Matching Items (9)
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- All Subjects: Applied Mathematics
- Creators: Mubayi, Anuj
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
This dissertation explores the impact of environmental dependent risk on disease dynamics within a Lagrangian modeling perspective; where the identity (defined by place of residency) of individuals is preserved throughout the epidemic process. In Chapter Three, the impact of individuals who refuse to be vaccinated is explored. MMR vaccination and birth rate data from the State of California are used to determine the impact of the anti-vaccine movement on the dynamics of growth of the anti-vaccine sub-population. Dissertation results suggest that under realistic California social dynamics scenarios, it is not possible to revert the influence of anti-vaccine
contagion. In Chapter Four, the dynamics of Zika virus are explored in two highly distinct idealized environments defined by a parameter that models highly distinctive levels of risk, the result of vector and host density and vector control measures. The underlying assumption is that these two communities are intimately connected due to economics with the impact of various patterns of mobility being incorporated via
the use of residency times. In short, a highly heterogeneous community is defined by its risk of acquiring a Zika infection within one of two "spaces," one lacking access to health services or effective vector control policies (lack of resources or ignored due to high levels of crime, or poverty, or both). Low risk regions are defined as those with access to solid health facilities and where vector control measures are implemented routinely. It was found that the better connected these communities are, the existence of communities where mobility between risk regions is not hampered, lower the overall, two patch Zika prevalence. Chapter Five focuses on the dynamics of tuberculosis (TB), a communicable disease, also on an idealized high-low risk set up. The impact of mobility within these two highly distinct TB-risk environments on the dynamics and control of this disease is systematically explored. It is found that collaboration and mobility, under some circumstances, can reduce the overall TB burden.
contagion. In Chapter Four, the dynamics of Zika virus are explored in two highly distinct idealized environments defined by a parameter that models highly distinctive levels of risk, the result of vector and host density and vector control measures. The underlying assumption is that these two communities are intimately connected due to economics with the impact of various patterns of mobility being incorporated via
the use of residency times. In short, a highly heterogeneous community is defined by its risk of acquiring a Zika infection within one of two "spaces," one lacking access to health services or effective vector control policies (lack of resources or ignored due to high levels of crime, or poverty, or both). Low risk regions are defined as those with access to solid health facilities and where vector control measures are implemented routinely. It was found that the better connected these communities are, the existence of communities where mobility between risk regions is not hampered, lower the overall, two patch Zika prevalence. Chapter Five focuses on the dynamics of tuberculosis (TB), a communicable disease, also on an idealized high-low risk set up. The impact of mobility within these two highly distinct TB-risk environments on the dynamics and control of this disease is systematically explored. It is found that collaboration and mobility, under some circumstances, can reduce the overall TB burden.
ContributorsMoreno Martínez, Victor Manuel (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Kang, Yun (Committee member) / Mubayi, Anuj (Committee member) / Arizona State University (Publisher)
Created2018
Description
The retina is the lining in the back of the eye responsible for vision. When light photons hits the retina, the photoreceptors within the retina respond by sending impulses to the optic nerve, which connects to the brain. If there is injury to the eye or heredity retinal problems, this part can become detached. Detachment leads to loss of nutrients, such as oxygen and glucose, to the cells in the eye and causes cell death. Sometimes the retina is able to be surgically reattached. If the photoreceptor cells have not died and the reattachment is successful, then these cells are able to regenerate their outer segments (OS) which are essential for their functionality and vitality. In this work we will explore how the regrowth of the photoreceptor cells in a healthy eye after retinal detachment can lead to a deeper understanding of how eye cells take up nutrients and regenerate. This work uses a mathematical model for a healthy eye in conjunction with data for photoreceptors' regrowth and decay. The parameters for the healthy eye model are estimated from the data and the ranges of these parameter values are centered +/- 10\% away from these values are used for sensitivity analysis. Using parameter estimation and sensitivity analysis we can better understand how certain processes represented by these parameters change within the model as a result of retinal detachment. Having a deeper understanding for any sort of photoreceptor death and growth can be used by the greater scientific community to help with these currently irreversible conditions that lead to blindness, such as retinal detachment. The analysis in this work shows that maximizing the carrying capacity of the trophic pool and the rate of RDCVF, as well as minimizing nutrient withdrawal of the rods and the cones from the trophic pool results in both the most regrowth and least cell death in retinal detachment.
