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- Member of: ASU Electronic Theses and Dissertations
Description
Signaling cascades transduce signals received on the cell membrane to the nucleus. While noise filtering, ultra-sensitive switches, and signal amplification have all been shown to be features of such signaling cascades, it is not understood why cascades typically show three or four layers. Using singular perturbation theory, Michaelis-Menten type equations are derived for open enzymatic systems. When these equations are organized into a cascade, it is demonstrated that the output signal as a function of time becomes sigmoidal with the addition of more layers. Furthermore, it is shown that the activation time will speed up to a point, after which more layers become superfluous. It is shown that three layers create a reliable sigmoidal response progress curve from a wide variety of time-dependent signaling inputs arriving at the cell membrane, suggesting that natural selection may have favored signaling cascades as a parsimonious solution to the problem of generating switch-like behavior in a noisy environment.
ContributorsYoung, Jonathan Trinity (Author) / Armbruster, Dieter (Thesis advisor) / Platte, Rodrigo (Committee member) / Nagy, John (Committee member) / Baer, Steven (Committee member) / Taylor, Jesse (Committee member) / Arizona State University (Publisher)
Created2013
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
Research shows that the subject of mathematics, although revered, remains a source of trepidation for many individuals, as they find it difficult to form a connection between the work they do on paper and their work's practical applications. This research study describes the impact of teaching a challenging introductive applied mathematics course on high school students' skills and attitudes towards mathematics in a college Summer Program. In the analysis of my research data, I identified several emerging changes in skills and attitudes towards mathematics, skills that high-school students needed or developed when taking the mathematical modeling course. Results indicated that the applied mathematics course had a positive impact on several students' attitudes, in general, such as, self-confidence, meanings of what mathematics is, and their perceptions of what solutions are. It also had a positive impact on several skills, such as translating real-life situations to mathematics via flow diagrams, translating the models' solutions back from mathematics to the real world, and interpreting graphs. Students showed positive results when the context of their problems was applied or graphical, and fewer improvement on problems that were not. Research also indicated some negatives outcomes, a decrease in confidence for certain students, and persistent negative ways of thinking about graphs. Based on these findings, I make recommendations for teaching similar mathematical modeling at the pre-university level, to encourage the development of young students through educational, research and similar mentorship activities, to increase their inspiration and interest in mathematics, and possibly consider a variety of sciences, technology, engineering and mathematics-related (STEM) fields and careers.
Contributorsagoune, linda (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Castillo-Garsow, Carlos W (Thesis advisor) / Mubayi, Anuj (Committee member) / Arizona State University (Publisher)
Created2020
Description
\begin{abstract}The human immunodeficiency virus (HIV) pandemic, which causes the syndrome of opportunistic infections that characterize the late stage HIV disease, known as the acquired immunodeficiency syndrome (AIDS), remains a major public health challenge to many parts of the world. This dissertation contributes in providing deeper qualitative insights into the transmission dynamics and control of the HIV/AIDS disease in Men who have Sex with Men (MSM) community. A new mathematical model (which is relatively basic), which incorporates some of the pertinent aspects of HIV epidemiology and immunology and fitted using the yearly new case data of the MSM population from the State of Arizona, was designed and used to assess the population-level impact of awareness of HIV infection status and condom-based intervention, on the transmission dynamics and control of HIV/AIDS in an MSM community. Conditions for the existence and asymptotic stability of the various equilibria ofthe model were derived. The numerical simulations showed that the prospects for the effective control and/or elimination of HIV/AIDS in the MSM community in the United States are very promising using a condom-based intervention, provided the condom efficacy is high and the compliance is moderate enough. The model was extended in Chapter 3 to account for the effect of risk-structure, staged-progression property of HIV disease, and the use of pre-exposure prophylaxis (PrEP) on the spread and control of the disease. The model was shown to undergo a PrEP-induced \textit{backward bifurcation} when the associated control reproduction number is less than one. It was shown that when the compliance in PrEP usage is $50%(80%)$ then about $19.1%(34.2%)$ of the yearly new HIV/AIDS cases recorded at the peak will have been prevented, in comparison to the worst-case scenario where PrEP-based intervention is not implemented in the MSM community. It was also shown that the HIV pandemic elimination is possible from the MSM community even for the scenario when the effective contact rate is increased by 5-fold from its baseline value, if low-risk individuals take at least 15 years before they change their risky behavior and transition to the high-risk group (regardless of the value of the transition rate from high-risk to low-risk susceptible population).
