Matching Items (14)
Filtering by
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
There has been important progress in understanding ecological dynamics through the development of the theory of ecological stoichiometry. This fast growing theory provides new constraints and mechanisms that can be formulated into mathematical models. Stoichiometric models incorporate the effects of both food quantity and food quality into a single framework that produce rich dynamics. While the effects of nutrient deficiency on consumer growth are well understood, recent discoveries in ecological stoichiometry suggest that consumer dynamics are not only affected by insufficient food nutrient content (low phosphorus (P): carbon (C) ratio) but also by excess food nutrient content (high P:C). This phenomenon, known as the stoichiometric knife edge, in which animal growth is reduced not only by food with low P content but also by food with high P content, needs to be incorporated into mathematical models. Here we present Lotka-Volterra type models to investigate the growth response of Daphnia to algae of varying P:C ratios. Using a nonsmooth system of two ordinary differential equations (ODEs), we formulate the first model to incorporate the phenomenon of the stoichiometric knife edge. We then extend this stoichiometric model by mechanistically deriving and tracking free P in the environment. This resulting full knife edge model is a nonsmooth system of three ODEs. Bifurcation analysis and numerical simulations of the full model, that explicitly tracks phosphorus, leads to quantitatively different predictions than previous models that neglect to track free nutrients. The full model shows that the grazer population is sensitive to excess nutrient concentrations as a dynamical free nutrient pool induces extreme grazer population density changes. These modeling efforts provide insight on the effects of excess nutrient content on grazer dynamics and deepen our understanding of the effects of stoichiometry on the mechanisms governing population dynamics and the interactions between trophic levels.
ContributorsPeace, Angela (Author) / Kuang, Yang (Thesis advisor) / Elser, James J (Committee member) / Baer, Steven (Committee member) / Tang, Wenbo (Committee member) / Kang, Yun (Committee member) / Arizona State University (Publisher)
Created2014
Description
In 1968, phycologist M.R. Droop published his famous discovery on the functional relationship between growth rate and internal nutrient status of algae in chemostat culture. The simple notion that growth is directly dependent on intracellular nutrient concentration is useful for understanding the dynamics in many ecological systems. The cell quota in particular lends itself to ecological stoichiometry, which is a powerful framework for mathematical ecology. Three models are developed based on the cell quota principal in order to demonstrate its applications beyond chemostat culture.
First, a data-driven model is derived for neutral lipid synthesis in green microalgae with respect to nitrogen limitation. This model synthesizes several established frameworks in phycology and ecological stoichiometry. The model demonstrates how the cell quota is a useful abstraction for understanding the metabolic shift to neutral lipid production that is observed in certain oleaginous species.
Next a producer-grazer model is developed based on the cell quota model and nutrient recycling. The model incorporates a novel feedback loop to account for animal toxicity due to accumulation of nitrogen waste. The model exhibits rich, complex dynamics which leave several open mathematical questions.
Lastly, disease dynamics in vivo are in many ways analogous to those of an ecosystem, giving natural extensions of the cell quota concept to disease modeling. Prostate cancer can be modeled within this framework, with androgen the limiting nutrient and the prostate and cancer cells as competing species. Here the cell quota model provides a useful abstraction for the dependence of cellular proliferation and apoptosis on androgen and the androgen receptor. Androgen ablation therapy is often used for patients in biochemical recurrence or late-stage disease progression and is in general initially effective. However, for many patients the cancer eventually develops resistance months to years after treatment begins. Understanding how and predicting when hormone therapy facilitates evolution of resistant phenotypes has immediate implications for treatment. Cell quota models for prostate cancer can be useful tools for this purpose and motivate applications to other diseases.
First, a data-driven model is derived for neutral lipid synthesis in green microalgae with respect to nitrogen limitation. This model synthesizes several established frameworks in phycology and ecological stoichiometry. The model demonstrates how the cell quota is a useful abstraction for understanding the metabolic shift to neutral lipid production that is observed in certain oleaginous species.
Next a producer-grazer model is developed based on the cell quota model and nutrient recycling. The model incorporates a novel feedback loop to account for animal toxicity due to accumulation of nitrogen waste. The model exhibits rich, complex dynamics which leave several open mathematical questions.
