows extended peak performance from 15 µm out to 20 µm and 40% performance to at least 30 µm. The results are folded into E-THEMIS for the NASA flagship mission: Europa Clipper.
Infrared camera systems are desired for the expanding smallsat community that can inherit risk and relax performance requirements. The Thermal-camera for Exploration, Science, and Imaging Spacecraft (THESIS) was developed for the Prox-1 microsat mission. THESIS, incorporating 2001 Mars Odyssey—THEMIS experience, consists of an infrared camera, a visible camera, and an instrument computer. THESIS was planned to provide images for demonstrating autonomous proximity operations between two spacecraft, verifying deployment of the Planetary Society’s LightSail-B, and conducting remote sensing of Earth. Prox-1—THESIS was selected as the finalist for the competed University Nanosatellite Program-7 and was awarded a launch on the maiden commercial SpaceX Falcon Heavy. THESIS captures 8-12 µm IR images with 100 mm optics and RGB color images with 25 mm optics. The instrument computer was capable of instrument commanding, automatic data processing, image storage, and telemetry recording. The completed THESIS has a mass of 2.04 kg, a combined volume of 3U, and uses 7W of power. THESIS was designed, fabricated, integrated, and tested in ASU’s 100K clean lab.
ContributorsVeto, Michael (Author) / Christensen, Philip C (Thesis advisor) / Bell III, Jim (Committee member) / Clarke, Amanda B (Committee member) / Asphaug, Erik (Committee member) / Sariapli, Srikanth (Committee member) / Ruff, Steven (Committee member) / Arizona State University (Publisher)
Created2018
Description
The role of climate change, as measured in terms of changes in the climatology of geophysical variables (such as temperature and rainfall), on the global distribution and burden of vector-borne diseases (VBDs) remains a subject of considerable debate. This dissertation attempts to contribute to this debate via the use of mathematical (compartmental) modeling and statistical data analysis. In particular, the objective is to find suitable values and/or ranges of the climate variables considered (typically temperature and rainfall) for maximum vector abundance and consequently, maximum transmission intensity of the disease(s) they cause.
Motivated by the fact that understanding the dynamics of disease vector is crucial to understanding the transmission and control of the VBDs they cause, a novel weather-driven deterministic model for the population biology of the mosquito is formulated and rigorously analyzed. Numerical simulations, using relevant weather and entomological data for Anopheles mosquito (the vector for malaria), show that maximum mosquito abundance occurs when temperature and rainfall values lie in the range [20-25]C and [105-115] mm, respectively.
The Anopheles mosquito ecology model is extended to incorporate human dynamics. The resulting weather-driven malaria transmission model, which includes many of the key aspects of malaria (such as disease transmission by asymptomatically-infectious humans, and enhanced malaria immunity due to repeated exposure), was rigorously analyzed. The model which also incorporates the effect of diurnal temperature range (DTR) on malaria transmission dynamics shows that increasing DTR shifts the peak temperature value for malaria transmission from 29C (when DTR is 0C) to about 25C (when DTR is 15C).
Finally, the malaria model is adapted and used to study the transmission dynamics of chikungunya, dengue and Zika, three diseases co-circulating in the Americas caused by the same vector (Aedes aegypti). The resulting model, which is fitted using data from Mexico, is used to assess a few hypotheses (such as those associated with the possible impact the newly-released dengue vaccine will have on Zika) and the impact of variability in climate variables on the dynamics of the three diseases. Suitable temperature and rainfall ranges for the maximum transmission intensity of the three diseases are obtained.
Motivated by the fact that understanding the dynamics of disease vector is crucial to understanding the transmission and control of the VBDs they cause, a novel weather-driven deterministic model for the population biology of the mosquito is formulated and rigorously analyzed. Numerical simulations, using relevant weather and entomological data for Anopheles mosquito (the vector for malaria), show that maximum mosquito abundance occurs when temperature and rainfall values lie in the range [20-25]C and [105-115] mm, respectively.
The Anopheles mosquito ecology model is extended to incorporate human dynamics. The resulting weather-driven malaria transmission model, which includes many of the key aspects of malaria (such as disease transmission by asymptomatically-infectious humans, and enhanced malaria immunity due to repeated exposure), was rigorously analyzed. The model which also incorporates the effect of diurnal temperature range (DTR) on malaria transmission dynamics shows that increasing DTR shifts the peak temperature value for malaria transmission from 29C (when DTR is 0C) to about 25C (when DTR is 15C).
Finally, the malaria model is adapted and used to study the transmission dynamics of chikungunya, dengue and Zika, three diseases co-circulating in the Americas caused by the same vector (Aedes aegypti). The resulting model, which is fitted using data from Mexico, is used to assess a few hypotheses (such as those associated with the possible impact the newly-released dengue vaccine will have on Zika) and the impact of variability in climate variables on the dynamics of the three diseases. Suitable temperature and rainfall ranges for the maximum transmission intensity of the three diseases are obtained.
ContributorsOkuneye, Kamaldeen O (Author) / Gumel, Abba B (Thesis advisor) / Kuang, Yang (Committee member) / Smith, Hal (Committee member) / Thieme, Horst (Committee member) / Nagy, John (Committee member) / Arizona State University (Publisher)
Created2018