ContributorsTollett, Queen Wiggs (Author) / Gumel, Abba (Thesis advisor) / Crook, Sharon (Committee member) / Fricks, John (Committee member) / Gardner, Carl (Committee member) / Nagy, John (Committee member) / Arizona State University (Publisher)
Created2023
Description
Understanding the consequences of changes in social networks is an important an-
thropological research goal. This dissertation looks at the role of data-driven social
networks on infectious disease transmission and evolution. The dissertation has two
projects. The first project is an examination of the effects of the superspreading
phenomenon, wherein a relatively few individuals are responsible for a dispropor-
tionate number of secondary cases, on the patterns of an infectious disease. The
second project examines the timing of the initial introduction of tuberculosis (TB) to
the human population. The results suggest that TB has a long evolutionary history
with hunter-gatherers. Both of these projects demonstrate the consequences of social
networks for infectious disease transmission and evolution.
The introductory chapter provides a review of social network-based studies in an-
thropology and epidemiology. Particular emphasis is paid to the concept and models
of superspreading and why to consider it, as this is central to the discussion in chapter
2. The introductory chapter also reviews relevant epidemic mathematical modeling
studies.
In chapter 2, social networks are connected with superspreading events, followed
by an investigation of how social networks can provide greater understanding of in-
fectious disease transmission through mathematical models. Using the example of
SARS, the research shows how heterogeneity in transmission rate impacts super-
spreading which, in turn, can change epidemiological inference on model parameters
for an epidemic.
Chapter 3 uses a different mathematical model to investigate the evolution of TB
in hunter-gatherers. The underlying question is the timing of the introduction of TB
to the human population. Chapter 3 finds that TB’s long latent period is consistent
with the evolutionary pressure which would be exerted by transmission on a hunter-
igatherer social network. Evidence of a long coevolution with humans indicates an
early introduction of TB to the human population.
Both of the projects in this dissertation are demonstrations of the impact of var-
ious characteristics and types of social networks on infectious disease transmission
dynamics. The projects together force epidemiologists to think about networks and
their context in nontraditional ways.
thropological research goal. This dissertation looks at the role of data-driven social
networks on infectious disease transmission and evolution. The dissertation has two
projects. The first project is an examination of the effects of the superspreading
phenomenon, wherein a relatively few individuals are responsible for a dispropor-
tionate number of secondary cases, on the patterns of an infectious disease. The
second project examines the timing of the initial introduction of tuberculosis (TB) to
the human population. The results suggest that TB has a long evolutionary history
with hunter-gatherers. Both of these projects demonstrate the consequences of social
networks for infectious disease transmission and evolution.
The introductory chapter provides a review of social network-based studies in an-
thropology and epidemiology. Particular emphasis is paid to the concept and models
of superspreading and why to consider it, as this is central to the discussion in chapter
2. The introductory chapter also reviews relevant epidemic mathematical modeling
studies.
In chapter 2, social networks are connected with superspreading events, followed
by an investigation of how social networks can provide greater understanding of in-
fectious disease transmission through mathematical models. Using the example of
SARS, the research shows how heterogeneity in transmission rate impacts super-
spreading which, in turn, can change epidemiological inference on model parameters
for an epidemic.
Chapter 3 uses a different mathematical model to investigate the evolution of TB
in hunter-gatherers. The underlying question is the timing of the introduction of TB
to the human population. Chapter 3 finds that TB’s long latent period is consistent
with the evolutionary pressure which would be exerted by transmission on a hunter-
igatherer social network. Evidence of a long coevolution with humans indicates an
early introduction of TB to the human population.
Both of the projects in this dissertation are demonstrations of the impact of var-
ious characteristics and types of social networks on infectious disease transmission
dynamics. The projects together force epidemiologists to think about networks and
their context in nontraditional ways.