Lastly, disease dynamics in vivo are in many ways analogous to those of an ecosystem, giving natural extensions of the cell quota concept to disease modeling. Prostate cancer can be modeled within this framework, with androgen the limiting nutrient and the prostate and cancer cells as competing species. Here the cell quota model provides a useful abstraction for the dependence of cellular proliferation and apoptosis on androgen and the androgen receptor. Androgen ablation therapy is often used for patients in biochemical recurrence or late-stage disease progression and is in general initially effective. However, for many patients the cancer eventually develops resistance months to years after treatment begins. Understanding how and predicting when hormone therapy facilitates evolution of resistant phenotypes has immediate implications for treatment. Cell quota models for prostate cancer can be useful tools for this purpose and motivate applications to other diseases.
ContributorsPacker, Aaron (Author) / Kuang, Yang (Thesis advisor) / Nagy, John (Committee member) / Smith, Hal (Committee member) / Kostelich, Eric (Committee member) / Kang, Yun (Committee member) / Arizona State University (Publisher)
Created2014
Description
The most advanced social insects, the eusocial insects, form often large societies in which there is reproductive division of labor, queens and workers, have overlapping generations, and cooperative brood care where daughter workers remain in the nest with their queen mother and care for their siblings. The eusocial insects are composed of representative species of bees and wasps, and all species of ants and termites. Much is known about their organizational structure, but remains to be discovered.
The success of social insects is dependent upon cooperative behavior and adaptive strategies shaped by natural selection that respond to internal or external conditions. The objective of my research was to investigate specific mechanisms that have helped shaped the structure of division of labor observed in social insect colonies, including age polyethism and nutrition, and phenomena known to increase colony survival such as egg cannibalism. I developed various Ordinary Differential Equation (ODE) models in which I applied dynamical, bifurcation, and sensitivity analysis to carefully study and visualize biological outcomes in social organisms to answer questions regarding the conditions under which a colony can survive. First, I investigated how the population and evolutionary dynamics of egg cannibalism and division of labor can promote colony survival. I then introduced a model of social conflict behavior to study the inclusion of different response functions that explore the benefits of cannibalistic behavior and how it contributes to age polyethism, the change in behavior of workers as they age, and its biological relevance. Finally, I introduced a model to investigate the importance of pollen nutritional status in a honeybee colony, how it affects population growth and influences division of labor within the worker caste. My results first reveal that both cannibalism and division of labor are adaptive strategies that increase the size of the worker population, and therefore, the persistence of the colony. I show the importance of food collection, consumption, and processing rates to promote good colony nutrition leading to the coexistence of brood and adult workers. Lastly, I show how taking into account seasonality for pollen collection improves the prediction of long term consequences.
The success of social insects is dependent upon cooperative behavior and adaptive strategies shaped by natural selection that respond to internal or external conditions. The objective of my research was to investigate specific mechanisms that have helped shaped the structure of division of labor observed in social insect colonies, including age polyethism and nutrition, and phenomena known to increase colony survival such as egg cannibalism. I developed various Ordinary Differential Equation (ODE) models in which I applied dynamical, bifurcation, and sensitivity analysis to carefully study and visualize biological outcomes in social organisms to answer questions regarding the conditions under which a colony can survive. First, I investigated how the population and evolutionary dynamics of egg cannibalism and division of labor can promote colony survival. I then introduced a model of social conflict behavior to study the inclusion of different response functions that explore the benefits of cannibalistic behavior and how it contributes to age polyethism, the change in behavior of workers as they age, and its biological relevance. Finally, I introduced a model to investigate the importance of pollen nutritional status in a honeybee colony, how it affects population growth and influences division of labor within the worker caste. My results first reveal that both cannibalism and division of labor are adaptive strategies that increase the size of the worker population, and therefore, the persistence of the colony. I show the importance of food collection, consumption, and processing rates to promote good colony nutrition leading to the coexistence of brood and adult workers. Lastly, I show how taking into account seasonality for pollen collection improves the prediction of long term consequences.
