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- All Subjects: Biology
- Creators: Kuang, Yang
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
The phycologist, M. R. Droop, studied vitamin B12 limitation in the flagellate Monochrysis lutheri and concluded that its specific growth rate depended on the concentration of the vitamin within the cell; i.e. the cell quota of the vitamin B12. The Droop model provides a mathematical expression to link growth rate to the intracellular concentration of a limiting nutrient. Although the Droop model has been an important modeling tool in ecology, it has only recently been applied to study cancer biology. Cancer cells live in an ecological setting, interacting and competing with normal and other cancerous cells for nutrients and space, and evolving and adapting to their environment. Here, the Droop equation is used to model three cancers.
First, prostate cancer is modeled, where androgen is considered the limiting nutrient since most tumors depend on androgen for proliferation and survival. The model's accuracy for predicting the biomarker for patients on intermittent androgen deprivation therapy is tested by comparing the simulation results to clinical data as well as to an existing simpler model. The results suggest that a simpler model may be more beneficial for a predictive use, although further research is needed in this field prior to implementing mathematical models as a predictive method in a clinical setting.
Next, two chronic myeloid leukemia models are compared that consider Imatinib treatment, a drug that inhibits the constitutively active tyrosine kinase BCR-ABL. Both models describe the competition of leukemic and normal cells, however the first model also describes intracellular dynamics by considering BCR-ABL as the limiting nutrient. Using clinical data, the differences in estimated parameters between the models and the capacity for each model to predict drug resistance are analyzed.
Last, a simple model is presented that considers ovarian tumor growth and tumor induced angiogenesis, subject to on and off anti-angiogenesis treatment. In this environment, the cell quota represents the intracellular concentration of necessary nutrients provided through blood supply. Mathematical analysis of the model is presented and model simulation results are compared to pre-clinical data. This simple model is able to fit both on- and off-treatment data using the same biologically relevant parameters.
First, prostate cancer is modeled, where androgen is considered the limiting nutrient since most tumors depend on androgen for proliferation and survival. The model's accuracy for predicting the biomarker for patients on intermittent androgen deprivation therapy is tested by comparing the simulation results to clinical data as well as to an existing simpler model. The results suggest that a simpler model may be more beneficial for a predictive use, although further research is needed in this field prior to implementing mathematical models as a predictive method in a clinical setting.
Next, two chronic myeloid leukemia models are compared that consider Imatinib treatment, a drug that inhibits the constitutively active tyrosine kinase BCR-ABL. Both models describe the competition of leukemic and normal cells, however the first model also describes intracellular dynamics by considering BCR-ABL as the limiting nutrient. Using clinical data, the differences in estimated parameters between the models and the capacity for each model to predict drug resistance are analyzed.
Last, a simple model is presented that considers ovarian tumor growth and tumor induced angiogenesis, subject to on and off anti-angiogenesis treatment. In this environment, the cell quota represents the intracellular concentration of necessary nutrients provided through blood supply. Mathematical analysis of the model is presented and model simulation results are compared to pre-clinical data. This simple model is able to fit both on- and off-treatment data using the same biologically relevant parameters.
ContributorsEverett, Rebecca Anne (Author) / Kuang, Yang (Thesis advisor) / Nagy, John (Committee member) / Milner, Fabio (Committee member) / Crook, Sharon (Committee member) / Jackiewicz, Zdzislaw (Committee member) / Arizona State University (Publisher)
Created2015
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
Predicting resistant prostate cancer is critical for lowering medical costs and improving the quality of life of advanced prostate cancer patients. I formulate, compare, and analyze two mathematical models that aim to forecast future levels of prostate-specific antigen (PSA). I accomplish these tasks by employing clinical data of locally advanced prostate cancer patients undergoing androgen deprivation therapy (ADT). I demonstrate that the inverse problem of parameter estimation might be too complicated and simply relying on data fitting can give incorrect conclusions, since there is a large error in parameter values estimated and parameters might be unidentifiable. I provide confidence intervals to give estimate forecasts using data assimilation via an ensemble Kalman Filter. Using the ensemble Kalman Filter, I perform dual estimation of parameters and state variables to test the prediction accuracy of the models. Finally, I present a novel model with time delay and a delay-dependent parameter. I provide a geometric stability result to study the behavior of this model and show that the inclusion of time delay may improve the accuracy of predictions. Also, I demonstrate with clinical data that the inclusion of the delay-dependent parameter facilitates the identification and estimation of parameters.
