Matching Items (49)
Description
Rewired biological pathways and/or rewired microRNA (miRNA)-mRNA interactions might also influence the activity of biological pathways. Here, rewired biological pathways is defined as differential (rewiring) effect of genes on the topology of biological pathways between controls and cases. Similarly, rewired miRNA-mRNA interactions are defined as the differential (rewiring) effects of miRNAs on the topology of biological pathways between controls and cases. In the dissertation, it is discussed that how rewired biological pathways (Chapter 1) and/or rewired miRNA-mRNA interactions (Chapter 2) aberrantly influence the activity of biological pathways and their association with disease.
This dissertation proposes two PageRank-based analytical methods, Pathways of Topological Rank Analysis (PoTRA) and miR2Pathway, discussed in Chapter 1 and Chapter 2, respectively. PoTRA focuses on detecting pathways with an altered number of hub genes in corresponding pathways between two phenotypes. The basis for PoTRA is that the loss of connectivity is a common topological trait of cancer networks, as well as the prior knowledge that a normal biological network is a scale-free network whose degree distribution follows a power law where a small number of nodes are hubs and a large number of nodes are non-hubs. However, from normal to cancer, the process of the network losing connectivity might be the process of disrupting the scale-free structure of the network, namely, the number of hub genes might be altered in cancer compared to that in normal samples. Hence, it is hypothesized that if the number of hub genes is different in a pathway between normal and cancer, this pathway might be involved in cancer. MiR2Pathway focuses on quantifying the differential effects of miRNAs on the activity of a biological pathway when miRNA-mRNA connections are altered from normal to disease and rank disease risk of rewired miRNA-mediated biological pathways. This dissertation explores how rewired gene-gene interactions and rewired miRNA-mRNA interactions lead to aberrant activity of biological pathways, and rank pathways for their disease risk. The two methods proposed here can be used to complement existing genomics analysis methods to facilitate the study of biological mechanisms behind disease at the systems-level.
This dissertation proposes two PageRank-based analytical methods, Pathways of Topological Rank Analysis (PoTRA) and miR2Pathway, discussed in Chapter 1 and Chapter 2, respectively. PoTRA focuses on detecting pathways with an altered number of hub genes in corresponding pathways between two phenotypes. The basis for PoTRA is that the loss of connectivity is a common topological trait of cancer networks, as well as the prior knowledge that a normal biological network is a scale-free network whose degree distribution follows a power law where a small number of nodes are hubs and a large number of nodes are non-hubs. However, from normal to cancer, the process of the network losing connectivity might be the process of disrupting the scale-free structure of the network, namely, the number of hub genes might be altered in cancer compared to that in normal samples. Hence, it is hypothesized that if the number of hub genes is different in a pathway between normal and cancer, this pathway might be involved in cancer. MiR2Pathway focuses on quantifying the differential effects of miRNAs on the activity of a biological pathway when miRNA-mRNA connections are altered from normal to disease and rank disease risk of rewired miRNA-mediated biological pathways. This dissertation explores how rewired gene-gene interactions and rewired miRNA-mRNA interactions lead to aberrant activity of biological pathways, and rank pathways for their disease risk. The two methods proposed here can be used to complement existing genomics analysis methods to facilitate the study of biological mechanisms behind disease at the systems-level.
ContributorsLi, Chaoxing (Author) / Dinu, Valentin (Thesis advisor) / Kuang, Yang (Thesis advisor) / Liu, Li (Committee member) / Wang, Xiao (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 role of climate change, as measured in terms of changes in the climatology of geophysical variables (such as temperature and rainfall), on the global distribution and burden of vector-borne diseases (VBDs) remains a subject of considerable debate. This dissertation attempts to contribute to this debate via the use of mathematical (compartmental) modeling and statistical data analysis. In particular, the objective is to find suitable values and/or ranges of the climate variables considered (typically temperature and rainfall) for maximum vector abundance and consequently, maximum transmission intensity of the disease(s) they cause.
