In this work we have developed three ordinary differential equation models of biological systems: body mass change in response to exercise, immune system response to a general inflammatory stimulus, and the immune system response in atherosclerosis. The purpose of developing such computational tools is to test hypotheses about the underlying biological processes that drive system outcomes as well as possible real medical interventions. Therefore, we focus our analysis on understanding key interactions between model parameters and outcomes to deepen our understanding of these complex processes as a means to developing effective treatments in obesity, sarcopenia, and inflammatory diseases. We develop a model of the dynamics of muscle hypertrophy in response to resistance exercise and have shown that the parameters controlling response vary between male and female group means in an elderly population. We further explore this individual variability by fitting to data from a clinical obesity study. We then apply logistic regression and classification tree methods to the analysis of between- and within-group differences in underlying physiology that lead to different long-term body composition outcomes following a diet or exercise program. Finally, we explore dieting strategies using optimal control methods. Next, we extend an existing model of inflammation to include different macrophage phenotypes. Complications with this phenotype switch can result in the accumulation of too many of either type and lead to chronic wounds or disease. With this model we are able to reproduce the expected timing of sequential influx of immune cells and mediators in a general inflammatory setting. We then calibrate this base model for the sequential response of immune cells with peritoneal cavity data from mice. Next, we develop a model for plaque formation in atherosclerosis by adapting the current inflammation model to capture the progression of macrophages to inflammatory foam cells in response to cholesterol consumption. The purpose of this work is ultimately to explore points of intervention that can lead to homeostasis.

The following thesis is a project in mathematical biology building upon the so-called "error minimization hypothesis" of the genetic code. After introducing the biological context of this hypothesis, I proceed to develop some relevant information-theoretic ideas, with the overall goal of studying the structure of the genetic code. I then apply the newfound understanding to an important question in the debate about the origin of life, namely, the question of the temperatures in which the genetic code, and life in general, underwent their early evolution. <br /><br /> The main advance in this thesis is a set of methods for calculating the primordial evolutionary pressures that shaped the genetic code. These pressures are due to genetic errors, and hence the statistical properties of the errors and of the genome are imprinted in the statistical properties of the code. Thus, by studying the code it is possible to reconstruct, to some extent, the primordial error rates and the composition of the primordial genome. In this way, I find evidence that the fixation of the genetic code occurred in organisms which were not thermophiles.

The following thesis is a project in mathematical biology building upon the so-called "error minimization hypothesis" of the genetic code. After introducing the biological context of this hypothesis, I proceed to develop some relevant information-theoretic ideas, with the overall goal of studying the structure of the genetic code. I then apply the newfound understanding to an important question in the debate about the origin of life, namely, the question of the temperatures in which the genetic code, and life in general, underwent their early evolution. <br /><br /> The main advance in this thesis is a set of methods for calculating the primordial evolutionary pressures that shaped the genetic code. These pressures are due to genetic errors, and hence the statistical properties of the errors and of the genome are imprinted in the statistical properties of the code. Thus, by studying the code it is possible to reconstruct, to some extent, the primordial error rates and the composition of the primordial genome. In this way, I find evidence that the fixation of the genetic code occurred in organisms which were not thermophiles.

This work uses mathematical models of evolutionary dynamics to address clinical questions about HIV treatment, public health questions about vaccination, and theoretical questions about evolution of high mutation rates.

No description available.

