Matching Items (63)
Description
Infectious diseases are a leading cause of death worldwide. With the development of drugs, vaccines and antibiotics, it was believed that for the first time in human history diseases would no longer be a major cause of mortality. Newly emerging diseases, re-emerging diseases and the emergence of microorganisms resistant to existing treatment have forced us to re-evaluate our optimistic perspective. In this study, a simple mathematical framework for super-infection is considered in order to explore the transmission dynamics of drug-resistance. Through its theoretical analysis, we identify the conditions necessary for the coexistence between sensitive strains and drug-resistant strains. Farther, in order to investigate the effectiveness of control measures, the model is extended so as to include vaccination and treatment. The impact that these preventive and control measures may have on its disease dynamics is evaluated. Theoretical results being confirmed via numerical simulations. Our theoretical results on two-strain drug-resistance models are applied in the context of Malaria, antimalarial drugs, and the administration of a possible partially effective vaccine. The objective is to develop a monitoring epidemiological framework that help evaluate the impact of antimalarial drugs and partially-effective vaccine in reducing the disease burden at the population level. Optimal control theory is applied in the context of this framework in order to assess the impact of time dependent cost-effective treatment efforts. It is shown that cost-effective combinations of treatment efforts depend on the population size, cost of implementing treatment controls, and the parameters of the model. We use these results to identify optimal control strategies for several scenarios.
ContributorsUrdapilleta, Alicia (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Wang, Xiaohong (Thesis advisor) / Wirkus, Stephen (Committee member) / Camacho, Erika (Committee member) / Arizona State University (Publisher)
Created2011
Description
Semiconductor nanowires are featured by their unique one-dimensional structure which makes them promising for small scale electronic and photonic device applications. Among them, III-V material nanowires are particularly outstanding due to their good electronic properties. In bulk, these materials reveal electron mobility much higher than conventional silicon based devices, for example at room temperature, InAs field effect transistor (FET) has electron mobility of 40,000 cm2/Vs more than 10 times of Si FET. This makes such materials promising for high speed nanowire FETs. With small bandgap, such as 0.354 eV for InAs and 1.52 eV for GaAs, it does not need high voltage to turn on such devices which leads to low power consumption devices. Another feature of direct bandgap allows their applications of optoelectronic devices such as avalanche photodiodes. However, there are challenges to face up. Due to their large surface to volume ratio, nanowire devices typically are strongly affected by the surface states. Although nanowires can be grown into single crystal structure, people observe crystal defects along the wires which can significantly affect the performance of devices. In this work, FETs made of two types of III-V nanowire, GaAs and InAs, are demonstrated. These nanowires are grown by catalyst-free MOCVD growth method. Vertically nanowires are transferred onto patterned substrates for coordinate calibration. Then electrodes are defined by e-beam lithography followed by deposition of contact metals. Prior to metal deposition, however, the substrates are dipped in ammonium hydroxide solution to remove native oxide layer formed on nanowire surface. Current vs. source-drain voltage with different gate bias are measured at room temperature. GaAs nanowire FETs show photo response while InAs nanowire FETs do not show that. Surface passivation is performed on GaAs FETs by using ammonium surfide solution. The best results on current increase is observed with around 20-30 minutes chemical treatment time. Gate response measurements are performed at room temperature, from which field effect mobility as high as 1490 cm2/Vs is extracted for InAs FETs. One major contributor for this is stacking faults defect existing along nanowires. For InAs FETs, thermal excitations observed from temperature dependent results which leads us to investigate potential barriers.