ContributorsBaez, Javier (Author) / Kuang, Yang (Thesis advisor) / Kostelich, Eric (Committee member) / Crook, Sharon (Committee member) / Gardner, Carl (Committee member) / Nagy, John (Committee member) / Arizona State University (Publisher)
Created2017
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 immune system plays a dual role during neoplastic progression. It can suppress tumor growth by eliminating cancer cells, and also promote neoplastic expansion by either selecting for tumor cells that are fitter to survive in an immunocompetent host or by establishing the right conditions within the tumor microenvironment. First, I present a model to study the dynamics of subclonal evolution of cancer. I model selection through time as an epistatic process. That is, the fitness change in a given cell is not simply additive, but depends on previous mutations. Simulation studies indicate that tumors are composed of myriads of small subclones at the time of diagnosis. Because some of these rare subclones harbor pre-existing treatment-resistant mutations, they present a major challenge to precision medicine. Second, I study the question of self and non-self discrimination by the immune system, which is fundamental in the field in cancer immunology. By performing a quantitative analysis of the biochemical properties of thousands of MHC class I peptides, I find that hydrophobicity of T cell receptors contact residues is a hallmark of immunogenic epitopes. Based on these findings, I further develop a computational model to predict immunogenic epitopes which facilitate the development of T cell vaccines against pathogen and tumor antigens. Lastly, I study the effect of early detection in the context of Ebola. I develope a simple mathematical model calibrated to the transmission dynamics of Ebola virus in West Africa. My findings suggest that a strategy that focuses on early diagnosis of high-risk individuals, caregivers, and health-care workers at the pre-symptomatic stage, when combined with public health measures to improve the speed and efficacy of isolation of infectious individuals, can lead to rapid reductions in Ebola transmission.
ContributorsChowell-Puente, Diego (Author) / Castillo-Chavez, Carlos (Thesis advisor) / Anderson, Karen S (Thesis advisor) / Maley, Carlo C (Committee member) / Wilson Sayres, Melissa A (Committee member) / Blattman, Joseph N (Committee member) / Arizona State University (Publisher)
Created2016
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
Description
Efforts to treat prostate cancer have seen an uptick, as the world’s most commoncancer in men continues to have increasing global incidence. Clinically, metastatic
prostate cancer is most commonly treated with hormonal therapy. The idea behind
hormonal therapy is to reduce androgen production, which prostate cancer cells
require for growth. Recently, the exploration of the synergistic effects of the drugs
used in hormonal therapy has begun. The aim was to build off of these recent
advancements and further refine the synergistic drug model. The advancements I
implement come by addressing biological shortcomings and improving the model’s
internal mechanistic structure. The drug families being modeled, anti-androgens,
and gonadotropin-releasing hormone analogs, interact with androgen production in a
way that is not completely understood in the scientific community. Thus the models
representing the drugs show progress through their ability to capture their effect
on serum androgen. Prostate-specific antigen is the primary biomarker for prostate
cancer and is generally how population models on the subject are validated. Fitting
the model to clinical data and comparing it to other clinical models through the
ability to fit and forecast prostate-specific antigen and serum androgen is how this
improved model achieves validation. The improved model results further suggest that
the drugs’ dynamics should be considered in adaptive therapy for prostate cancer.
prostate cancer is most commonly treated with hormonal therapy. The idea behind
hormonal therapy is to reduce androgen production, which prostate cancer cells
require for growth. Recently, the exploration of the synergistic effects of the drugs
used in hormonal therapy has begun. The aim was to build off of these recent
advancements and further refine the synergistic drug model. The advancements I
implement come by addressing biological shortcomings and improving the model’s
internal mechanistic structure. The drug families being modeled, anti-androgens,
and gonadotropin-releasing hormone analogs, interact with androgen production in a
way that is not completely understood in the scientific community. Thus the models
representing the drugs show progress through their ability to capture their effect
on serum androgen. Prostate-specific antigen is the primary biomarker for prostate
cancer and is generally how population models on the subject are validated. Fitting
the model to clinical data and comparing it to other clinical models through the
ability to fit and forecast prostate-specific antigen and serum androgen is how this
improved model achieves validation. The improved model results further suggest that
the drugs’ dynamics should be considered in adaptive therapy for prostate cancer.