ContributorsNesse, Hans P (Author) / Hurtado, Ana Magdalena (Thesis advisor) / Castillo-Chavez, Carlos (Committee member) / Mubayi, Anuj (Committee member) / Arizona State University (Publisher)
Created2019
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
Description
Combination therapy has shown to improve success for cancer treatment. Oncolytic virotherapy is cancer treatment that uses engineered viruses to specifically infect and kill cancer cells, without harming healthy cells. Immunotherapy boosts the body's natural defenses towards cancer. The combination of oncolytic virotherapy and immunotherapy is explored through deterministic systems of nonlinear differential equations, constructed to match experimental data for murine melanoma. Mathematical analysis was done in order to gain insight on the relationship between cancer, viruses and immune response. One extension of the model focuses on clinical needs, with the underlying goal to seek optimal treatment regimens; for both frequency and dose quantity. The models in this work were first used to estimate parameters from preclinical experimental data, to identify biologically realistic parameter values. Insight gained from the mathematical analysis in the first model, allowed for numerical analysis to explore optimal treatment regimens of combination oncolytic virotherapy and dendritic vaccinations. Permutations accounting for treatment scheduled were done to find regimens that reduce tumor size. Observations from the produced data lead to in silico exploration of immune-viral interactions. Results suggest under optimal settings, combination treatment works better than monotherapy of either type. The most optimal result suggests treatment over a longer period of time, with fractioned doses, while reducing the total dendritic vaccination quantity, and maintaining the maximum virotherapy used in the experimental work.
ContributorsSummer, Ilyssa Aimee (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Nagy, John (Thesis advisor) / Mubayi, Anuj (Committee member) / Kang, Yun (Committee member) / Arizona State University (Publisher)
Created2016
Description
The Mathematical and Theoretical Biology Institute (MTBI) is a summer research program for undergraduate students, largely from underrepresented minority groups. Founded in 1996, it serves as a 'life-long' mentorship program, providing continuous support for its students and alumni. This study investigates how MTBI supports student development in applied mathematical research. This includes identifying of motivational factors to pursue and develop capacity to complete higher education.
The theoretical lens of developmental psychologists Lev Vygotsky (1978, 1987) and Lois Holzman (2010) that sees learning and development as a social process is used. From this view student development in MTBI is attributed to the collaborative and creative way students co-create the process of becoming scientists. This results in building a continuing network of academic and professional relationships among peers and mentors, in which around three quarters of MTBI PhD graduates come from underrepresented groups.
The extent to which MTBI creates a Vygotskian learning environment is explored from the perspectives of participants who earned doctoral degrees. Previously hypothesized factors (Castillo-Garsow, Castillo-Chavez and Woodley, 2013) that affect participants’ educational and professional development are expanded on.
Factors identified by participants are a passion for the mathematical sciences; desire to grow; enriching collaborative and peer-like interactions; and discovering career options. The self-recognition that they had the ability to be successful, key element of the Vygotskian-Holzman theoretical framework, was a commonly identified theme for their educational development and professional growth.
Participants characterize the collaborative and creative aspects of MTBI. They reported that collaborative dynamics with peers were strengthened as they co-created a learning environment that facilitated and accelerated their understanding of the mathematics needed to address their research. The dynamics of collaboration allowed them to complete complex homework assignments, and helped them formulate and complete their projects. Participants identified the creative environments of their research projects as where creativity emerged in the dynamics of the program.
These data-driven findings characterize for the first time a summer program in the mathematical sciences as a Vygotskian-Holzman environment, that is, a `place’ where participants are seen as capable applied mathematicians, where the dynamics of collaboration and creativity are fundamental components.
The theoretical lens of developmental psychologists Lev Vygotsky (1978, 1987) and Lois Holzman (2010) that sees learning and development as a social process is used. From this view student development in MTBI is attributed to the collaborative and creative way students co-create the process of becoming scientists. This results in building a continuing network of academic and professional relationships among peers and mentors, in which around three quarters of MTBI PhD graduates come from underrepresented groups.
The extent to which MTBI creates a Vygotskian learning environment is explored from the perspectives of participants who earned doctoral degrees. Previously hypothesized factors (Castillo-Garsow, Castillo-Chavez and Woodley, 2013) that affect participants’ educational and professional development are expanded on.
Factors identified by participants are a passion for the mathematical sciences; desire to grow; enriching collaborative and peer-like interactions; and discovering career options. The self-recognition that they had the ability to be successful, key element of the Vygotskian-Holzman theoretical framework, was a commonly identified theme for their educational development and professional growth.
Participants characterize the collaborative and creative aspects of MTBI. They reported that collaborative dynamics with peers were strengthened as they co-created a learning environment that facilitated and accelerated their understanding of the mathematics needed to address their research. The dynamics of collaboration allowed them to complete complex homework assignments, and helped them formulate and complete their projects. Participants identified the creative environments of their research projects as where creativity emerged in the dynamics of the program.
These data-driven findings characterize for the first time a summer program in the mathematical sciences as a Vygotskian-Holzman environment, that is, a `place’ where participants are seen as capable applied mathematicians, where the dynamics of collaboration and creativity are fundamental components.
