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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
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
In this research we consider stochastic models of Glioblastoma Multiforme brain tumors. We first look at a model by K. Swanson et al., which describes the dynamics as random diffusion plus deterministic logistic growth. We introduce a stochastic component in the logistic growth in the form of a random growth rate defined by a Poisson process. We show that this stochastic logistic growth model leads to a more accurate evaluation of the tumor growth compared its deterministic counterpart. We also discuss future plans to incorporate individual patient geometry, extend the model to three dimensions and to incorporate effects of different treatments into our model, in collaboration with a local hospital.
ContributorsManning, Michael Clare (Author) / Kostelich, Eric (Thesis director) / Kuang, Yang (Committee member) / Gardner, Carl (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of Letters and Sciences (Contributor) / School of Human Evolution and Social Change (Contributor)
Created2013-12
Description
Five immunocompetent C57BL/6-cBrd/cBrd/Cr (albino C57BL/6) mice were injected with GL261-luc2 cells, a cell line sharing characteristics of human glioblastoma multiforme (GBM). The mice were imaged using magnetic resonance (MR) at five separate time points to characterize growth and development of the tumor. After 25 days, the final tumor volumes of the mice varied from 12 mm3 to 62 mm3, even though mice were inoculated from the same tumor cell line under carefully controlled conditions. We generated hypotheses to explore large variances in final tumor size and tested them with our simple reaction-diffusion model in both a 3-dimensional (3D) finite difference method and a 2-dimensional (2D) level set method. The parameters obtained from a best-fit procedure, designed to yield simulated tumors as close as possible to the observed ones, vary by an order of magnitude between the three mice analyzed in detail. These differences may reflect morphological and biological variability in tumor growth, as well as errors in the mathematical model, perhaps from an oversimplification of the tumor dynamics or nonidentifiability of parameters. Our results generate parameters that match other experimental in vitro and in vivo measurements. Additionally, we calculate wave speed, which matches with other rat and human measurements.
ContributorsRutter, Erica (Author) / Stepien, Tracy (Author) / Anderies, Barrett (Author) / Plasencia, Jonathan (Author) / Woolf, Eric C. (Author) / Scheck, Adrienne C. (Author) / Turner, Gregory H. (Author) / Liu, Qingwei (Author) / Frakes, David (Author) / Kodibagkar, Vikram (Author) / Kuang, Yang (Author) / Preul, Mark C. (Author) / Kostelich, Eric (Author) / College of Liberal Arts and Sciences (Contributor)
Created2017-05-31
Description
Over time, tumor treatment resistance inadvertently develops when androgen de-privation therapy (ADT) is applied to metastasized prostate cancer (PCa). To combat tumor resistance, while reducing the harsh side effects of hormone therapy, the clinician may opt to cyclically alternates the patient’s treatment on and off. This method,known as intermittent ADT, is an alternative to continuous ADT that improves the patient’s quality of life while testosterone levels recover between cycles. In this paper,we explore the response of intermittent ADT to metastasized prostate cancer by employing a previously clinical data validated mathematical model to new clinical data from patients undergoing Abiraterone therapy. This cell quota model, a system of ordinary differential equations constructed using Droop’s nutrient limiting theory, assumes the tumor comprises of castration-sensitive (CS) and castration-resistant (CR)cancer sub-populations. The two sub-populations rely on varying levels of intracellular androgen for growth, death and transformation. Due to the complexity of the model,we carry out sensitivity analyses to study the effect of certain parameters on their outputs, and to increase the identifiability of each patient’s unique parameter set. The model’s forecasting results show consistent accuracy for patients with sufficient data,which means the model could give useful information in practice, especially to decide whether an additional round of treatment would be effective.
ContributorsBennett, Justin Klark (Author) / Kuang, Yang (Thesis director) / Kostelich, Eric (Committee member) / Phan, Tin (Committee member) / School of Mathematical and Statistical Sciences (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2021-05
Description
Magnetic resonance imaging (MRI) data of metastatic brain cancer patients at the Barrow Neurological Institute sparked interest in the radiology department due to the possibility that tumor size distributions might mimic a power law or an exponential distribution. In order to consider the question regarding the growth trends of metastatic brain tumors, this thesis analyzes the volume measurements of the tumor sizes from the BNI data and attempts to explain such size distributions through mathematical models. More specifically, a basic stochastic cellular automaton model is used and has three-dimensional results that show similar size distributions of those of the BNI data. Results of the models are investigated using the likelihood ratio test suggesting that, when the tumor volumes are measured based on assuming tumor sphericity, the tumor size distributions significantly mimic the power law over an exponential distribution.
