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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
Background: National and international strategies to increase physical activity emphasize environmental and policy changes that can have widespread and long-lasting impact. Evidence from multiple countries using comparable methods is required to strengthen the evidence base for such initiatives. Because some environment and policy changes could have generalizable effects and others may depend on each country's context, only international studies using comparable methods can identify the relevant differences. Methods: Currently 12 countries are participating in the International Physical Activity and the Environment Network (IPEN) study. The IPEN Adult study design involves recruiting adult participants from neighborhoods with wide variations in environmental walkability attributes and socioeconomic status (SES). Results: Eleven of twelve countries are providing accelerometer data and 11 are providing GIS data. Current projections indicate that 14,119 participants will provide survey data on built environments and physical activity and 7145 are likely to provide objective data on both the independent and dependent variables. Though studies are highly comparable, some adaptations are required based on the local context. Conclusions: This study was designed to inform evidence-based international and country-specific physical activity policies and interventions to help prevent obesity and other chronic diseases that are high in developed countries and growing rapidly in developing countries.
ContributorsKerr, Jacqueline (Author) / Sallis, James F. (Author) / Owen, Neville (Author) / De Bourdeaudhuij, Ilse (Author) / Cerin, Ester (Author) / Sugiyama, Takemi (Author) / Reis, Rodrigo (Author) / Sarmiento, Olga (Author) / Froemel, Karel (Author) / Mitas, Josef (Author) / Troelsen, Jens (Author) / Christiansen, Lars Breum (Author) / Macfarlane, Duncan (Author) / Salvo, Deborah (Author) / Schofield, Grant (Author) / Badland, Hannah (Author) / Guillen-Grima, Francisco (Author) / Aguinaga-Ontoso, Ines (Author) / Davey, Rachel (Author) / Bauman, Adrian (Author) / Saelens, Brian (Author) / Riddoch, Chris (Author) / Ainsworth, Barbara (Author) / Pratt, Michael (Author) / Schmidt, Tom (Author) / Frank, Lawrence (Author) / Adams, Marc (Author) / Conway, Terry (Author) / Cain, Kelli (Author) / Van Dyck, Delfien (Author) / Bracy, Nicole (Author) / College of Health Solutions (Contributor) / School of Nutrition and Health Promotion (Contributor)
Created2013
Description
Background
Increasing empirical evidence supports associations between neighborhood environments and physical activity. However, since most studies were conducted in a single country, particularly western countries, the generalizability of associations in an international setting is not well understood. The current study examined whether associations between perceived attributes of neighborhood environments and physical activity differed by country.
Methods
Population representative samples from 11 countries on five continents were surveyed using comparable methodologies and measurement instruments. Neighborhood environment × country interactions were tested in logistic regression models with meeting physical activity recommendations as the outcome, adjusted for demographic characteristics. Country-specific associations were reported.
Results
Significant neighborhood environment attribute × country interactions implied some differences across countries in the association of each neighborhood attribute with meeting physical activity recommendations. Across the 11 countries, land-use mix and sidewalks had the most consistent associations with physical activity. Access to public transit, bicycle facilities, and low-cost recreation facilities had some associations with physical activity, but with less consistency across countries. There was little evidence supporting the associations of residential density and crime-related safety with physical activity in most countries.
Conclusion
There is evidence of generalizability for the associations of land use mix, and presence of sidewalks with physical activity. Associations of other neighborhood characteristics with physical activity tended to differ by country. Future studies should include objective measures of neighborhood environments, compare psychometric properties of reports across countries, and use better specified models to further understand the similarities and differences in associations across countries.
Increasing empirical evidence supports associations between neighborhood environments and physical activity. However, since most studies were conducted in a single country, particularly western countries, the generalizability of associations in an international setting is not well understood. The current study examined whether associations between perceived attributes of neighborhood environments and physical activity differed by country.