ContributorsEvangelista, Arlene Morales (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Holmes, Raquell M. (Committee member) / Mubayi, Anuj (Committee member) / Arizona State University (Publisher)
Created2015
Description
The 2009-10 influenza and the 2014-15 Ebola pandemics brought once again urgency to an old question: What are the limits on prediction and what can be proposed that is useful in the face of an epidemic outbreak?
This thesis looks first at the impact that limited access to vaccine stockpiles may have on a single influenza outbreak. The purpose is to highlight the challenges faced by populations embedded in inadequate health systems and to identify and assess ways of ameliorating the impact of resource limitations on public health policy.
Age-specific per capita constraint rates play an important role on the dynamics of communicable diseases and, influenza is, of course, no exception. Yet the challenges associated with estimating age-specific contact rates have not been decisively met. And so, this thesis attempts to connect contact theory with age-specific contact data in the context of influenza outbreaks in practical ways. In mathematical epidemiology, proportionate mixing is used as the preferred theoretical mixing structure and so, the frame of discussion of this dissertation follows this specific theoretical framework. The questions that drive this dissertation, in the context of influenza dynamics, proportionate mixing, and control, are:
I. What is the role of age-aggregation on the dynamics of a single outbreak? Or simply speaking, does the number and length of the age-classes used to model a population make a significant difference on quantitative predictions?
II. What would the age-specific optimal influenza vaccination policies be? Or, what are the age-specific vaccination policies needed to control an outbreak in the presence of limited or unlimited vaccine stockpiles?
Intertwined with the above questions are issues of resilience and uncertainty including, whether or not data collected on mixing (by social scientists) can be used effectively to address both questions in the context of influenza and proportionate mixing. The objective is to provide answers to these questions by assessing the role of aggregation (number and length of age classes) and model robustness (does the aggregation scheme selected makes a difference on influenza dynamics and control) via comparisons between purely data-driven model and proportionate mixing models.
This thesis looks first at the impact that limited access to vaccine stockpiles may have on a single influenza outbreak. The purpose is to highlight the challenges faced by populations embedded in inadequate health systems and to identify and assess ways of ameliorating the impact of resource limitations on public health policy.
Age-specific per capita constraint rates play an important role on the dynamics of communicable diseases and, influenza is, of course, no exception. Yet the challenges associated with estimating age-specific contact rates have not been decisively met. And so, this thesis attempts to connect contact theory with age-specific contact data in the context of influenza outbreaks in practical ways. In mathematical epidemiology, proportionate mixing is used as the preferred theoretical mixing structure and so, the frame of discussion of this dissertation follows this specific theoretical framework. The questions that drive this dissertation, in the context of influenza dynamics, proportionate mixing, and control, are:
I. What is the role of age-aggregation on the dynamics of a single outbreak? Or simply speaking, does the number and length of the age-classes used to model a population make a significant difference on quantitative predictions?
II. What would the age-specific optimal influenza vaccination policies be? Or, what are the age-specific vaccination policies needed to control an outbreak in the presence of limited or unlimited vaccine stockpiles?
Intertwined with the above questions are issues of resilience and uncertainty including, whether or not data collected on mixing (by social scientists) can be used effectively to address both questions in the context of influenza and proportionate mixing. The objective is to provide answers to these questions by assessing the role of aggregation (number and length of age classes) and model robustness (does the aggregation scheme selected makes a difference on influenza dynamics and control) via comparisons between purely data-driven model and proportionate mixing models.
ContributorsMorales, Romarie (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Mubayi, Anuj (Thesis advisor) / Towers, Sherry (Committee member) / Arizona State University (Publisher)
Created2016
Description
Statistical Methods have been widely used in understanding factors for clinical and public health data. Statistical hypotheses are procedures for testing pre-stated hypotheses. The development and properties of these procedures as well as their performance are based upon certain assumptions. Desirable properties of statistical tests are to maintain validity and to perform well even if these assumptions are not met. A statistical test that maintains such desirable properties is called robust. Mathematical models are typically mechanistic framework, used to study dynamic interactions between components (mechanisms) of a system, and how these interactions give rise to the changes in behavior (patterns) of the system as a whole over time.
In this thesis, I have developed a study that uses novel techniques to link robust statistical tests and mathematical modeling methods guided by limited data from developed and developing regions in order to address pressing clinical and epidemiological questions of interest. The procedure in this study consists of three primary steps, namely, data collection, uncertainty quantification in data, and linking dynamic model to collected data.
