Matching Items (48)
Description
Dopamine (DA) is a neurotransmitter involved in attention, goal oriented behavior, movement, reward learning, and short term and working memory. For the past four decades, mathematical and computational modeling approaches have been useful in DA research, and although every modeling approach has limitations, a model is an efficient way to generate and explore hypotheses. This work develops a model of DA dynamics in a representative, single DA neuron by integrating previous experimental, theoretical and computational research. The model consists of three compartments: the cytosol, the vesicles, and the extracellular space and forms the basis of a new mathematical paradigm for examining the dynamics of DA synthesis, storage, release and reuptake. The model can be driven by action potentials generated by any model of excitable membrane potential or even from experimentally induced depolarization voltage recordings. Here the model is forced by a previously published model of the excitable membrane of a mesencephalic DA neuron in order to study the biochemical processes involved in extracellular DA production. After demonstrating that the model exhibits realistic dynamics resembling those observed experimentally, the model is used to examine the functional changes in presynaptic mechanisms due to application of cocaine. Sensitivity analysis and numerical studies that focus on various possible mechanisms for the inhibition of DAT by cocaine provide insight for the complex interactions involved in DA dynamics. In particular, comparing numerical results for a mixed inhibition mechanism to those for competitive, non-competitive and uncompetitive inhibition mechanisms reveals many behavioral similarities for these different types of inhibition that depend on inhibition parameters and levels of cocaine. Placing experimental results within this context of mixed inhibition provides a possible explanation for the conflicting views of uptake inhibition mechanisms found in experimental neuroscience literature.
ContributorsTello-Bravo, David (Author) / Crook, Sharon M (Thesis advisor) / Greenwood, Priscilla E (Thesis advisor) / Baer, Steven M. (Committee member) / Castaneda, Edward (Committee member) / Castillo-Chavez, Carlos (Committee member) / Arizona State University (Publisher)
Created2012
Description
A sequence of models is developed to describe urban population growth in the context of the embedded physical, social and economic environments and an urban disease are developed. This set of models is focused on urban growth and the relationship between the desire to move and the utility derived from city life. This utility is measured in terms of the economic opportunities in the city, the level of human constructed amenity, and the level of amenity caused by the natural environment. The set of urban disease models is focused on examining prospects of eliminating a disease for which a vaccine does not exist. It is inspired by an outbreak of the vector-borne disease dengue fever in Peru, during 2000-2001.
ContributorsMurillo, D (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Anderies, John M (Thesis advisor) / Boone, Christopher (Committee member) / Arizona State University (Publisher)
Created2012
Description
This dissertation is intended to tie together a body of work which utilizes a variety of methods to study applied mathematical models involving heterogeneity often omitted with classical modeling techniques. I posit three cogent classifications of heterogeneity: physiological, behavioral, and local (specifically connectivity in this work). I consider physiological heterogeneity using the method of transport equations to study heterogeneous susceptibility to diseases in open populations (those with births and deaths). I then present three separate models of behavioral heterogeneity. An SIS/SAS model of gonorrhea transmission in a population of highly active men-who-have-sex-with-men (MSM) is presented to study the impact of safe behavior (prevention and self-awareness) on the prevalence of this endemic disease. Behavior is modeled in this examples via static parameters describing consistent condom use and frequency of STD testing. In an example of behavioral heterogeneity, in the absence of underlying dynamics, I present a generalization to ``test theory without an answer key" (also known as cultural consensus modeling or CCM). CCM is commonly used to study the distribution of cultural knowledge within a population. The generalized framework presented allows for selecting the best model among various extensions of CCM: multiple subcultures, estimating the degree to which individuals guess yes, and making competence homogenous in the population. This permits model selection based on the principle of information criteria. The third behaviorally heterogeneous model studies adaptive behavioral response based on epidemiological-economic theory within an $SIR$ epidemic setting. Theorems used to analyze the stability of such models with a generalized, non-linear incidence structure are adapted and applied to the case of standard incidence and adaptive incidence. As an example of study in spatial heterogeneity I provide an explicit solution to a generalization of the continuous time approximation of the Albert-Barabasi scale-free network algorithm. The solution is found by recursively solving the differential equations via integrating factors, identifying a pattern for the coefficients and then proving this observed pattern is consistent using induction. An application to disease dynamics on such evolving structures is then studied.