Motivated by the fact that understanding the dynamics of disease vector is crucial to understanding the transmission and control of the VBDs they cause, a novel weather-driven deterministic model for the population biology of the mosquito is formulated and rigorously analyzed. Numerical simulations, using relevant weather and entomological data for Anopheles mosquito (the vector for malaria), show that maximum mosquito abundance occurs when temperature and rainfall values lie in the range [20-25]C and [105-115] mm, respectively.
The Anopheles mosquito ecology model is extended to incorporate human dynamics. The resulting weather-driven malaria transmission model, which includes many of the key aspects of malaria (such as disease transmission by asymptomatically-infectious humans, and enhanced malaria immunity due to repeated exposure), was rigorously analyzed. The model which also incorporates the effect of diurnal temperature range (DTR) on malaria transmission dynamics shows that increasing DTR shifts the peak temperature value for malaria transmission from 29C (when DTR is 0C) to about 25C (when DTR is 15C).
Finally, the malaria model is adapted and used to study the transmission dynamics of chikungunya, dengue and Zika, three diseases co-circulating in the Americas caused by the same vector (Aedes aegypti). The resulting model, which is fitted using data from Mexico, is used to assess a few hypotheses (such as those associated with the possible impact the newly-released dengue vaccine will have on Zika) and the impact of variability in climate variables on the dynamics of the three diseases. Suitable temperature and rainfall ranges for the maximum transmission intensity of the three diseases are obtained.
Motivated by the fact that understanding the dynamics of disease vector is crucial to understanding the transmission and control of the VBDs they cause, a novel weather-driven deterministic model for the population biology of the mosquito is formulated and rigorously analyzed. Numerical simulations, using relevant weather and entomological data for Anopheles mosquito (the vector for malaria), show that maximum mosquito abundance occurs when temperature and rainfall values lie in the range [20-25]C and [105-115] mm, respectively.
The Anopheles mosquito ecology model is extended to incorporate human dynamics. The resulting weather-driven malaria transmission model, which includes many of the key aspects of malaria (such as disease transmission by asymptomatically-infectious humans, and enhanced malaria immunity due to repeated exposure), was rigorously analyzed. The model which also incorporates the effect of diurnal temperature range (DTR) on malaria transmission dynamics shows that increasing DTR shifts the peak temperature value for malaria transmission from 29C (when DTR is 0C) to about 25C (when DTR is 15C).
Finally, the malaria model is adapted and used to study the transmission dynamics of chikungunya, dengue and Zika, three diseases co-circulating in the Americas caused by the same vector (Aedes aegypti). The resulting model, which is fitted using data from Mexico, is used to assess a few hypotheses (such as those associated with the possible impact the newly-released dengue vaccine will have on Zika) and the impact of variability in climate variables on the dynamics of the three diseases. Suitable temperature and rainfall ranges for the maximum transmission intensity of the three diseases are obtained.
ContributorsOkuneye, Kamaldeen O (Author) / Gumel, Abba B (Thesis advisor) / Kuang, Yang (Committee member) / Smith, Hal (Committee member) / Thieme, Horst (Committee member) / Nagy, John (Committee member) / Arizona State University (Publisher)
Created2018
Description
Rabies is an infectious viral disease. It is usually fatal if a victim reaches the rabid stage, which starts after the appearance of disease symptoms. The disease virus attacks the central nervous system, and then it migrates from peripheral nerves to the spinal cord and brain. At the time when the rabies virus reaches the brain, the incubation period is over and the symptoms of clinical disease appear on the victim. From the brain, the virus travels via nerves to the salivary glands and saliva.
A mathematical model is developed for the spread of rabies in a spatially distributed fox population to model the spread of the rabies epizootic through middle Europe that occurred in the second half of the 20th century. The model considers both territorial and wandering rabid foxes and includes a latent period for the infection. Since the model assumes these two kinds of rabid foxes, it is a system of both partial differential and integral equations (with integration
over space and, occasionally, also over time). To study the spreading speeds of the rabies epidemic, the model is reduced to a scalar Volterra-Hammerstein integral equation, and space-time Laplace transform of the integral equation is used to derive implicit formulas for the spreading speed. The spreading speeds are discussed and implicit formulas are given for latent periods of fixed length, exponentially distributed length, Gamma distributed length, and log-normally distributed length. A number of analytic and numerical results are shown pertaining to the spreading speeds.