Malaria poses a serious threat to much of the developing world and an enormous effort is under way to design vaccines and other novel interventions. Nevertheless, we understand very little about the ecology and evolution of malaria parasites. For instance, while scientists have had considerable success identifying factors involved in regulating parasite growth within hosts, it is extremely hard to disentangle the relative influences of host immunity and other within-host factors on infection dynamics. Many mathematical models have been directed at understanding the dynamics of malaria infections, and these have provided valuable insights. However, these models have also been criticized, most notably for lacking any statistical analysis of the goodness of fit of model predictions to data. Here, we develop a new modeling approach that improves on previous work, and apply it to a novel data set from a simplified rodent malaria system. We find that resource availability and competition are important drivers of dynamics, and we identify a number of parasite traits that may underlie differences in virulence between parasite strains. These include the number of progeny parasites produced per infected cell (burst size) and the invasion rates of target cells. We test these predictions with further experiments and find broad support for the role of burst sizes in determining virulence, but the role of invasion rates is less certain. We also find evidence of potential plasticity in these parasite traits in response to within-host environmental factors. These within-host interactions between parasites and hosts have effects that will scale up to between-host processes; we discuss the growing body of theory that seeks to combine these levels (‘embedded models’). Using between-host and embedded models, we test the plausibility of various hypotheses to explain why there are so few transmissible malaria parasite forms, yet vast numbers of host-damaging asexual forms are produced. We show that a specific form of density-dependent transmission-blocking immunity and the occurrence of multiple infections can each generate selection for this pattern. Overall, this thesis contributes to a better under- standing of malaria parasites, while providing a framework for addressing unanswered questions in disease biology, and offering interesting paths for future empirical work. / Thesis (Ph.D, Biology) -- Queen's University, 2009-08-20 06:41:14.198

Pathogen evolution poses a significant challenge to public health, as efforts to control the spread of infectious diseases struggle to keep up with a shifting target. To better understand this adaptive process, we turn to mathematical modelling. Specifically, we use multi-type branching processes to describe a pathogen's stochastic spread among members of a host population or growth within a single host. In each case, there is potential for new pathogen strains with different characteristics to arise through mutation. We first develop a specific model to study the emergence of a newly introduced infectious disease, where the pathogen must adapt to its new host or face extinction in this population. In an extension of previous models, we separate the processes of host-to-host contacts and disease transmission, in order to consider each of their contributions in isolation. We also allow for an arbitrary distribution of host contacts and arbitrary mutational pathways/rates among strains. This framework enables us to assess the impact of these various factors on the chance that the process develops into a large-scale epidemic. We obtain some intriguing results when interpreted in a biological context. Secondly, motivated by a desire to investigate the time course of pathogen evolutionary processes more closely, we derive some novel theoretical results for multi-type branching processes. Specifically, we obtain equations for: (1) the distribution of waiting time for a particular type to arise; and (2) the distribution of population numbers over time, conditioned on a particular type not having yet appeared. A few numerical examples scratch the surface of potential applications for these results, which we hope to develop further. / Thesis (Master, Mathematics & Statistics) -- Queen's University, 2010-07-28 11:43:22.984

Chlamydia, caused by the bacterium Chlamydia trachomatis, is one of the most important sexually-transmitted infections globally. In addition to accounting for millions of cases every year, the disease causes numerous irreversible complications such as chronic pelvic pain, infertility in females and pelvic inflammatory disease. This thesis presents a number of mathematical models, of the form of deterministic systems of non-linear differential equations, for gaining qualitative insight into the transmission dynamics and control of Chlamydia within an infected host (in vivo) and in a population. The models designed address numerous important issues relating to the transmission dynamics of Chlamydia trachomatis, such as the roles of immune response, sex structure, time delay (in modelling the latency period) and risk structure (i.e., risk of acquiring or transmitting infection). The in-host model is shown to have a globally-asymptotically stable Chlamydia-free equilibrium whenever a certain biological threshold is less than unity. It has a unique Chlamydia-present equilibrium when the threshold exceeds unity. Unlike the in-host model, the two-group (males and females) population-level model undergoes a backward bifurcation, where a stable disease-free equilibrium co-exists with one or more stable endemic equilibria when the associated reproduction number is less than unity. This phenomenon, which is shown to be caused by the re-infection of recovered individuals, makes the effort to eliminate the disease from the population more difficult. Extending the two-group model to incorporate risk structure shows that the backward bifurcation phenomenon persists even when recovered individuals do not acquire re-infection. In other words, it is shown that stratifying the sexually-active population in terms of risk of acquiring or transmitting infection guarantees the presence of backward bifurcation in the transmission dynamics of Chlamydia in a population. Finally, it is shown (via numerical simulations) that a future Chlamydia vaccine that boosts cell-mediated immune response will be more effective in curtailing Chlamydia burden in vivo than a vaccine that enhances humoral immune response. The population-level impact of various targeted treatment strategies, in controlling the spread of Chlamydia in a population, are compared. In particular, it is shown that the use of treatment could have positive or negative population-level impact (depending on the sign of a certain epidemiological threshold).