ContributorsMorin, Benjamin (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Hiebeler, David (Thesis advisor) / Hruschka, Daniel (Committee member) / Suslov, Sergei (Committee member) / Arizona State University (Publisher)
Created2012
Description
Diseases have been part of human life for generations and evolve within the population, sometimes dying out while other times becoming endemic or the cause of recurrent outbreaks. The long term influence of a disease stems from different dynamics within or between pathogen-host, that have been analyzed and studied by many researchers using mathematical models. Co-infection with different pathogens is common, yet little is known about how infection with one pathogen affects the host's immunological response to another. Moreover, no work has been found in the literature that considers the variability of the host immune health or that examines a disease at the population level and its corresponding interconnectedness with the host immune system. Knowing that the spread of the disease in the population starts at the individual level, this thesis explores how variability in immune system response within an endemic environment affects an individual's vulnerability, and how prone it is to co-infections. Immunology-based models of Malaria and Tuberculosis (TB) are constructed by extending and modifying existing mathematical models in the literature. The two are then combined to give a single nine-variable model of co-infection with Malaria and TB. Because these models are difficult to gain any insight analytically due to the large number of parameters, a phenomenological model of co-infection is proposed with subsystems corresponding to the individual immunology-based model of a single infection. Within this phenomenological model, the variability of the host immune health is also incorporated through three different pathogen response curves using nonlinear bounded Michaelis-Menten functions that describe the level or state of immune system (healthy, moderate and severely compromised). The immunology-based models of Malaria and TB give numerical results that agree with the biological observations. The Malaria--TB co-infection model gives reasonable results and these suggest that the order in which the two diseases are introduced have an impact on the behavior of both. The subsystems of the phenomenological models that correspond to a single infection (either of Malaria or TB) mimic much of the observed behavior of the immunology-based counterpart and can demonstrate different behavior depending on the chosen pathogen response curve. In addition, varying some of the parameters and initial conditions in the phenomenological model yields a range of topologically different mathematical behaviors, which suggests that this behavior may be able to be observed in the immunology-based models as well. The phenomenological models clearly replicate the qualitative behavior of primary and secondary infection as well as co-infection. The mathematical solutions of the models correspond to the fundamental states described by immunologists: virgin state, immune state and tolerance state. The phenomenological model of co-infection also demonstrates a range of parameter values and initial conditions in which the introduction of a second disease causes both diseases to grow without bound even though those same parameters and initial conditions did not yield unbounded growth in the corresponding subsystems. This results applies to all three states of the host immune system. In terms of the immunology-based system, this would suggest the following: there may be parameter values and initial conditions in which a person can clear Malaria or TB (separately) from their system but in which the presence of both can result in the person dying of one of the diseases. Finally, this thesis studies links between epidemiology (population level) and immunology in an effort to assess the impact of pathogen's spread within the population on the immune response of individuals. Models of Malaria and TB are proposed that incorporate the immune system of the host into a mathematical model of an epidemic at the population level.