Further, a numerical algorithm is described for the simulation
of the spread of rabies in a spatially distributed fox population on a bounded domain with Dirichlet boundary conditions. I propose the following methods for the numerical approximation of solutions. The partial differential and integral equations are discretized in the space variable by central differences of second order and by
the composite trapezoidal rule. Next, the ordinary or delay differential equations that are obtained this way are discretized in time by explicit
continuous Runge-Kutta methods of fourth order for ordinary and delay differential systems. My particular interest
is in how the partition of rabid foxes into
territorial and diffusing rabid foxes influences
the spreading speed, a question that can be answered by purely analytic means only for small basic reproduction numbers. I will restrict the numerical analysis
to latent periods of fixed length and to exponentially
distributed latent periods.
The results of the numerical calculations
are compared for latent periods
of fixed and exponentially distributed length
and for various proportions of territorial
and wandering rabid foxes.
The speeds of spread observed in the
simulations are compared
to spreading speeds obtained by numerically solving the analytic formulas
and to observed speeds of epizootic frontlines
in the European rabies outbreak 1940 to 1980.
A mathematical model is developed for the spread of rabies in a spatially distributed fox population to model the spread of the rabies epizootic through middle Europe that occurred in the second half of the 20th century. The model considers both territorial and wandering rabid foxes and includes a latent period for the infection. Since the model assumes these two kinds of rabid foxes, it is a system of both partial differential and integral equations (with integration
over space and, occasionally, also over time). To study the spreading speeds of the rabies epidemic, the model is reduced to a scalar Volterra-Hammerstein integral equation, and space-time Laplace transform of the integral equation is used to derive implicit formulas for the spreading speed. The spreading speeds are discussed and implicit formulas are given for latent periods of fixed length, exponentially distributed length, Gamma distributed length, and log-normally distributed length. A number of analytic and numerical results are shown pertaining to the spreading speeds.
Further, a numerical algorithm is described for the simulation
of the spread of rabies in a spatially distributed fox population on a bounded domain with Dirichlet boundary conditions. I propose the following methods for the numerical approximation of solutions. The partial differential and integral equations are discretized in the space variable by central differences of second order and by
the composite trapezoidal rule. Next, the ordinary or delay differential equations that are obtained this way are discretized in time by explicit
continuous Runge-Kutta methods of fourth order for ordinary and delay differential systems. My particular interest
is in how the partition of rabid foxes into
territorial and diffusing rabid foxes influences
the spreading speed, a question that can be answered by purely analytic means only for small basic reproduction numbers. I will restrict the numerical analysis
to latent periods of fixed length and to exponentially
distributed latent periods.
The results of the numerical calculations
are compared for latent periods
of fixed and exponentially distributed length
and for various proportions of territorial
and wandering rabid foxes.
The speeds of spread observed in the
simulations are compared
to spreading speeds obtained by numerically solving the analytic formulas
and to observed speeds of epizootic frontlines
in the European rabies outbreak 1940 to 1980.