ContributorsRodríguez Messan, Marisabel (Author) / Kang, Yun (Thesis advisor) / Castillo-Chavez, Carlos (Thesis advisor) / Kuang, Yang (Committee member) / Page Jr., Robert E (Committee member) / Gardner, Carl (Committee member) / Arizona State University (Publisher)
Created2018
Description
The modern web presents an opportunity for educators and researchers to create tools that are highly accessible. Because of the near-ubiquity of modern web browsers, developers who hope to create educational and analytical tools can reach a large au- dience by creating web applications. Using JavaScript, HTML, and other modern web development technologies, Genie was developed as a simulator to help educators in biology, genetics, and evolution classrooms teach their students about population genetics. Because Genie was designed for the modern web, it is highly accessible to both educators and students, who can access the web application using any modern web browser on virtually any device. Genie demonstrates the efficacy of web devel- opment technologies for demonstrating and simulating complex processes, and it will be a unique educational tool for educators who teach population genetics.
ContributorsRoos, Benjamin Hirsch (Author) / Cartwright, Reed (Thesis director) / Wilson Sayres, Melissa (Committee member) / Mayron, Liam (Committee member) / Barrett, The Honors College (Contributor) / Computer Science and Engineering Program (Contributor)
Created2015-05
Description
For colonies of ponerine ant species, sterility regulation after a founding queen's death is not totally achieved in the worker caste, and the possibility of sexual reproduction is opened to workers. The persisting survival of these colonies is dependent on capturing the optimal reproductive ratio; yet, an informational gap bounds the mechanisms detailing the selection of new reproductives and the suppression of ovarian development in rejected reproductives. We investigated the mechanisms of worker policing, one of the primary methods of ovarian suppression, through continuous video observation for a period of five days at the start of colony instability. Observations suggest policing in H. saltator is performed by a majority of a colony, including potential reproductives, and requires multiple events to fully discourage ovarian growth.
ContributorsChien, Jeffrey (Co-author) / Barat Ali, Fatima (Co-author) / Kang, Yun (Thesis director) / Liebig, Juergen (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Mechanical and Aerospace Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2018-12
Description
Lactase persistence is the ability of adults to digest lactose in milk (Segurel & Bon, 2017). Mammals are generally distinguished by their mammary glands which gives females the ability to produce milk and feed their newborn children. The new born therefore requires the ability to breakdown the lactose in the milk to ensure its proper digestion (Segurel & Bon, 2017). Generally, humans lose the expression of lactase after weaning, which prevents them being able to breakdown lactose from dairy (Flatz, 1987).
My research is focused on the people of Turkana, a human pastoral population inhabiting Northwest Kenya. The people of Turkana are Nilotic people that are native to the Turkana district. There are currently no conclusive studies done on evidence for genetic lactase persistence in Turkana. Therefore, my research will be on the evolution of lactase persistence in the people of Turkana. The goal of this project is to investigate the evolutionary history of two genes with known involvement in lactase persistence, LCT and MCM6, in the Turkana. Variants in these genes have previously been identified to result in the ability to digest lactose post-weaning age. Furthermore, an additional study found that a closely related population to the Turkana, the Massai, showed stronger signals of recent selection for lactase persistence than Europeans in these genes. My goal is to characterize known variants associated with lactase persistence by calculating their allele frequencies in the Turkana and conduct selection scans to determine if LCT/MCM6 show signatures of positive selection. In doing this, we conducted a pilot study consisting of 10 female Turkana individuals and 10 females from four different populations from the 1000 genomes project namely: the Yoruba in Ibadan, Nigeria (YRI); Luhya in Webuye, Kenya; Utah Residents with Northern and Western European Ancestry (CEU); and the Southern Han Chinese. The allele frequency calculation suggested that the CEU (Utah Residents with Northern and Western European Ancestry) population had a higher lactase persistence associated allele frequency than all the other populations analyzed here, including the Turkana population. Our Tajima’s D calculations and analysis suggested that both the Turkana population and the four haplotype map populations shows signatures of positive selection in the same region. The iHS selection scans we conducted to detect signatures of positive selection on all five populations showed that the Southern Han Chinese (CHS), the LWK (Luhya in Webuye, Kenya) and the YRI (Yoruba in Ibadan, Nigeria) populations had stronger signatures of positive selection than the Turkana population. The LWK (Luhya in Webuye, Kenya) and the YRI (Yoruba in Ibadan, Nigeria) populations showed the strongest signatures of positive selection in this region. This project serves as a first step in the investigation of lactase persistence in the Turkana population and its evolution over time.