Methods
Population representative samples from 11 countries on five continents were surveyed using comparable methodologies and measurement instruments. Neighborhood environment × country interactions were tested in logistic regression models with meeting physical activity recommendations as the outcome, adjusted for demographic characteristics. Country-specific associations were reported.
Results
Significant neighborhood environment attribute × country interactions implied some differences across countries in the association of each neighborhood attribute with meeting physical activity recommendations. Across the 11 countries, land-use mix and sidewalks had the most consistent associations with physical activity. Access to public transit, bicycle facilities, and low-cost recreation facilities had some associations with physical activity, but with less consistency across countries. There was little evidence supporting the associations of residential density and crime-related safety with physical activity in most countries.
Conclusion
There is evidence of generalizability for the associations of land use mix, and presence of sidewalks with physical activity. Associations of other neighborhood characteristics with physical activity tended to differ by country. Future studies should include objective measures of neighborhood environments, compare psychometric properties of reports across countries, and use better specified models to further understand the similarities and differences in associations across countries.
ContributorsDing, Ding (Author) / Adams, Marc (Author) / Sallis, James F. (Author) / Norman, Gregory J. (Author) / Hovell, Melbourn F. (Author) / Chambers, Christina D. (Author) / Hofstetter, C. Richard (Author) / Bowles, Heather R. (Author) / Hagstromer, Maria (Author) / Craig, Cora L. (Author) / Fernando Gomez, Luis (Author) / De Bourdeaudhuij, Ilse (Author) / Macfarlane, Duncan J. (Author) / Ainsworth, Barbara (Author) / Bergman, Patrick (Author) / Bull, Fiona C. (Author) / Carr, Harriette (Author) / Klasson-Heggebo, Lena (Author) / Inoue, Shigeru (Author) / Murase, Norio (Author) / Matsudo, Sandra (Author) / Matsudo, Victor (Author) / McLean, Grant (Author) / Sjostrom, Michael (Author) / Tomten, Heidi (Author) / Lefevre, Johan (Author) / Volbekiene, Vida (Author) / Bauman, Adrian E. (Author) / College of Health Solutions (Contributor) / School of Nutrition and Health Promotion (Contributor)
Created2013-05-14
Description
Background
Neighborhood environment studies of physical activity (PA) have been mainly single-country focused. The International Prevalence Study (IPS) presented a rare opportunity to examine neighborhood features across countries. The purpose of this analysis was to: 1) detect international neighborhood typologies based on participants’ response patterns to an environment survey and 2) to estimate associations between neighborhood environment patterns and PA.
Methods
A Latent Class Analysis (LCA) was conducted on pooled IPS adults (N=11,541) aged 18 to 64 years old (mean=37.5 ±12.8 yrs; 55.6% women) from 11 countries including Belgium, Brazil, Canada, Colombia, Hong Kong, Japan, Lithuania, New Zealand, Norway, Sweden, and the U.S. This subset used the Physical Activity Neighborhood Environment Survey (PANES) that briefly assessed 7 attributes within 10–15 minutes walk of participants’ residences, including residential density, access to shops/services, recreational facilities, public transit facilities, presence of sidewalks and bike paths, and personal safety. LCA derived meaningful subgroups from participants’ response patterns to PANES items, and participants were assigned to neighborhood types. The validated short-form International Physical Activity Questionnaire (IPAQ) measured likelihood of meeting the 150 minutes/week PA guideline. To validate derived classes, meeting the guideline either by walking or total PA was regressed on neighborhood types using a weighted generalized linear regression model, adjusting for gender, age and country.
Results
A 5-subgroup solution fitted the dataset and was interpretable. Neighborhood types were labeled, “Overall Activity Supportive (52% of sample)”, “High Walkable and Unsafe with Few Recreation Facilities (16%)”, “Safe with Active Transport Facilities (12%)”, “Transit and Shops Dense with Few Amenities (15%)”, and “Safe but Activity Unsupportive (5%)”. Country representation differed by type (e.g., U.S. disproportionally represented “Safe but Activity Unsupportive”). Compared to the Safe but Activity Unsupportive, two types showed greater odds of meeting PA guideline for walking outcome (High Walkable and Unsafe with Few Recreation Facilities, OR= 2.26 (95% CI 1.18-4.31); Overall Activity Supportive, OR= 1.90 (95% CI 1.13-3.21). Significant but smaller odds ratios were also found for total PA.