ContributorsGoldman, Miriam Ayla (Author) / Camacho, Erikia (Thesis director) / Wirkus, Stephen (Committee member) / School of Mathematical and Natural Sciences (Contributor, Contributor) / Barrett, The Honors College (Contributor)
Created2017-05
Description
The Visceral Leishmaniasis (VL) is primarily endemic in five countries, with India and Sudan having the highest burden. The risk factors associated with VL are either unknown in some regions or vary drastically among empirical studies. Here, a dynamical model, motivated and informed by field data from the literature, is analyzed and employed to identify and quantify the impact of region dependent risks on the VL transmission dynamics. Parameter estimation procedures were developed using model-derived quantities and empirical data from multiple resources. The dynamics of VL depend on the estimates of the control reproductive number, RC, interpreted as the average number of secondary infections generated by a single infectious individual during the infectious period. The distribution of RC was estimated for both India (with mean 2.1 ± 1.1) and Sudan (with mean 1.45 ± 0.57). This suggests that VL can be established in naive regions of India more easily than in naive regions of Sudan. The parameter sensitivity analysis on RC suggests that the average biting rate and transmission probabilities between host and vector are among the most sensitive parameters for both countries. The comparative assessment of VL transmission dynamics in both India and Sudan was carried out by parameter sensitivity analysis on VL-related prevalences (such as prevalences of asymptomatic hosts, symptomatic hosts, and infected vectors). The results identify that the treatment and symptoms’ developmental rates are parameters that are highly sensitive to VL symptomatic and asymptomatic host prevalence, respectively, for both countries. It is found that the estimates of transmission probability are significantly different between India (from human to sandflies with mean of 0.39 ± 0.12; from sandflies to human with mean 0.0005 ± 0.0002) and Sudan (from human to sandflies with mean 0.26 ± 0.07; from sandflies to human with mean 0.0002 ± 0.0001). The results have significant implications for elimination. An increasing focus on elimination requires a review of priorities within the VL control agenda. The development of systematic implementation of control programs based on identified risk factors (such as monitoring of asymptomatically infected individuals) has a high transmission-blocking potential.
ContributorsBarley, Kamal K (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Mubayi, Anuj (Thesis advisor) / Safan, Muntaser (Committee member) / Arizona State University (Publisher)
Created2016
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 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
Neglected tropical diseases (NTDs) comprise of diverse communicable diseases that affect mostly the developing economies of the world, the “neglected” populations. The NTDs Visceral Leishmaniasis (VL) and Soil-transmitted Helminthiasis (STH) are among the top contributors of global mortality and/or morbidity. They affect resource-limited regions (poor health-care literacy, infrastructure, etc.) and patients’ treatment behavior is irregular due to the social constraints. Through two case studies, VL in India and STH in Ghana, this work aims to: (i) identify the additional and potential hidden high-risk population and its behaviors critical for improving interventions and surveillance; (ii) develop models with those behaviors to study the role of improved control programs on diseases’ dynamics; (iii) optimize resources for treatment-related interventions.
Treatment non-adherence is a less focused (so far) but crucial factor for the hindrance in WHO’s past VL elimination goals. Moreover, treatment non-adherers, hidden from surveillance, lead to high case-underreporting. Dynamical models are developed capturing the role of treatment-related human behaviors (patients’ infectivity, treatment access and non-adherence) on VL dynamics. The results suggest that the average duration of treatment adherence must be increased from currently 10 days to 17 days for a 28-day Miltefosine treatment to eliminate VL.
For STH, children are considered as a high-risk group due to their hygiene behaviors leading to higher exposure to contamination. Hence, Ghana, a resource-limited country, currently implements a school-based Mass Drug Administration (sMDA) program only among children. School staff (adults), equally exposed to this high environmental contamination of STH, are largely ignored under the current MDA program. Cost-effective MDA policies were modeled and compared using alternative definitions of “high-risk population”. This work optimized and evaluated how MDA along with the treatment for high-risk adults makes a significant improvement in STH control under the same budget. The criticality of risk-structured modeling depends on the infectivity coefficient being substantially different for the two adult risk groups.
This dissertation pioneers in highlighting the cruciality of treatment-related risk groups for NTD-control. It provides novel approaches to quantify relevant metrics and impact of population factors. Compliance with the principles and strategies from this study would require a change in political thinking in the neglected regions in order to achieve persistent NTD-control.