My research is focused on the people of Turkana, a human pastoral population inhabiting Northwest Kenya. The people of Turkana are Nilotic people that are native to the Turkana district. There are currently no conclusive studies done on evidence for genetic lactase persistence in Turkana. Therefore, my research will be on the evolution of lactase persistence in the people of Turkana. The goal of this project is to investigate the evolutionary history of two genes with known involvement in lactase persistence, LCT and MCM6, in the Turkana. Variants in these genes have previously been identified to result in the ability to digest lactose post-weaning age. Furthermore, an additional study found that a closely related population to the Turkana, the Massai, showed stronger signals of recent selection for lactase persistence than Europeans in these genes. My goal is to characterize known variants associated with lactase persistence by calculating their allele frequencies in the Turkana and conduct selection scans to determine if LCT/MCM6 show signatures of positive selection. In doing this, we conducted a pilot study consisting of 10 female Turkana individuals and 10 females from four different populations from the 1000 genomes project namely: the Yoruba in Ibadan, Nigeria (YRI); Luhya in Webuye, Kenya; Utah Residents with Northern and Western European Ancestry (CEU); and the Southern Han Chinese. The allele frequency calculation suggested that the CEU (Utah Residents with Northern and Western European Ancestry) population had a higher lactase persistence associated allele frequency than all the other populations analyzed here, including the Turkana population. Our Tajima’s D calculations and analysis suggested that both the Turkana population and the four haplotype map populations shows signatures of positive selection in the same region. The iHS selection scans we conducted to detect signatures of positive selection on all five populations showed that the Southern Han Chinese (CHS), the LWK (Luhya in Webuye, Kenya) and the YRI (Yoruba in Ibadan, Nigeria) populations had stronger signatures of positive selection than the Turkana population. The LWK (Luhya in Webuye, Kenya) and the YRI (Yoruba in Ibadan, Nigeria) populations showed the strongest signatures of positive selection in this region. This project serves as a first step in the investigation of lactase persistence in the Turkana population and its evolution over time.
ContributorsJobe, Ndey Bassin (Author) / Wilson Sayres, Melissa (Thesis director) / Paaijmans, Krijn (Committee member) / Taravella, Angela (Committee member) / School of Earth and Space Exploration (Contributor) / School of Life Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2019-05
Description
Unlike the autosomes, recombination on the sex chromosomes is limited to the pseudoautosomal regions (PARs) at each end of the chromosome. PAR1 spans approximately 2.7 Mb from the tip of the proximal arm of each sex chromosome, and a pseudoautosomal boundary between the PAR1 and non-PAR region is thought to have evolved from a Y-specific inversion that suppressed recombination across the boundary. In addition to the two PARs, there is also a human-specific X-transposed region (XTR) that was duplicated from the X to the Y chromosome. Genetic diversity is expected to be higher in recombining than nonrecombining regions, particularly because recombination reduces the effects of linked selection, allowing neutral variation to accumulate. We previously showed that diversity decreases linearly across the previously defined pseudoautosomal boundary (rather than drop suddenly at the boundary), suggesting that the pseudoautosomal boundary may not be as strict as previously thought. In this study, we analyzed data from 1271 genetic females to explore the extent to which the pseudoautosomal boundary varies among human populations (broadly, African, European, South Asian, East Asian, and the Americas). We found that, in all populations, genetic diversity was significantly higher in the PAR1 and XTR than in the non-PAR regions, and that diversity decreased linearly from the PAR1 to finally reach a non-PAR value well past the pseudoautosomal boundary in all populations. However, we also found that the location at which diversity changes from reflecting the higher PAR1 diversity to the lower nonPAR diversity varied by as much as 500 kb among populations. The lack of genetic evidence for a strict pseudoautosomal boundary and the variability in patterns of diversity across the pseudoautosomal boundary are consistent with two potential explanations: (1) the boundary itself may vary across populations, or (2) that population-specific demographic histories have shaped diversity across the pseudoautosomal boundary.