ContributorsFreed, Rebecca (Co-author) / Snopko, Morgan (Co-author) / Kostelich, Eric (Thesis director) / Kuang, Yang (Committee member) / WPC Graduate Programs (Contributor) / School of Accountancy (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-12
Description
Prostate cancer is the second most common kind of cancer in men. Fortunately, it has a 99% survival rate. To achieve such a survival rate, a variety of aggressive therapies are used to treat prostate cancers that are caught early. Androgen deprivation therapy (ADT) is a therapy that is given in cycles to patients. This study attempted to analyze what factors in a group of 79 patients caused them to stick with or discontinue the treatment. This was done using naïve Bayes classification, a machine-learning algorithm. The usage of this algorithm identified high testosterone as an indicator of a patient persevering with the treatment, but failed to produce statistically significant high rates of prediction.
ContributorsMillea, Timothy Michael (Author) / Kostelich, Eric (Thesis director) / Kuang, Yang (Committee member) / Computer Science and Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2016-12
Description
Glioblastoma multiforme (GBM) is a malignant, aggressive and infiltrative cancer of the central nervous system with a median survival of 14.6 months with standard care. Diagnosis of GBM is made using medical imaging such as magnetic resonance imaging (MRI) or computed tomography (CT). Treatment is informed by medical images and includes chemotherapy, radiation therapy, and surgical removal if the tumor is surgically accessible. Treatment seldom results in a significant increase in longevity, partly due to the lack of precise information regarding tumor size and location. This lack of information arises from the physical limitations of MR and CT imaging coupled with the diffusive nature of glioblastoma tumors. GBM tumor cells can migrate far beyond the visible boundaries of the tumor and will result in a recurring tumor if not killed or removed. Since medical images are the only readily available information about the tumor, we aim to improve mathematical models of tumor growth to better estimate the missing information. Particularly, we investigate the effect of random variation in tumor cell behavior (anisotropy) using stochastic parameterizations of an established proliferation-diffusion model of tumor growth. To evaluate the performance of our mathematical model, we use MR images from an animal model consisting of Murine GL261 tumors implanted in immunocompetent mice, which provides consistency in tumor initiation and location, immune response, genetic variation, and treatment. Compared to non-stochastic simulations, stochastic simulations showed improved volume accuracy when proliferation variability was high, but diffusion variability was found to only marginally affect tumor volume estimates. Neither proliferation nor diffusion variability significantly affected the spatial distribution accuracy of the simulations. While certain cases of stochastic parameterizations improved volume accuracy, they failed to significantly improve simulation accuracy overall. Both the non-stochastic and stochastic simulations failed to achieve over 75% spatial distribution accuracy, suggesting that the underlying structure of the model fails to capture one or more biological processes that affect tumor growth. Two biological features that are candidates for further investigation are angiogenesis and anisotropy resulting from differences between white and gray matter. Time-dependent proliferation and diffusion terms could be introduced to model angiogenesis, and diffusion weighed imaging (DTI) could be used to differentiate between white and gray matter, which might allow for improved estimates brain anisotropy.
ContributorsAnderies, Barrett James (Author) / Kostelich, Eric (Thesis director) / Kuang, Yang (Committee member) / Stepien, Tracy (Committee member) / Harrington Bioengineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Climate change is one of the most pressing issues affecting the world today. One of the impacts of climate change is on the transmission of mosquito-borne diseases (MBDs), such as West Nile Virus (WNV). Climate is known to influence vector and host demography as well as MBD transmission. This dissertation addresses the questions of how vector and host demography impact WNV dynamics, and how expected and likely climate change scenarios will affect demographic and epidemiological processes of WNV transmission. First, a data fusion method is developed that connects non-autonomous logistic model parameters to mosquito time series data. This method captures the inter-annual and intra-seasonal variation of mosquito populations within a geographical location. Next, a three-population WNV model between mosquito vectors, bird hosts, and human hosts with infection-age structure for the vector and bird host populations is introduced. A sensitivity analysis uncovers which parameters have the most influence on WNV outbreaks. Finally, the WNV model is extended to include the non-autonomous population model and temperature-dependent processes. Model parameterization using historical temperature and human WNV case data from the Greater Toronto Area (GTA) is conducted. Parameter fitting results are then used to analyze possible future WNV dynamics under two climate change scenarios. These results suggest that WNV risk for the GTA will substantially increase as temperature increases from climate change, even under the most conservative assumptions. This demonstrates the importance of ensuring that the warming of the planet is limited as much as possible.
ContributorsMancuso, Marina (Author) / Milner, Fabio A (Thesis advisor) / Kuang, Yang (Committee member) / Kostelich, Eric (Committee member) / Eikenberry, Steffen (Committee member) / Manore, Carrie (Committee member) / Arizona State University (Publisher)
Created2023