Matching Items (6)
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- All Subjects: Differential Equations
- Creators: Kuang, Yang
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
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 recent decades, marine ecologists have conducted extensive field work and experiments to understand the interactions between bacteria and bacteriophage (phage) in marine environments. This dissertation provides a detailed rigorous framework for gaining deeper insight into these interactions. Specific features of the dissertation include the design of a new deterministic Lotka-Volterra model with n + 1 bacteria, n
+ 1 phage, with explicit nutrient, where the jth phage strain infects the first j bacterial strains, a perfectly nested infection network (NIN). This system is subject to trade-off conditions on the life-history traits of both bacteria and phage given in an earlier study Jover et al. (2013). Sufficient conditions are provided to show that a bacteria-phage community of arbitrary size with NIN can arise through the succession of permanent subcommunities, by the successive addition of one new population. Using uniform persistence theory, this entire community is shown to be permanent (uniformly persistent), meaning that all populations ultimately survive.
It is shown that a modified version of the original NIN Lotka-Volterra model with implicit nutrient considered by Jover et al. (2013) is permanent. A new one-to-one infection network (OIN) is also considered where each bacterium is infected by only one phage, and that phage infects only that bacterium. This model does not use the trade-offs on phage infection range, and bacterium resistance to phage. The OIN model is shown to be permanent, and using Lyapunov function theory, coupled with LaSalle’s Invariance Principle, the unique coexistence equilibrium associated with the NIN is globally asymptotically stable provided that the inter- and intra-specific bacterial competition coefficients are equal across all bacteria.
Finally, the OIN model is extended to a “Kill the Winner” (KtW) Lotka-Volterra model
of marine communities consisting of bacteria, phage, and zooplankton. The zooplankton
acts as a super bacteriophage, which infects all bacteria. This model is shown to be permanent.
+ 1 phage, with explicit nutrient, where the jth phage strain infects the first j bacterial strains, a perfectly nested infection network (NIN). This system is subject to trade-off conditions on the life-history traits of both bacteria and phage given in an earlier study Jover et al. (2013). Sufficient conditions are provided to show that a bacteria-phage community of arbitrary size with NIN can arise through the succession of permanent subcommunities, by the successive addition of one new population. Using uniform persistence theory, this entire community is shown to be permanent (uniformly persistent), meaning that all populations ultimately survive.
It is shown that a modified version of the original NIN Lotka-Volterra model with implicit nutrient considered by Jover et al. (2013) is permanent. A new one-to-one infection network (OIN) is also considered where each bacterium is infected by only one phage, and that phage infects only that bacterium. This model does not use the trade-offs on phage infection range, and bacterium resistance to phage. The OIN model is shown to be permanent, and using Lyapunov function theory, coupled with LaSalle’s Invariance Principle, the unique coexistence equilibrium associated with the NIN is globally asymptotically stable provided that the inter- and intra-specific bacterial competition coefficients are equal across all bacteria.
Finally, the OIN model is extended to a “Kill the Winner” (KtW) Lotka-Volterra model
of marine communities consisting of bacteria, phage, and zooplankton. The zooplankton
acts as a super bacteriophage, which infects all bacteria. This model is shown to be permanent.
ContributorsKorytowski, Daniel (Author) / Smith, Hal (Thesis advisor) / Gumel, Abba (Committee member) / Kuang, Yang (Committee member) / Gardner, Carl (Committee member) / Thieme, Horst (Committee member) / Arizona State University (Publisher)
Created2016
Description
Using a simple $SI$ infection model, I uncover the
overall dynamics of the system and how they depend on the incidence
function. I consider both an epidemic and endemic perspective of the
model, but in both cases, three classes of incidence
functions are identified.
In the epidemic form,
power incidences, where the infective portion $I^p$ has $p\in(0,1)$,
cause unconditional host extinction,
homogeneous incidences have host extinction for certain parameter constellations and
host survival for others, and upper density-dependent incidences
never cause host extinction. The case of non-extinction in upper
density-dependent
incidences extends to the case where a latent period is included.
Using data from experiments with rhanavirus and salamanders,
maximum likelihood estimates are applied to the data.
With these estimates,
I generate the corrected Akaike information criteria, which
reward a low likelihood and punish the use of more parameters.
This generates the Akaike weight, which is used to fit
parameters to the data, and determine which incidence functions
fit the data the best.
From an endemic perspective, I observe
that power incidences cause initial condition dependent host extinction for
some parameter constellations and global stability for others,
homogeneous incidences have host extinction for certain parameter constellations and
host survival for others, and upper density-dependent incidences
never cause host extinction.
