The thesis uses mathematical modeling and analysis to provide insights into the transmission dynamics of Human papillomavirus (HPV), and associated cancers and warts, in a community. A new deterministic model is designed and used to assess the community-wide impact of mass vaccination of new sexually-active susceptible females with the anti-HPV Gardasil vaccine. Conditions for the existence and asymptotic stability of the associated equilibria are derived. Numerical simulations show that the use of Gardasil vaccine could lead to the effective control of the spread of HPV in the community if the vaccine coverage is at least 78%. The model is extended to include the dynamics of the low- and high-risk HPV types and the combined use of the Gardasil and Cervarix anti-HPV vaccines. Overall, this study shows that the prospect of the effective community-wide control of HPV using the currently-available anti-HPV vaccines are encouraging.

No description available.

Expanding cell populations extracted from patients or animals is essential to the process of tissue engineering and is commonly performed in laboratory incubation devices known as bioreactors. Bioreactors provide a means of controlling the chemical and mechanical environment experienced by cells to ensure growth of a functional population. However, maximising this growth requires detailed knowledge of how cell proliferation is affected by bioreactor operating conditions, such as the flow rate of culture medium into the bioreactor, and by the initial cell seeding distribution in the bioreactor. Mathematical modelling can provide insight into the effects of these factors on cell expansion by describing the chemical and physical processes that affect growth and how they interact over different length- and time-scales. In this thesis we develop models to investigate how cell expansion in bioreactors is affected by fluid flow, solute transport and cell seeding. For this purpose, a perfused single-fibre hollow fibre bioreactor is used as a model system. We start by developing a model of the growth of a homogeneous cell layer on the outer surface of the hollow fibre in response to local nutrient and waste product concentrations and fluid shear stress. We use the model to simulate the cell layer growth with different flow configurations and operating conditions for cell types with different nutrient demands and responses to fluid shear stress. We then develop a 2D continuum model to investigate the influence of oxygen delivery, fluid shear stress and cell seeding on cell aggregate growth along the outer surface of the fibre. Using the model we predict operating conditions and initial aggregate distributions that maximise the rate of growth to confluence over the fibre surface for different cell types. A potential limitation of these models is that they do not explicitly consider individual cell interaction, movement and growth. To address this, we conclude the thesis by assessing the suitability of a hybrid framework for modelling bioreactor cell aggregate growth, with a discrete cell model coupled to a continuum nutrient transport model. We consider a simple set-up with a 1D cell aggregate growing along the base of a 2D nutrient bath. Motivated by trying to reduce the high computational cost of simulating large numbers of cells with a cell-based model, and to assess the validity of our previous continuum description of cell aggregate growth, we derive a continuum approximation of the discrete model in the large cell number limit and determine whether it agrees with the discrete model via numerical simulations.

Colorectal cancer has the third highest mortality and incidence rates of all cancers worldwide, but the prognosis for long-term survival is good if diagnosed early. It is a well-characterised disease, and is initiated in colonic crypts which line the colon wall. The aim of this thesis is to use mathematical modelling to describe the heavily regulated cell renewal cycle in the crypt to determine the key features of the system kinetics, and help to explain the initiation of tumourigenesis. The dynamics of a single colorectal crypt is considered using a compartmental approach, which accounts for populations of stem, transit-amplifying and fullydifferentiated cells. A number of different model formulations are derived, and their validity and suitability are discussed. Two mechanisms are presented that could regulate the growth of cell numbers and maintain homeostasis (equilibrium), and it is illustrated how a model can describe both regulated and unregulated growth, with cancer-driving cells deriving from stem and/or transit cells. This model is used to explain the long lag phases observed in carcinogenesis, which occur between periods of rapid tumour expansion, before unlimited growth in cell numbers ensues. Significantly, it is found that, contrary to general belief, the proportion of cancer-driving cells in the exponential growth phase of a tumour may vary depending on tumour type. The process of cells accumulating mutations is also examined by considering both a stochastic individual cell-based model and an analytic approach. Finally, an ordinary differential equation model is shown to be valid by considering a simplified description of a one-dimensional spatial model, and the latter is used to consider the effect of changing the crypt shape. The suitability of this modelling approach to tracking stem cells in a niche, as well as mutant cell clones as they propagate in the crypt, is also discussed.

The availability of large scale protein interaction networks for several species has motivated many comparative studies in recent years. These studies typically employ network alignment algorithms for the task and use the sequence similarity of proteins to aid the alignment process. In this thesis I use a quantitative measure of protein functional similarity and show that the results are superior to sequence based network alignment. I present a method for module detection that combines results from network alignments with clustering measures to achieve superior results over several existing methods. Next, I address the issue of generally low conservation detected by alignments of interaction networks from model organisms. By explicitly modelling evolutionary mechanisms on pairs of networks I test the hypothesis that divergent evolution alone may be the cause. I use a distance metric based on graph summary statistics to assess the fit between experimental and simulated network alignments. Our results indicate that network evolution alone is unlikely to account for the poor quality alignments given by real data. We also find that false positives appear to affect network alignments little compared to false negatives indicating that incompleteness, not spurious links, is the major challenge for interactome-level comparisons. Finally, I focus on the comparative analysis of a subset of the interaction network related to mitosis in Yeast, Human and Fly. Manual ordering of mitosis-related functional annotations allows the study of temporal aspects of the network. I also use a Markov random field approach to infer temporal labels for unlabelled proteins. Sequence based network alignment of the mitotic networks in the three species finds little conservation despite the proteins being functionally very similar. Further investigation suggests a fuzzy relationship between protein sequence and function that may have implications for future network alignment studies.