ContributorsSoho, Edmé L (Author) / Wirkus, Stephen (Thesis advisor) / Castillo-Chavez, Carlos (Thesis advisor) / Chowell-Puente, Gerardo (Committee member) / Arizona State University (Publisher)
Created2011
Description
The Quantum Harmonic Oscillator is one of the most important models in Quantum Mechanics. Analogous to the classical mass vibrating back and forth on a spring, the quantum oscillator system has attracted substantial attention over the years because of its importance in many advanced and difficult quantum problems. This dissertation deals with solving generalized models of the time-dependent Schrodinger equation which are called generalized quantum harmonic oscillators, and these are characterized by an arbitrary quadratic Hamiltonian of linear momentum and position operators. The primary challenge in this work is that most quantum models with timedependence are not solvable explicitly, yet this challenge became the driving motivation for this work. In this dissertation, the methods used to solve the time-dependent Schrodinger equation are the fundamental singularity (or Green's function) and the Fourier (eigenfunction expansion) methods. Certain Riccati- and Ermakov-type systems arise, and these systems are highlighted and investigated. The overall aims of this dissertation are to show that quadratic Hamiltonian systems are completely integrable systems, and to provide explicit approaches to solving the time-dependent Schr¨odinger equation governed by an arbitrary quadratic Hamiltonian operator. The methods and results established in the dissertation are not yet well recognized in the literature, yet hold for high promise for further future research. Finally, the most recent results in the dissertation correspond to the harmonic oscillator group and its symmetries. A simple derivation of the maximum kinematical invariance groups of the free particle and quantum harmonic oscillator is constructed from the view point of the Riccati- and Ermakov-type systems, which shows an alternative to the traditional Lie Algebra approach. To conclude, a missing class of solutions of the time-dependent Schr¨odinger equation for the simple harmonic oscillator in one dimension is constructed. Probability distributions of the particle linear position and momentum, are emphasized with Mathematica animations. The eigenfunctions qualitatively differ from the traditional standing waves of the one-dimensional Schrodinger equation. The physical relevance of these dynamic states is still questionable, and in order to investigate their physical meaning, animations could also be created for the squeezed coherent states. This will be addressed in future work.
ContributorsLopez, Raquel (Author) / Suslov, Sergei K (Thesis advisor) / Radunskaya, Ami (Committee member) / Castillo-Chavez, Carlos (Committee member) / Platte, Rodrigo (Committee member) / Arizona State University (Publisher)
Created2012
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
Diabetes is a disease characterized by reduced insulin action and secretion, leading to elevated blood glucose. In the 1990s, studies showed that intravenous injection of fatty acids led to a sharp negative response in insulin action that subsided hours after the injection. The molecule associated with diminished insulin signalling response was a byproduct of fatty acids, diacylglycerol. This dissertation is focused on the formulation of a model built around the known mechanisms of glucose and fatty acid storage and metabolism within myocytes, as well as downstream effects of diacylglycerol on insulin action. Data from euglycemic-hyperinsulinemic clamp with fatty acid infusion studies are used to validate the qualitative behavior of the model and estimate parameters. The model closely matches clinical data and suggests a new metric to determine quantitative measurements of insulin action downregulation. Analysis and numerical simulation of the long term, piecewise smooth system of ordinary differential equations demonstrates a discontinuous bifurcation implicating nutrient excess as a driver of muscular insulin resistance.
ContributorsBurkow, Daniel Harrison (Author) / Li, Jiaxu (Thesis advisor) / Castillo-Chavez, Carlos (Thesis advisor) / Kuang, Yang (Committee member) / Holechek, Susan (Committee member) / Arizona State University (Publisher)
Created2017
Description
In this dissertation the potential impact of some social, cultural and economic factors on
Ebola Virus Disease (EVD) dynamics and control are studied. In Chapter two, the inability
to detect and isolate a large fraction of EVD-infected individuals before symptoms onset is
addressed. A mathematical model, calibrated with data from the 2014 West African outbreak,
is used to show the dynamics of EVD control under various quarantine and isolation
effectiveness regimes. It is shown that in order to make a difference it must reach a high
proportion of the infected population. The effect of EVD-dead bodies has been incorporated
in the quarantine effectiveness. In Chapter four, the potential impact of differential
risk is assessed. A two-patch model without explicitly incorporate quarantine is used to
assess the impact of mobility on communities at risk of EVD. It is shown that the
overall EVD burden may lessen when mobility in this artificial high-low risk society is allowed.