The dynamics when the incidence function is homogeneous are deeply explored.
I expand the endemic considerations in the homogeneous case
by adding a predator into the model.
Using persistence theory, I show the conditions for the persistence of each of the
predator, prey, and parasite species. Potential dynamics of the system include parasite mediated
persistence of the predator, survival of the ecosystem at high initial predator levels and
ecosystem collapse at low initial predator levels, persistence of all three species, and much more.
overall dynamics of the system and how they depend on the incidence
function. I consider both an epidemic and endemic perspective of the
model, but in both cases, three classes of incidence
functions are identified.
In the epidemic form,
power incidences, where the infective portion $I^p$ has $p\in(0,1)$,
cause unconditional host extinction,
homogeneous incidences have host extinction for certain parameter constellations and
host survival for others, and upper density-dependent incidences
never cause host extinction. The case of non-extinction in upper
density-dependent
incidences extends to the case where a latent period is included.
Using data from experiments with rhanavirus and salamanders,
maximum likelihood estimates are applied to the data.
With these estimates,
I generate the corrected Akaike information criteria, which
reward a low likelihood and punish the use of more parameters.
This generates the Akaike weight, which is used to fit
parameters to the data, and determine which incidence functions
fit the data the best.
From an endemic perspective, I observe
that power incidences cause initial condition dependent host extinction for
some parameter constellations and global stability for others,
homogeneous incidences have host extinction for certain parameter constellations and
host survival for others, and upper density-dependent incidences
never cause host extinction.
The dynamics when the incidence function is homogeneous are deeply explored.
I expand the endemic considerations in the homogeneous case
by adding a predator into the model.
Using persistence theory, I show the conditions for the persistence of each of the
predator, prey, and parasite species. Potential dynamics of the system include parasite mediated
persistence of the predator, survival of the ecosystem at high initial predator levels and
ecosystem collapse at low initial predator levels, persistence of all three species, and much more.
ContributorsFarrell, Alexander E. (Author) / Thieme, Horst R (Thesis advisor) / Smith, Hal (Committee member) / Kuang, Yang (Committee member) / Tang, Wenbo (Committee member) / Collins, James (Committee member) / Arizona State University (Publisher)
Created2017
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
Synthetic biology (SB) has become an important field of science focusing on designing and engineering new biological parts and systems, or re-designing existing biological systems for useful purposes. The dramatic growth of SB throughout the past two decades has not only provided us numerous achievements, but also brought us more timely and underexplored problems. In SB's entire history, mathematical modeling has always been an indispensable approach to predict the experimental outcomes, improve experimental design and obtain mechanism-understanding of the biological systems. \textit{Escherichia coli} (\textit{E. coli}) is one of the most important experimental platforms, its growth dynamics is the major research objective in this dissertation. Chapter 2 employs a reaction-diffusion model to predict the \textit{E. coli} colony growth on a semi-solid agar plate under multiple controls. In that chapter, a density-dependent diffusion model with non-monotonic growth to capture the colony's non-linear growth profile is introduced. Findings of the new model to experimental data are compared and contrasted with those from other proposed models. In addition, the cross-sectional profile of the colony are computed and compared with experimental data. \textit{E. coli} colony is also used to perform spatial patterns driven by designed gene circuits. In Chapter 3, a gene circuit (MINPAC) and its corresponding pattern formation results are presented. Specifically, a series of partial differential equation (PDE) models are developed to describe the pattern formation driven by the MINPAC circuit. Model simulations of the patterns based on different experimental conditions and numerical analysis of the models to obtain a deeper understanding of the mechanisms are performed and discussed. Mathematical analysis of the simplified models, including traveling wave analysis and local stability analysis, is also presented and used to explore the control strategies of the pattern formation. The interaction between the gene circuit and the host \textit{E. coli} may be crucial and even greatly affect the experimental outcomes. Chapter 4 focuses on the growth feedback between the circuit and the host cell under different nutrient conditions. Two ordinary differential equation (ODE) models are developed to describe such feedback with nutrient variation. Preliminary results on data fitting using both two models and the model dynamical analysis are included.
ContributorsHe, Changhan (Author) / Kuang, Yang (Thesis advisor) / Wang, Xiao (Committee member) / Kostelich, Eric (Committee member) / Tian, Xiaojun (Committee member) / Gumel, Abba (Committee member) / Arizona State University (Publisher)
Created2021