Conclusions
Meaningful neighborhood patterns generalized across countries and explained practical differences in PA. These observational results support WHO/UN recommendations for programs and policies targeted to improve features of the neighborhood environment for PA.
Neighborhood environment studies of physical activity (PA) have been mainly single-country focused. The International Prevalence Study (IPS) presented a rare opportunity to examine neighborhood features across countries. The purpose of this analysis was to: 1) detect international neighborhood typologies based on participants’ response patterns to an environment survey and 2) to estimate associations between neighborhood environment patterns and PA.
Methods
A Latent Class Analysis (LCA) was conducted on pooled IPS adults (N=11,541) aged 18 to 64 years old (mean=37.5 ±12.8 yrs; 55.6% women) from 11 countries including Belgium, Brazil, Canada, Colombia, Hong Kong, Japan, Lithuania, New Zealand, Norway, Sweden, and the U.S. This subset used the Physical Activity Neighborhood Environment Survey (PANES) that briefly assessed 7 attributes within 10–15 minutes walk of participants’ residences, including residential density, access to shops/services, recreational facilities, public transit facilities, presence of sidewalks and bike paths, and personal safety. LCA derived meaningful subgroups from participants’ response patterns to PANES items, and participants were assigned to neighborhood types. The validated short-form International Physical Activity Questionnaire (IPAQ) measured likelihood of meeting the 150 minutes/week PA guideline. To validate derived classes, meeting the guideline either by walking or total PA was regressed on neighborhood types using a weighted generalized linear regression model, adjusting for gender, age and country.
Results
A 5-subgroup solution fitted the dataset and was interpretable. Neighborhood types were labeled, “Overall Activity Supportive (52% of sample)”, “High Walkable and Unsafe with Few Recreation Facilities (16%)”, “Safe with Active Transport Facilities (12%)”, “Transit and Shops Dense with Few Amenities (15%)”, and “Safe but Activity Unsupportive (5%)”. Country representation differed by type (e.g., U.S. disproportionally represented “Safe but Activity Unsupportive”). Compared to the Safe but Activity Unsupportive, two types showed greater odds of meeting PA guideline for walking outcome (High Walkable and Unsafe with Few Recreation Facilities, OR= 2.26 (95% CI 1.18-4.31); Overall Activity Supportive, OR= 1.90 (95% CI 1.13-3.21). Significant but smaller odds ratios were also found for total PA.
Conclusions
Meaningful neighborhood patterns generalized across countries and explained practical differences in PA. These observational results support WHO/UN recommendations for programs and policies targeted to improve features of the neighborhood environment for PA.
ContributorsAdams, Marc (Author) / Ding, Ding (Author) / Sallis, James F. (Author) / Bowles, Heather R. (Author) / Ainsworth, Barbara (Author) / Bergman, Patrick (Author) / Bull, Fiona C. (Author) / Carr, Harriette (Author) / Craig, Cora L. (Author) / De Bourdeaudhuij, Ilse (Author) / Fernando Gomez, Luis (Author) / Hagstromer, Maria (Author) / Klasson-Heggebo, Lena (Author) / Inoue, Shigeru (Author) / Lefevre, Johan (Author) / Macfarlane, Duncan J. (Author) / Matsudo, Sandra (Author) / Matsudo, Victor (Author) / McLean, Grant (Author) / Murase, Norio (Author) / Sjostrom, Michael (Author) / Tomten, Heidi (Author) / Volbekiene, Vida (Author) / Bauman, Adrian (Author) / College of Health Solutions (Contributor) / School of Nutrition and Health Promotion (Contributor)
Created2013-03-07
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