ContributorsLiang, Hanshuang (Author) / Yu, Hongbin (Thesis advisor) / Ferry, David (Committee member) / Tracy, Clarence (Committee member) / Arizona State University (Publisher)
Created2011
Description
The concept of vaccination dates back further than Edward Jenner's first vaccine using cowpox pustules to confer immunity against smallpox in 1796. Nevertheless, it was Jenner's success that gave vaccines their name and made vaccinia virus (VACV) of particular interest. More than 200 years later there is still the need to understand vaccination from vaccine design to prediction of vaccine efficacy using mathematical models. Post-exposure vaccination with VACV has been suggested to be effective if administered within four days of smallpox exposure although this has not been definitively studied in humans. The first and second chapters analyze post-exposure prophylaxis of VACV in an animal model using v50ΔB13RMγ, a recombinant VACV expressing murine interferon gamma (IFN-γ) also known as type II IFN. While untreated animals infected with wild type VACV die by 10 days post-infection (dpi), animals treated with v50ΔB13RMγ 1 dpi had decreased morbidity and 100% survival. Despite these differences, the viral load was similar in both groups suggesting that v50ΔB13RMγ acts as an immunoregulator rather than as an antiviral. One of the main characteristics of VACV is its resistance to type I IFN, an effect primarily mediated by the E3L protein, which has a Z-DNA binding domain and a double-stranded RNA (dsRNA) binding domain. In the third chapter a VACV that independently expresses both domains of E3L was engineered and compared to wild type in cells in culture. The dual expression virus was unable to replicate in the JC murine cell line where both domains are needed together for replication. Moreover, phosphorylation of the dsRNA dependent protein kinase (PKR) was observed at late times post-infection which indicates that both domains need to be linked together in order to block the IFN response. Because smallpox has already been eradicated, the utility of mathematical modeling as a tool for predicting disease spread and vaccine efficacy was explored in the last chapter using dengue as a disease model. Current modeling approaches were reviewed and the 2000-2001 dengue outbreak in a Peruvian region was analyzed. This last section highlights the importance of interdisciplinary collaboration and how it benefits research on infectious diseases.
ContributorsHolechek, Susan A (Author) / Jacobs, Bertram L (Thesis advisor) / Castillo-Chavez, Carlos (Committee member) / Frasch, Wayne (Committee member) / Hogue, Brenda (Committee member) / Stout, Valerie (Committee member) / Arizona State University (Publisher)
Created2011
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
This study contributes to the ongoing discussion of Mathematical Knowledge for Teaching (MKT). It investigates the case of Rico, a high school mathematics teacher who had become known to his colleagues and his students as a superbly effective mathematics teacher. His students not only developed excellent mathematical skills, they also developed deep understanding of the mathematics they learned. Moreover, Rico redesigned his curricula and instruction completely so that they provided a means of support for his students to learn mathematics the way he intended. The purpose of this study was to understand the sources of Rico's effectiveness. The data for this study was generated in three phases. Phase I included videos of Rico's lessons during one semester of an Algebra II course, post-lesson reflections, and Rico's self-constructed instructional materials. An analysis of Phase I data led to Phase II, which consisted of eight extensive stimulated-reflection interviews with Rico. Phase III consisted of a conceptual analysis of the prior phases with the aim of creating models of Rico's mathematical conceptions, his conceptions of his students' mathematical understandings, and his images of instruction and instructional design. Findings revealed that Rico had developed profound personal understandings, grounded in quantitative reasoning, of the mathematics that he taught, and profound pedagogical understandings that supported these very same ways of thinking in his students. Rico's redesign was driven by three factors: (1) the particular way in which Rico himself understood the mathematics he taught, (2) his reflective awareness of those ways of thinking, and (3) his ability to envision what students might learn from different instructional approaches. Rico always considered what someone might already need to understand in order to understand "this" in the way he was thinking of it, and how understanding "this" might help students understand related ideas or methods. Rico's continual reflection on the mathematics he knew so as to make it more coherent, and his continual orientation to imagining how these meanings might work for students' learning, made Rico's mathematics become a mathematics of students--impacting how he assessed his practice and engaging him in a continual process of developing MKT.