Treatment non-adherence is a less focused (so far) but crucial factor for the hindrance in WHO’s past VL elimination goals. Moreover, treatment non-adherers, hidden from surveillance, lead to high case-underreporting. Dynamical models are developed capturing the role of treatment-related human behaviors (patients’ infectivity, treatment access and non-adherence) on VL dynamics. The results suggest that the average duration of treatment adherence must be increased from currently 10 days to 17 days for a 28-day Miltefosine treatment to eliminate VL.
For STH, children are considered as a high-risk group due to their hygiene behaviors leading to higher exposure to contamination. Hence, Ghana, a resource-limited country, currently implements a school-based Mass Drug Administration (sMDA) program only among children. School staff (adults), equally exposed to this high environmental contamination of STH, are largely ignored under the current MDA program. Cost-effective MDA policies were modeled and compared using alternative definitions of “high-risk population”. This work optimized and evaluated how MDA along with the treatment for high-risk adults makes a significant improvement in STH control under the same budget. The criticality of risk-structured modeling depends on the infectivity coefficient being substantially different for the two adult risk groups.
This dissertation pioneers in highlighting the cruciality of treatment-related risk groups for NTD-control. It provides novel approaches to quantify relevant metrics and impact of population factors. Compliance with the principles and strategies from this study would require a change in political thinking in the neglected regions in order to achieve persistent NTD-control.
ContributorsThakur, Mugdha (Author) / Mubayi, Anuj (Thesis advisor) / Hurtado, Ana M (Committee member) / Paaijmans, Krijn (Committee member) / Michael, Edwin (Committee member) / Arizona State University (Publisher)
Created2020
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
The dissertation addresses questions tied in to the challenges posed by the impact of environmental factors on the nonlinear dynamics of social upward mobility. The proportion of educated individuals from various socio-economic backgrounds is used as a proxy for the environmental impact on the status quo state.
Chapter 1 carries out a review of the mobility models found in the literature and sets the economic context of this dissertation. Chapter 2 explores a simple model that considers poor and rich classes and the impact that educational success may have on altering mobility patterns. The role of the environment is modeled through the use of a modified version of the invasion/extinction model of Richard Levins. Chapter 3 expands the socio-economic classes to include a large middle class to study the role of social mobility in the presence of higher heterogeneity. Chapter 4 includes demographic growth and explores what would be the time scales needed to accelerate mobility. The dissertation asked how long it will take to increase by 22% the proportion of educated from the poor classes under demographic versus non-demographic growth conditions. Chapter 5 summarizes results and includes a discussion of results. It also explores ways of modeling the influence of nonlinear dynamics of mobility, via exogenous factors. Finally, Chapter 6 presents economic perspectives about the role of environmental influence on college success. The framework can be used to incorporate the impact of economic factors and social changes, such as unemployment, or gap between the haves and have nots. The dissertation shows that peer influence (poor influencing the poor) has a larger effect than class influence (rich influencing the poor). Additionally, more heterogeneity may ease mobility of groups but results depend on initial conditions. Finally, average well-being of the community and income disparities may improve over time. Finally, population growth may extend time scales needed to achieve a specific goal of educated poor.
Chapter 1 carries out a review of the mobility models found in the literature and sets the economic context of this dissertation. Chapter 2 explores a simple model that considers poor and rich classes and the impact that educational success may have on altering mobility patterns. The role of the environment is modeled through the use of a modified version of the invasion/extinction model of Richard Levins. Chapter 3 expands the socio-economic classes to include a large middle class to study the role of social mobility in the presence of higher heterogeneity. Chapter 4 includes demographic growth and explores what would be the time scales needed to accelerate mobility. The dissertation asked how long it will take to increase by 22% the proportion of educated from the poor classes under demographic versus non-demographic growth conditions. Chapter 5 summarizes results and includes a discussion of results. It also explores ways of modeling the influence of nonlinear dynamics of mobility, via exogenous factors. Finally, Chapter 6 presents economic perspectives about the role of environmental influence on college success. The framework can be used to incorporate the impact of economic factors and social changes, such as unemployment, or gap between the haves and have nots. The dissertation shows that peer influence (poor influencing the poor) has a larger effect than class influence (rich influencing the poor). Additionally, more heterogeneity may ease mobility of groups but results depend on initial conditions. Finally, average well-being of the community and income disparities may improve over time. Finally, population growth may extend time scales needed to achieve a specific goal of educated poor.
ContributorsMontalvo, Cesar Paul (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Mubayi, Anuj (Thesis advisor) / Perrings, Charles (Committee member) / Kang, Yun (Committee member) / Arizona State University (Publisher)
Created2020