Chlamydia, caused by the bacterium Chlamydia trachomatis, is one of the most important sexually-transmitted infections globally. In addition to accounting for millions of cases every year, the disease causes numerous irreversible complications such as chronic pelvic pain, infertility in females and pelvic inflammatory disease. This thesis presents a number of mathematical models, of the form of deterministic systems of non-linear differential equations, for gaining qualitative insight into the transmission dynamics and control of Chlamydia within an infected host (in vivo) and in a population. The models designed address numerous important issues relating to the transmission dynamics of Chlamydia trachomatis, such as the roles of immune response, sex structure, time delay (in modelling the latency period) and risk structure (i.e., risk of acquiring or transmitting infection). The in-host model is shown to have a globally-asymptotically stable Chlamydia-free equilibrium whenever a certain biological threshold is less than unity. It has a unique Chlamydia-present equilibrium when the threshold exceeds unity. Unlike the in-host model, the two-group (males and females) population-level model undergoes a backward bifurcation, where a stable disease-free equilibrium co-exists with one or more stable endemic equilibria when the associated reproduction number is less than unity. This phenomenon, which is shown to be caused by the re-infection of recovered individuals, makes the effort to eliminate the disease from the population more difficult. Extending the two-group model to incorporate risk structure shows that the backward bifurcation phenomenon persists even when recovered individuals do not acquire re-infection. In other words, it is shown that stratifying the sexually-active population in terms of risk of acquiring or transmitting infection guarantees the presence of backward bifurcation in the transmission dynamics of Chlamydia in a population. Finally, it is shown (via numerical simulations) that a future Chlamydia vaccine that boosts cell-mediated immune response will be more effective in curtailing Chlamydia burden in vivo than a vaccine that enhances humoral immune response. The population-level impact of various targeted treatment strategies, in controlling the spread of Chlamydia in a population, are compared. In particular, it is shown that the use of treatment could have positive or negative population-level impact (depending on the sign of a certain epidemiological threshold).

The typical response of cancer patients to treatment is only temporary, and is often followed by relapse. The failure of various therapeutic strategies is commonly attributed to the emergence of drug resistance. The response patterns for patients under such treatments indicate that complex dynamics regulate the response of the tumour to the therapy. The environment in which the tumour lives (the stroma) is known to be a modulator of multiple mechanisms that lead to drug resistance and seems to be a likely candidate for explaining some of this complexity. Understanding the role of stromal cells in the promotion of drug resistance is critical for the design of optimal treatment strategies, and for the development of novel therapies that selectively target both the tumour and the stroma. In this thesis we design two novel mathematical models that describe cancer growth within its environment and the evolution of drug resistance within spatially complex and temporally dynamic tumours. A compartment model captures clinically observed dynamics and allows direct comparison with experimental data, facilitating model parametrisation and the understanding of inter-tumour heterogeneity. An individual cell-based model highlights the key role of local interactions, determining heterogeneity at the tissue scale, that will eventually determine treatment outcome. A non-spatial approximation of this second model allows us to find analytic guidelines for the design of effective therapy. These tools allow the simulation of a range of treatment strategies (including combination of different drugs and variation of schedule) as well as the investigation of therapy response based on patient- or organ-specic parameters. The work developed in this dissertation is based on the paradigmatic biology of melanoma and non-small cell lung cancer. Its results are therefore applicable to a variety of cancer treatments that target similar processes, and whose therapeutic failure can be attributed to environment-mediated drug resistance.