ContributorsLage Ramírez, Ana Elisa (Author) / Thompson, Patrick W. (Thesis advisor) / Carlson, Marilyn P. (Committee member) / Castillo-Chavez, Carlos (Committee member) / Saldanha, Luis (Committee member) / Middleton, James A. (Committee member) / Arizona State University (Publisher)
Created2011
Description
Solution methods for certain linear and nonlinear evolution equations are presented in this dissertation. Emphasis is placed mainly on the analytical treatment of nonautonomous differential equations, which are challenging to solve despite the existent numerical and symbolic computational software programs available. Ideas from the transformation theory are adopted allowing one to solve the problems under consideration from a non-traditional perspective. First, the Cauchy initial value problem is considered for a class of nonautonomous and inhomogeneous linear diffusion-type equation on the entire real line. Explicit transformations are used to reduce the equations under study to their corresponding standard forms emphasizing on natural relations with certain Riccati(and/or Ermakov)-type systems. These relations give solvability results for the Cauchy problem of the parabolic equation considered. The superposition principle allows to solve formally this problem from an unconventional point of view. An eigenfunction expansion approach is also considered for this general evolution equation. Examples considered to corroborate the efficacy of the proposed solution methods include the Fokker-Planck equation, the Black-Scholes model and the one-factor Gaussian Hull-White model. The results obtained in the first part are used to solve the Cauchy initial value problem for certain inhomogeneous Burgers-type equation. The connection between linear (the Diffusion-type) and nonlinear (Burgers-type) parabolic equations is stress in order to establish a strong commutative relation. Traveling wave solutions of a nonautonomous Burgers equation are also investigated. Finally, it is constructed explicitly the minimum-uncertainty squeezed states for quantum harmonic oscillators. They are derived by the action of corresponding maximal kinematical invariance group on the standard ground state solution. It is shown that the product of the variances attains the required minimum value only at the instances that one variance is a minimum and the other is a maximum, when the squeezing of one of the variances occurs. Such explicit construction is possible due to the relation between the diffusion-type equation studied in the first part and the time-dependent Schrodinger equation. A modication of the radiation field operators for squeezed photons in a perfect cavity is also suggested with the help of a nonstandard solution of Heisenberg's equation of motion.
ContributorsVega-Guzmán, José Manuel, 1982- (Author) / Sulov, Sergei K (Thesis advisor) / Castillo-Chavez, Carlos (Thesis advisor) / Platte, Rodrigo (Committee member) / Chowell-Puente, Gerardo (Committee member) / Arizona State University (Publisher)
Created2013
Description
Olfaction is an important sensory modality for behavior since odors inform animals of the presence of food, potential mates, and predators. The fruit fly, Drosophila melanogaster, is a favorable model organism for the investigation of the biophysical mechanisms that contribute to olfaction because its olfactory system is anatomically similar to but simpler than that of vertebrates. In the Drosophila olfactory system, sensory transduction takes place in olfactory receptor neurons housed in the antennae and maxillary palps on the front of the head. The first stage of olfactory processing resides in the antennal lobe, where the structural unit is the glomerulus. There are at least three classes of neurons in the antennal lobe - excitatory projection neurons, excitatory local neurons, and inhibitory local neurons. The arborizations of the local neurons are confined to the antennal lobe, and output from the antennal lobe is carried by projection neurons to higher regions of the brain. Different views exist of how circuits of the Drosophila antennal lobe translate input from the olfactory receptor neurons into projection neuron output. We construct a conductance based neuronal network model of the Drosophila antennal lobe with the aim of understanding possible mechanisms within the antennal lobe that account for the variety of projection neuron activity observed in experimental data. We explore possible outputs obtained from olfactory receptor neuron input that mimic experimental recordings under different connectivity paradigms. First, we develop realistic minimal cell models for the excitatory local neurons, inhibitory local neurons, and projections neurons based on experimental data for Drosophila channel kinetics, and explore the firing characteristics and mathematical structure of these models. We then investigate possible interglomerular and intraglomerular connectivity patterns in the Drosophila antennal lobe, where olfactory receptor neuron input to the antennal lobe is modeled with Poisson spike trains, and synaptic connections within the antennal lobe are mediated by chemical synapses and gap junctions as described in the Drosophila antennal lobe literature. Our simulation results show that inhibitory local neurons spread inhibition among all glomeruli, where projection neuron responses are decreased relatively uniformly for connections of synaptic strengths that are homogeneous. Also, in the case of homogeneous excitatory synaptic connections, the excitatory local neuron network facilitates odor detection in the presence of weak stimuli. Excitatory local neurons can spread excitation from projection neurons that receive more input from olfactory receptor neurons to projection neurons that receive less input from olfactory receptor neurons. For the parameter values for the network models associated with these results, eLNs decrease the ability of the network to discriminate among single odors.