ContributorsCotter, Daniel Juetten (Author) / Wilson Sayres, Melissa (Thesis director) / Stone, Anne (Committee member) / Webster, Timothy (Committee member) / School of Life Sciences (Contributor) / School of International Letters and Cultures (Contributor) / Barrett, The Honors College (Contributor)
Created2016-12
Description
Division of Labor among social insects is frequently discussed in regards to the colony's worker population. However, before a colony achieves a worker population, a queen is required to perform all of the tasks necessary for her survival: foraging, building the colony, and brood care. A simple ODE model was developed through the use of a framework of replicator equations in dynamical environments to investigate how queen ants perform and distribute all of the tasks necessary for her and her colony's survival by incorporating individual internal thresholds and environmental stimulus. Modi�cations to the internal threshold, risk of performing the task, and the rate of increase of the environmental stimulus were also explored. Because of the simplicity of the model, it could also be used to measure the task performance of larger populations of social insects. However, the model has only been applied to the data collected from Pogonomyrmex barbatus single queen ants.
ContributorsKincade, Katherine Margaret (Author) / Kang, Yun (Thesis director) / Fewell, Jennifer (Committee member) / Lanchier, Nicolas (Committee member) / School of Mathematical and Statistical Sciences (Contributor) / Computer Science and Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2016-12
Description
A key factor in the success of social animals is their organization of work. Mathematical models have been instrumental in unraveling how simple, individual-based rules can generate collective patterns via self-organization. However, existing models offer limited insights into how these patterns are shaped by behavioral differences within groups, in part because they focus on analyzing specific rules rather than general mechanisms that can explain behavior at the individual-level. My work argues for a more principled approach that focuses on the question of how individuals make decisions in costly environments.
In Chapters 2 and 3, I demonstrate how this approach provides novel insights into factors that shape the flexibility and robustness of task organization in harvester ant colonies (Pogonomyrmex barbatus). My results show that the degree to which colonies can respond to work in fluctuating environments depends on how individuals weigh the costs of activity and update their behavior in response to social information. In Chapter 4, I introduce a mathematical framework to study the emergence of collective organization in heterogenous groups. My approach, which is based on the theory of multi-agent systems, focuses on myopic agents whose behavior emerges out of an independent valuation of alternative choices in a given work environment. The product of this dynamic is an equilibrium organization in which agents perform different tasks (or abstain from work) with an analytically defined set of threshold probabilities. The framework is minimally developed, but can be extended to include other factors known to affect task decisions including individual experience and social facilitation. This research contributes a novel approach to developing (and analyzing) models of task organization that can be applied in a broader range of contexts where animals cooperate.
In Chapters 2 and 3, I demonstrate how this approach provides novel insights into factors that shape the flexibility and robustness of task organization in harvester ant colonies (Pogonomyrmex barbatus). My results show that the degree to which colonies can respond to work in fluctuating environments depends on how individuals weigh the costs of activity and update their behavior in response to social information. In Chapter 4, I introduce a mathematical framework to study the emergence of collective organization in heterogenous groups. My approach, which is based on the theory of multi-agent systems, focuses on myopic agents whose behavior emerges out of an independent valuation of alternative choices in a given work environment. The product of this dynamic is an equilibrium organization in which agents perform different tasks (or abstain from work) with an analytically defined set of threshold probabilities. The framework is minimally developed, but can be extended to include other factors known to affect task decisions including individual experience and social facilitation. This research contributes a novel approach to developing (and analyzing) models of task organization that can be applied in a broader range of contexts where animals cooperate.
ContributorsUdiani, Oyita (Author) / Kang, Yun (Thesis advisor) / Fewell, Jennifer H (Thesis advisor) / Janssen, Marcus A (Committee member) / Castillo-Chavez, Carlos (Committee member) / Arizona State University (Publisher)
Created2016