The cost that individuals in the low-risk patch must pay, as measured by secondary
cases is highlighted. In Chapter five a model explicitly incorporating patch-specific quarantine
levels is used to show that quarantine a large enough proportion of the population
under effective isolation leads to a measurable reduction of secondary cases in the presence
of mobility. It is shown that sharing limited resources can improve the effectiveness of
EVD effective control in the two-patch high-low risk system. Identifying the conditions
under which the low-risk community would be willing to accept the increases in EVD risk,
needed to reduce the total number of secondary cases in a community composed of two
patches with highly differentiated risks has not been addressed. In summary, this dissertation
looks at EVD dynamics within an idealized highly polarized world where resources
are primarily in the hands of a low-risk community – a community of lower density, higher
levels of education and reasonable health services – that shares a “border” with a high-risk
community that lacks minimal resources to survive an EVD outbreak.
Ebola Virus Disease (EVD) dynamics and control are studied. In Chapter two, the inability
to detect and isolate a large fraction of EVD-infected individuals before symptoms onset is
addressed. A mathematical model, calibrated with data from the 2014 West African outbreak,
is used to show the dynamics of EVD control under various quarantine and isolation
effectiveness regimes. It is shown that in order to make a difference it must reach a high
proportion of the infected population. The effect of EVD-dead bodies has been incorporated
in the quarantine effectiveness. In Chapter four, the potential impact of differential
risk is assessed. A two-patch model without explicitly incorporate quarantine is used to
assess the impact of mobility on communities at risk of EVD. It is shown that the
overall EVD burden may lessen when mobility in this artificial high-low risk society is allowed.
The cost that individuals in the low-risk patch must pay, as measured by secondary
cases is highlighted. In Chapter five a model explicitly incorporating patch-specific quarantine
levels is used to show that quarantine a large enough proportion of the population
under effective isolation leads to a measurable reduction of secondary cases in the presence
of mobility. It is shown that sharing limited resources can improve the effectiveness of
EVD effective control in the two-patch high-low risk system. Identifying the conditions
under which the low-risk community would be willing to accept the increases in EVD risk,
needed to reduce the total number of secondary cases in a community composed of two
patches with highly differentiated risks has not been addressed. In summary, this dissertation
looks at EVD dynamics within an idealized highly polarized world where resources
are primarily in the hands of a low-risk community – a community of lower density, higher
levels of education and reasonable health services – that shares a “border” with a high-risk
community that lacks minimal resources to survive an EVD outbreak.
ContributorsEspinoza Cortes, Baltazar (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Kang, Yun (Committee member) / Safan, Muntaser (Committee member) / Arizona State University (Publisher)
Created2018
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
Foraging strategies in social animals are often shaped by change in an organism's natural surrounding. Foraging behavior can hence be highly plastic, time, and condition dependent. The motivation of my research is to explore the effects of dispersal behavior in predators or parasites on population dynamics in heterogeneous environments by developing varied models in different contexts through closely working with ecologists. My models include Ordinary Differential Equation (ODE)-type meta population models and Delay Differential Equation (DDE) models with validation through data. I applied dynamical theory and bifurcation theory with carefully designed numerical simulations to have a better understanding on the profitability and cost of an adaptive dispersal in organisms. My work on the prey-predator models provide important insights on how different dispersal strategies may have different impacts on the spatial patterns and also shows that the change of dispersal strategy in organisms may have stabilizing or destabilizing effects leading to extinction or coexistence of species. I also develop models for honeybee population dynamics and its interaction with the parasitic Varroa mite. At first, I investigate the effect of dispersal on honeybee colonies under infestation by the Varroa mites. I then provide another single patch model by considering a stage structure time delay system from brood to adult honeybee. Through a close collaboration with a biologist, a honeybee and mite population data was first used to validate my model and I estimated certain unknown parameters by utilizing least square Monte Carlo method. My analytical, bifurcations, sensitivity analysis, and numerical studies first reveal the dynamical outcomes of migration. In addition, the results point us in the direction of the most sensitive life history parameters affecting the population size of a colony. These results provide novel insights on the effects of foraging and Varroa mites on colony survival.
ContributorsMessan, Komi Segno (Author) / Kang, Yun (Thesis advisor) / Castillo-Chavez, Carlos (Thesis advisor) / Degrandi-Hoffman, Gloria D (Committee member) / Janssen, Marco A (Committee member) / Arizona State University (Publisher)
Created2017