ContributorsLuli, Dori (Author) / Crook, Sharon (Thesis advisor) / Baer, Steven (Committee member) / Castillo-Chavez, Carlos (Committee member) / Smith, Brian (Committee member) / Arizona State University (Publisher)
Created2013
Description
Mathematical modeling of infectious diseases can help public health officials to make decisions related to the mitigation of epidemic outbreaks. However, over or under estimations of the morbidity of any infectious disease can be problematic. Therefore, public health officials can always make use of better models to study the potential implication of their decisions and strategies prior to their implementation. Previous work focuses on the mechanisms underlying the different epidemic waves observed in Mexico during the novel swine origin influenza H1N1 pandemic of 2009 and showed extensions of classical models in epidemiology by adding temporal variations in different parameters that are likely to change during the time course of an epidemic, such as, the influence of media, social distancing, school closures, and how vaccination policies may affect different aspects of the dynamics of an epidemic. This current work further examines the influence of different factors considering the randomness of events by adding stochastic processes to meta-population models. I present three different approaches to compare different stochastic methods by considering discrete and continuous time. For the continuous time stochastic modeling approach I consider the continuous-time Markov chain process using forward Kolmogorov equations, for the discrete time stochastic modeling I consider stochastic differential equations using Wiener's increment and Poisson point increments, and also I consider the discrete-time Markov chain process. These first two stochastic modeling approaches will be presented in a one city and two city epidemic models using, as a base, our deterministic model. The last one will be discussed briefly on a one city SIS and SIR-type model.
ContributorsCruz-Aponte, Maytee (Author) / Wirkus, Stephen A. (Thesis advisor) / Castillo-Chavez, Carlos (Thesis advisor) / Camacho, Erika T. (Committee member) / Kang, Yun (Committee member) / Arizona State University (Publisher)
Created2014
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
ABSTRACT An Ensemble Monte Carlo (EMC) computer code has been developed to simulate, semi-classically, spin-dependent electron transport in quasi two-dimensional (2D) III-V semiconductors. The code accounts for both three-dimensional (3D) and quasi-2D transport, utilizing either 3D or 2D scattering mechanisms, as appropriate. Phonon, alloy, interface roughness, and impurity scattering mechanisms are included, accounting for the Pauli Exclusion Principle via a rejection algorithm. The 2D carrier states are calculated via a self-consistent 1D Schrödinger-3D-Poisson solution in which the charge distribution of the 2D carriers in the quantization direction is taken as the spatial distribution of the squared envelope functions within the Hartree approximation. The wavefunctions, subband energies, and 2D scattering rates are updated periodically by solving a series of 1D Schrödinger wave equations (SWE) over the real-space domain of the device at fixed time intervals. The electrostatic potential is updated by periodically solving the 3D Poisson equation. Spin-polarized transport is modeled via a spin density-matrix formalism that accounts for D'yakanov-Perel (DP) scattering. Also, the code allows for the easy inclusion of additional scattering mechanisms and structural modifications to devices. As an application of the simulator, the current voltage characteristics of an InGaAs/InAlAs HEMT are simulated, corresponding to nanoscale III-V HEMTs currently being fabricated by Intel Corporation. The comparative effects of various scattering parameters, material properties and structural attributes are investigated and compared with experiments where reasonable agreement is obtained. The spatial evolution of spin-polarized carriers in prototypical Spin Field Effect Transistor (SpinFET) devices is then simulated. Studies of the spin coherence times in quasi-2D structures is first investigated and compared to experimental results. It is found that the simulated spin coherence times for GaAs structures are in reasonable agreement with experiment. The SpinFET structure studied is a scaled-down version of the InGaAs/InAlAs HEMT discussed in this work, in which spin-polarized carriers are injected at the source, and the coherence length is studied as a function of gate voltage via the Rashba effect.
ContributorsTierney, Brian David (Author) / Goodnick, Stephen (Thesis advisor) / Ferry, David (Committee member) / Akis, Richard (Committee member) / Saraniti, Marco (Committee member) / Vasileska, Dragica (Committee member) / Arizona State University (Publisher)
Created2011