ContributorsReckell, Trevor (Author) / Kostelich, Eric (Thesis advisor) / Kuang, Yang (Committee member) / Mahalov, Alex (Committee member) / Arizona State University (Publisher)
Created2020
Description
Cancer is a disease involving abnormal growth of cells. Its growth dynamics is perplexing. Mathematical modeling is a way to shed light on this progress and its medical treatments. This dissertation is to study cancer invasion in time and space using a mathematical approach. Chapter 1 presents a detailed review of literature on cancer modeling.
Chapter 2 focuses sorely on time where the escape of a generic cancer out of immune control is described by stochastic delayed differential equations (SDDEs). Without time delay and noise, this system demonstrates bistability. The effects of response time of the immune system and stochasticity in the tumor proliferation rate are studied by including delay and noise in the model. Stability, persistence and extinction of the tumor are analyzed. The result shows that both time delay and noise can induce the transition from low tumor burden equilibrium to high tumor equilibrium. The aforementioned work has been published (Han et al., 2019b).
In Chapter 3, Glioblastoma multiforme (GBM) is studied using a partial differential equation (PDE) model. GBM is an aggressive brain cancer with a grim prognosis. A mathematical model of GBM growth with explicit motility, birth, and death processes is proposed. A novel method is developed to approximate key characteristics of the wave profile, which can be compared with MRI data. Several test cases of MRI data of GBM patients are used to yield personalized parameterizations of the model. The aforementioned work has been published (Han et al., 2019a).
Chapter 4 presents an innovative way of forecasting spatial cancer invasion. Most mathematical models, including the ones described in previous chapters, are formulated based on strong assumptions, which are hard, if not impossible, to verify due to complexity of biological processes and lack of quality data. Instead, a nonparametric forecasting method using Gaussian processes is proposed. By exploiting the local nature of the spatio-temporal process, sparse (in terms of time) data is sufficient for forecasting. Desirable properties of Gaussian processes facilitate selection of the size of the local neighborhood and computationally efficient propagation of uncertainty. The method is tested on synthetic data and demonstrates promising results.
Chapter 2 focuses sorely on time where the escape of a generic cancer out of immune control is described by stochastic delayed differential equations (SDDEs). Without time delay and noise, this system demonstrates bistability. The effects of response time of the immune system and stochasticity in the tumor proliferation rate are studied by including delay and noise in the model. Stability, persistence and extinction of the tumor are analyzed. The result shows that both time delay and noise can induce the transition from low tumor burden equilibrium to high tumor equilibrium. The aforementioned work has been published (Han et al., 2019b).
In Chapter 3, Glioblastoma multiforme (GBM) is studied using a partial differential equation (PDE) model. GBM is an aggressive brain cancer with a grim prognosis. A mathematical model of GBM growth with explicit motility, birth, and death processes is proposed. A novel method is developed to approximate key characteristics of the wave profile, which can be compared with MRI data. Several test cases of MRI data of GBM patients are used to yield personalized parameterizations of the model. The aforementioned work has been published (Han et al., 2019a).
Chapter 4 presents an innovative way of forecasting spatial cancer invasion. Most mathematical models, including the ones described in previous chapters, are formulated based on strong assumptions, which are hard, if not impossible, to verify due to complexity of biological processes and lack of quality data. Instead, a nonparametric forecasting method using Gaussian processes is proposed. By exploiting the local nature of the spatio-temporal process, sparse (in terms of time) data is sufficient for forecasting. Desirable properties of Gaussian processes facilitate selection of the size of the local neighborhood and computationally efficient propagation of uncertainty. The method is tested on synthetic data and demonstrates promising results.
ContributorsHan, Lifeng (Author) / Kuang, Yang (Thesis advisor) / Fricks, John (Thesis advisor) / Kostelich, Eric (Committee member) / Baer, Steve (Committee member) / Gumel, Abba (Committee member) / Arizona State University (Publisher)
Created2020