ContributorsAlanazi, Khalaf Matar (Author) / Thieme, Horst R. (Thesis advisor) / Jackiewicz, Zdzislaw (Committee member) / Baer, Steven (Committee member) / Gardner, Carl (Committee member) / Kuang, Yang (Committee member) / Smith, Hal (Committee member) / Arizona State University (Publisher)
Created2018
Description
Glioblastoma multiforme (GBM) is a malignant, aggressive and infiltrative cancer of the central nervous system with a median survival of 14.6 months with standard care. Diagnosis of GBM is made using medical imaging such as magnetic resonance imaging (MRI) or computed tomography (CT). Treatment is informed by medical images and includes chemotherapy, radiation therapy, and surgical removal if the tumor is surgically accessible. Treatment seldom results in a significant increase in longevity, partly due to the lack of precise information regarding tumor size and location. This lack of information arises from the physical limitations of MR and CT imaging coupled with the diffusive nature of glioblastoma tumors. GBM tumor cells can migrate far beyond the visible boundaries of the tumor and will result in a recurring tumor if not killed or removed. Since medical images are the only readily available information about the tumor, we aim to improve mathematical models of tumor growth to better estimate the missing information. Particularly, we investigate the effect of random variation in tumor cell behavior (anisotropy) using stochastic parameterizations of an established proliferation-diffusion model of tumor growth. To evaluate the performance of our mathematical model, we use MR images from an animal model consisting of Murine GL261 tumors implanted in immunocompetent mice, which provides consistency in tumor initiation and location, immune response, genetic variation, and treatment. Compared to non-stochastic simulations, stochastic simulations showed improved volume accuracy when proliferation variability was high, but diffusion variability was found to only marginally affect tumor volume estimates. Neither proliferation nor diffusion variability significantly affected the spatial distribution accuracy of the simulations. While certain cases of stochastic parameterizations improved volume accuracy, they failed to significantly improve simulation accuracy overall. Both the non-stochastic and stochastic simulations failed to achieve over 75% spatial distribution accuracy, suggesting that the underlying structure of the model fails to capture one or more biological processes that affect tumor growth. Two biological features that are candidates for further investigation are angiogenesis and anisotropy resulting from differences between white and gray matter. Time-dependent proliferation and diffusion terms could be introduced to model angiogenesis, and diffusion weighed imaging (DTI) could be used to differentiate between white and gray matter, which might allow for improved estimates brain anisotropy.
ContributorsAnderies, Barrett James (Author) / Kostelich, Eric (Thesis director) / Kuang, Yang (Committee member) / Stepien, Tracy (Committee member) / Harrington Bioengineering Program (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2016-05
Description
Magnetic resonance imaging (MRI) data of metastatic brain cancer patients at the Barrow Neurological Institute sparked interest in the radiology department due to the possibility that tumor size distributions might mimic a power law or an exponential distribution. In order to consider the question regarding the growth trends of metastatic brain tumors, this thesis analyzes the volume measurements of the tumor sizes from the BNI data and attempts to explain such size distributions through mathematical models. More specifically, a basic stochastic cellular automaton model is used and has three-dimensional results that show similar size distributions of those of the BNI data. Results of the models are investigated using the likelihood ratio test suggesting that, when the tumor volumes are measured based on assuming tumor sphericity, the tumor size distributions significantly mimic the power law over an exponential distribution.
ContributorsFreed, Rebecca (Co-author) / Snopko, Morgan (Co-author) / Kostelich, Eric (Thesis director) / Kuang, Yang (Committee member) / WPC Graduate Programs (Contributor) / School of Accountancy (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / Barrett, The Honors College (Contributor)
Created2018-12
Description
In this research we consider stochastic models of Glioblastoma Multiforme brain tumors. We first look at a model by K. Swanson et al., which describes the dynamics as random diffusion plus deterministic logistic growth. We introduce a stochastic component in the logistic growth in the form of a random growth rate defined by a Poisson process. We show that this stochastic logistic growth model leads to a more accurate evaluation of the tumor growth compared its deterministic counterpart. We also discuss future plans to incorporate individual patient geometry, extend the model to three dimensions and to incorporate effects of different treatments into our model, in collaboration with a local hospital.
ContributorsManning, Michael Clare (Author) / Kostelich, Eric (Thesis director) / Kuang, Yang (Committee member) / Gardner, Carl (Committee member) / Barrett, The Honors College (Contributor) / School of Mathematical and Statistical Sciences (Contributor) / School of Letters and Sciences (Contributor) / School of Human Evolution and Social Change (Contributor)
Created2013-12
Description
Prostate cancer is the second most common kind of cancer in men. Fortunately, it has a 99% survival rate. To achieve such a survival rate, a variety of aggressive therapies are used to treat prostate cancers that are caught early. Androgen deprivation therapy (ADT) is a therapy that is given in cycles to patients. This study attempted to analyze what factors in a group of 79 patients caused them to stick with or discontinue the treatment. This was done using naïve Bayes classification, a machine-learning algorithm. The usage of this algorithm identified high testosterone as an indicator of a patient persevering with the treatment, but failed to produce statistically significant high rates of prediction.