Major efforts to sequence cancer genomes are now occurring throughout the world. Though the emerging data from these studies are illuminating, their reconciliation with epidemiologic and clinical observations poses a major challenge. Here we present mathematical models that begin to address this challenge. First we present a model of accumulation of driver and passenger mutations during tumor progression and derive a formula for the number of driver mutations as a function of the total number of mutations in a tumor. Fitting this formula to recent experimental data, we were able to calculate the selective advantage provided by a typical driver mutation. Second, we performed a quantitative analysis of pancreatic cancer metastasis genetic data. The results of this analysis define a broad time window for detection of pancreatic cancer before metastatic dissemination. Finally, we model the evolution of resistance to targeted cancer therapy. We apply our model to experimental data on the response to panitumumab, targeted therapy against colorectal cancer. Our modeling suggested that cells resistant to therapy were likely present in patients’ tumors prior to the start of therapy. / Mathematics

Quorum sensing is a cell communication mechanism used to coordinate group behaviour based on population density. A mathematical model of quorum sensing in bacterial biofilms is developed, consisting of a nonlinear diffusion reaction system describing the effects of a growing biofilm on bacterial quorum sensing behaviour. In numerical experiments, the influence of the hydrodynamic environment and nutrient conditions on biofilm growth and quorum sensing behaviour are studied, and flow-facilitated inter-colony communication and spatiotemporal quorum sensing induction patterns are observed. The model is extended to include an impact of quorum sensing on biofilm growth, through the explicit description of EPS, the protective biomass layer surrounding bacterial biofilm cells. The circumstances under which quorum sensing-regulated EPS production is a beneficial strategy for cells are identified. Biofilm colonies that use this strategy have lower cell populations than non-quorum sensing colonies, but may secure nutrients in a space-limited environment and outcompete neighbouring colonies.

The use of agricultural fungicides exerts very strong selection pressures on plant pathogens. This can lead to the spread of fungicide resistance in the pathogen population, which leads to a reduction in efficacy of disease control and loss of yield. In this thesis, we use mathematical modelling to investigate how the spread of fungicide resistant pathogen strains can be slowed, using epidemiological models to understand how application strategies can be optimised. A range of different fungicide application strategies have been proposed as anti-resistance strategies. Two of the most often considered strategies rely on combining two fungicides with different modes of action. The first involves spraying the two fungicides at the same time (mixture) and the second spraying them alternately at different times (alternation). These strategies have been compared both experimentally and by mathematical modellers for decades, but no firm conclusion as to which is better has been reached, although mixtures have in general often been favoured. We use mathematical models of septoria leaf blotch (Zymoseptoria tritici) on winter wheat and powdery mildew on grapevine (Erysiphe necator) to investigate the relative performance of these two strategies. We show that depending on the exact way in which the strategies are compared and the exact case, either strategy can be the more effective. However, when aiming to optimise yield in the long-term, we show that mixtures are very likely to be the most effective strategy in any given case. The structure of mathematical models clearly impacts on the conclusions of those models. As well as investigating the sensitivity of our conclusions to the structure of the models, we use a range of nested models to isolate mechanisms driving the differential performance of fungicide mixtures and alternation. Although the fine detail of a model’s predictions depends on its exact structure, we find a number of conserved patterns. In particular we find no case in which mixtures do not produce the overall largest yield over the time for which the fungicide remains effective. We also investigate the effects of the timing of an individual fungicide spray on its contribution toward resistance development and disease control. A set of so-called “governing principles” to understand the performance of resistance-management strategies was recently introduced by van den Bosch et al., formalising concepts from earlier literature. These quantify selection rates by examining the difference between the growth rates of fungicide-sensitive and fungicide resistant pathogen strains. Throughout the thesis, we concentrate on the extent to which these governing principles can be used to explain the relative performance of the resistance-management strategies that are considered.

An epidemiological model that incorporates individual adoption of protective behaviours due to fear of contracting an infectious disease is presented. These adaptive behaviours are assumed to lower an individual's risk of infection. The dynamics of this model are analyzed and the effects of fear on important public health metrics such as outbreak length, final size, and peak prevalence are investigated. It is concluded that the coupled dynamics of fear- and disease-spread are rich and can lead to counter-intuitive effects on the public health metrics considered. In particular, it is not always the case that more effective protective behaviours lead to the most favourable population-level outcomes; intermediate levels of effectiveness are optimal in some cases. This result depends on when fearful individuals become infected with respect to the main outbreak that is mostly driven by the infection of fully susceptible individuals. / Thesis / Master of Science (MSc)

In this dissertation, we investigate the mechanisms behind diseases and the immune responses required for successful disease resolution in three projects: i) A study of HIV and HPV co-infection, ii) A germinal center dynamics model, iii) A study of monoclonal antibody therapy. We predict that the condition leading to HPV persistence during HIV/HPV co-infection is the permissive immune environment created by HIV, rather than the direct HIV/HPV interaction. In the second project, we develop a germinal center model to understand the mechanisms that lead to the formation of potent long-lived plasma. We predict that the T follicular helper cells are a limiting resource and present possible mechanisms that can revert this limitation in the presence of non-mutating and mutating antigen. Finally, we develop a pharmacokinetic model of 3BNC117 antibody dynamics and HIV viral dynamics following antibody therapy. We fit the models to clinical trial data and conclude that antibody binding is delayed and that the combined effects of initial CD4 T cell count, initial HIV levels, and virus production are strong indicators of a good response to antibody immunotherapy. / Ph. D.