The first part of the study focuses on designing, collecting, and summarizing empirical data from the only national survey of hospitals ever conducted regarding patient controlled analgesia (PCA) practices among 168 hospitals across 40 states, in order to assess risks before putting patients on PCA. I used statistical relational models and exploratory data analysis to address the question. Risk factors assessed indicate a great concern for the safety of patients from one healthcare institution to other.
In the second part, I quantify uncertainty associated with data obtained from James A Lovell Federal Healthcare Center to primarily study the effect of Benign Prostatic Hypertrophy (BPH) on sleep architecture in patients with Obstructive Sleep Apnea (OSA). Patients with OSA and BPH demonstrated significant difference in their sleep architecture in comparison to patients without BPH. One of the ways to validate these differences in sleep architecture between the two groups may be to carry out a similar study that evaluates the effect of some other chronic disease on sleep architecture in patients with OSA.
Additionally, I also address theoretical statistical questions such as (1) how to estimate the distribution of a variable in order to retest null hypothesis when the sample size is limited, and (2) how changes on assumptions (like monotonicity and nonlinearity) translate into the effect of the independent variable on the outcome variable. To address these questions we use multiple techniques such as Partial Rank Correlation Coefficients (PRCC) based sensitivity analysis, Fractional Polynomials, and statistical relational models.
In the third part, my goal was to identify socio-economic-environment-related risk factors for Visceral Leishmaniasis (VL) and use the identified critical factors to develop a mathematical model to understand VL transmission dynamics when data is highly underreported. I primarily studied the role of age-specific- susceptibility and epidemiological quantities on the dynamics of VL in the Indian state of Bihar. Statistical results provided ideas on the choice of the modeling framework and estimates of model parameters.
In the conclusion, this study addressed three primary theoretical modeling-related questions (1) how to analyze collected data when sample size limited, and how modeling assumptions varies results of data analysis? (2) Is it possible to identify hidden associations and nonlinearity of these associations using such underpowered data and (3) how statistical models provide more reasonable structure to mathematical modeling framework that can be used in turn to understand dynamics of the system.
In this thesis, I have developed a study that uses novel techniques to link robust statistical tests and mathematical modeling methods guided by limited data from developed and developing regions in order to address pressing clinical and epidemiological questions of interest. The procedure in this study consists of three primary steps, namely, data collection, uncertainty quantification in data, and linking dynamic model to collected data.
The first part of the study focuses on designing, collecting, and summarizing empirical data from the only national survey of hospitals ever conducted regarding patient controlled analgesia (PCA) practices among 168 hospitals across 40 states, in order to assess risks before putting patients on PCA. I used statistical relational models and exploratory data analysis to address the question. Risk factors assessed indicate a great concern for the safety of patients from one healthcare institution to other.
In the second part, I quantify uncertainty associated with data obtained from James A Lovell Federal Healthcare Center to primarily study the effect of Benign Prostatic Hypertrophy (BPH) on sleep architecture in patients with Obstructive Sleep Apnea (OSA). Patients with OSA and BPH demonstrated significant difference in their sleep architecture in comparison to patients without BPH. One of the ways to validate these differences in sleep architecture between the two groups may be to carry out a similar study that evaluates the effect of some other chronic disease on sleep architecture in patients with OSA.
Additionally, I also address theoretical statistical questions such as (1) how to estimate the distribution of a variable in order to retest null hypothesis when the sample size is limited, and (2) how changes on assumptions (like monotonicity and nonlinearity) translate into the effect of the independent variable on the outcome variable. To address these questions we use multiple techniques such as Partial Rank Correlation Coefficients (PRCC) based sensitivity analysis, Fractional Polynomials, and statistical relational models.
In the third part, my goal was to identify socio-economic-environment-related risk factors for Visceral Leishmaniasis (VL) and use the identified critical factors to develop a mathematical model to understand VL transmission dynamics when data is highly underreported. I primarily studied the role of age-specific- susceptibility and epidemiological quantities on the dynamics of VL in the Indian state of Bihar. Statistical results provided ideas on the choice of the modeling framework and estimates of model parameters.
In the conclusion, this study addressed three primary theoretical modeling-related questions (1) how to analyze collected data when sample size limited, and how modeling assumptions varies results of data analysis? (2) Is it possible to identify hidden associations and nonlinearity of these associations using such underpowered data and (3) how statistical models provide more reasonable structure to mathematical modeling framework that can be used in turn to understand dynamics of the system.
ContributorsGonzalez, Beverly, 1980- (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Mubayi, Anuj (Thesis advisor) / Nuno, Miriam (Committee member) / Arizona State University (Publisher)
Created2015