ContributorsMillea, Timothy Michael (Author) / Kostelich, Eric (Thesis director) / Kuang, Yang (Committee member) / Computer Science and Engineering Program (Contributor) / Barrett, The Honors College (Contributor)
Created2016-12
Description
Cancer is a major health problem in the world today and is expected to become an even larger one in the future. Although cancer therapy has improved for many cancers in the last several decades, there is much room for further improvement. Mathematical modeling has the advantage of being able to test many theoretical therapies without having to perform clinical trials and experiments. Mathematical oncology will continue to be an important tool in the future regarding cancer therapies and management.
This dissertation is structured as a growing tumor. Chapters 2 and 3 consider spheroid models. These models are adept at describing 'early-time' tumors, before the tumor needs to co-opt blood vessels to continue sustained growth. I consider two partial differential equation (PDE) models for spheroid growth of glioblastoma. I compare these models to in vitro experimental data for glioblastoma tumor cell lines and other proposed models. Further, I investigate the conditions under which traveling wave solutions exist and confirm numerically.
As a tumor grows, it can no longer be approximated by a spheroid, and it becomes necessary to use in vivo data and more sophisticated modeling to model the growth and diffusion. In Chapter 4, I explore experimental data and computational models for describing growth and diffusion of glioblastoma in murine brains. I discuss not only how the data was obtained, but how the 3D brain geometry is created from Magnetic Resonance (MR) images. A 3D finite-difference code is used to model tumor growth using a basic reaction-diffusion equation. I formulate and test hypotheses as to why there are large differences between the final tumor sizes between the mice.
Once a tumor has reached a detectable size, it is diagnosed, and treatment begins. Chapter 5 considers modeling the treatment of prostate cancer. I consider a joint model with hormonal therapy as well as immunotherapy. I consider a timing study to determine whether changing the vaccine timing has any effect on the outcome of the patient. In addition, I perform basic analysis on the six-dimensional ordinary differential equation (ODE). I also consider the limiting case, and perform a full global analysis.
This dissertation is structured as a growing tumor. Chapters 2 and 3 consider spheroid models. These models are adept at describing 'early-time' tumors, before the tumor needs to co-opt blood vessels to continue sustained growth. I consider two partial differential equation (PDE) models for spheroid growth of glioblastoma. I compare these models to in vitro experimental data for glioblastoma tumor cell lines and other proposed models. Further, I investigate the conditions under which traveling wave solutions exist and confirm numerically.
As a tumor grows, it can no longer be approximated by a spheroid, and it becomes necessary to use in vivo data and more sophisticated modeling to model the growth and diffusion. In Chapter 4, I explore experimental data and computational models for describing growth and diffusion of glioblastoma in murine brains. I discuss not only how the data was obtained, but how the 3D brain geometry is created from Magnetic Resonance (MR) images. A 3D finite-difference code is used to model tumor growth using a basic reaction-diffusion equation. I formulate and test hypotheses as to why there are large differences between the final tumor sizes between the mice.
Once a tumor has reached a detectable size, it is diagnosed, and treatment begins. Chapter 5 considers modeling the treatment of prostate cancer. I consider a joint model with hormonal therapy as well as immunotherapy. I consider a timing study to determine whether changing the vaccine timing has any effect on the outcome of the patient. In addition, I perform basic analysis on the six-dimensional ordinary differential equation (ODE). I also consider the limiting case, and perform a full global analysis.
ContributorsRutter, Erica Marie (Author) / Kuang, Yang (Thesis advisor) / Kostelich, Eric J (Thesis advisor) / Frakes, David (Committee member) / Gardner, Carl (Committee member) / Jackiewicz, Zdzislaw (Committee member) / Arizona State University (Publisher)
Created2016
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