Controlling infectious disease spread and preventing disease onset are ongoing challenges, especially in the presence of newly emerging diseases. While vaccines have successfully eradicated smallpox and reduced occurrence of many diseases, there still exists challenges such as fear of vaccination, the cost and difficulty of transporting vaccines, and the ability of attenuated viruses to evolve, leading to instances such as vaccine derived poliovirus. Antibiotic resistance due to mistreatment of antibiotics and quickly evolving bacteria contributes to the difficulty of eradicating diseases such as tuberculosis. Additionally, bacteria and fungi are able to produce an extracellular matrix in biofilms that protects them from antibiotics/antifungals. Mathematical models are an effective way of measuring the success of various control measures, allowing for cost savings and efficient implementation of those measures. While many models exist to investigate the dynamics on a human population scale, it is also beneficial to use models on a microbial scale to further capture the biology behind infectious diseases. In this dissertation, we develop mathematical models at several spatial scales to help improve disease control. At the scale of human populations, we develop differential equation models with quarantine control. We investigate how the distribution of exposed and infectious periods affects the control efficacy and suggest when it is important for models to include realistically narrow distributions. At the microbial scale, we use an agent-based stochastic spatial simulation to model the social interactions between two yeast strains in a biofilm. While cheater strains have been proposed as a control strategy to disrupt the harmful cooperative biofilm, some yeast strains cooperate only with other cooperators via kin recognition. We study under what circumstances kin recognition confers the greatest fitness benefit to a cooperative strain. Finally, we look at a multiscale, two-patch model for the dynamics between wild-type (WT) poliovirus and defective interfering particles (DIPs) as they travel between organs. DIPs are non-viable variants of the WT that lack essential elements needed for reproduction, causing them to steal these elements from the WT. We investigate when DIPs can lower the WT population in the host.

Made available in DSpace on 2015-03-26T13:35:24Z (GMT). No. of bitstreams: 1 01 - capa_abstract.pdf: 134195 bytes, checksum: 45ccca4315780ed037185fce918f9327 (MD5) Previous issue date: 2007-03-21 / Universidade Federal de Viçosa / Despite of the recent progress in cancer diagnosis and treatment, the survival rates of patients with tumors in unresectable locations, recurrent or metastatic tumors are still low. On the quest for alternative treatments, oncolytic virotherapy and encapsulation of chemotherapeutic drugs into nanoscale vehicles emerge as promissing strategies. However, several fundamental process and issues still must be understood in order to enhance the efficacy of these treatments. The nonlinearities and complexities inherent to tumor-oncolytic virus and tumor-drug interactions claim for a mathematical approach. Quantitative models allow to enlarge our understanding of the parameters influencing therapeutic outcomes, guide essays by indicating relevant physiological processes for further investigation, and prevent excessive experimentation. The multiescale models for virotherapy presented and discussed in this thesis suggest the appropriate traits an oncolytic virus must have and the less agressive ways to modulate the antiviral immune response in order to maximize the tumor erradication probability. Concerning the model for treatment with chemotherapeutic drugs encapsulated into nanoparticles, we focused on chimeric polymers attached with the doxorubicin drug, that recently are under active investigation. Using the same parameters that characterize these particles and the experimental protocols commonly used for their administration, our results indicate some of the basic features of these nanoparticles that should be developed in order to maximize the therapy's success. / A maior parte das terapias anti-câncer clinicamente usadas tem se desenvolvido empiricamente [1] mas a resposta do tumor e do organismo a essas terapias é não-linear. Portanto, modelos matemáticos podem ser ferramentas complementares (e talvez necessárias) para a compreensão da dinâmica da resposta à droga ou terapia no organismo. Nesta dissertação de mestrado alguns desses modelos são estudados. Em particular, propomos uma estratégia para crescer agregados isotrópicos do modelo de Eden na rede, um modelo estocástico básico para o crescimento de tumores avasculares, Os padrões gerados são caracterizados pela largura da interface, que é calculada considerando o centro da rede ou o centro de massa do agregado como referência, e pela diferença entre as probabilidades de crescimento axial e diagonal. Também foi estudado um modelo de multiescala para viroterapia em tumores avasculares em que as concentrações de nutrientes e vírus são descritas por equações de reação-difusão macroscópicas e as ações de células tumorais são governadas por regras estocásticas microscópicas. O objetivo central dessa parte do trabalho é a determinação do diagrama de estados no espaço de parâmetros. A faixa de parâmetros envolvidos foi estimada a partir de dados experimentais e a resposta das células tumorais à injeção viral apresenta quatro comportamentos diferentes, todos observados experimentalmente. Os valores dos parâmetros que geram predominantemente cada um desses comportamentos são determinados. / Não foi localizado o texto completo O texto publicado trata-se do resumo

High dimensional space-time datasets are available nowadays in various aspects of life such as economy, agriculture, health, environment, etc. Meanwhile, it is challenging to reveal possible connections between climate change and weather extreme events such as hurricanes or tornadoes. In particular, the relationship between tornado occurrence and climate change has remained elusive. Moreover, modeling multivariate spatio-temporal data is computationally expensive. There is great need to computationally feasible models that account for temporal, spatial, and inter-variables dependence. Our research focuses on those areas in two ways. First, we investigate connections between changes in tornado risk and the increase in atmospheric instability over Oklahoma. Second, we propose two multiscale spatio-temporal models, one for multivariate Gaussian data, and the other for matrix-variate Gaussian data. Those frameworks are novel additions to the existing literature on Bayesian multiscale models. In addition, we have proposed parallelizable MCMC algorithms to sample from the posterior distributions of the model parameters with enhanced computations. / Doctor of Philosophy / Over 1000 tornadoes are reported every year in the United States causing massive losses in lives and possessions according to the National Oceanic and Atmospheric Administration. Therefore, it is worthy to investigate possible connections between climate change and tornado occurrence. However, there are massive environmental datasets in three or four dimensions (2 or 3 dimensional space, and time), and the relationship between tornado occurrence and climate change has remained elusive. Moreover, it is computationally expensive to analyze those high dimensional space-time datasets. In part of our research, we have found a significant relationship between occurrence of strong tornadoes over Oklahoma and meteorological variables. Some of those meteorological variables have been affected by ozone depletion and emissions of greenhouse gases. Additionally, we propose two Bayesian frameworks to analyze multivariate space-time datasets with fast and feasible computations. Finally, our analyses indicate different patterns of temperatures at atmospheric altitudes with distinctive rates over the United States.

PhD (Mathematics) / Department of Mathematics and Applied Mathematics / In this study, we developed multiscale models of vector-borne diseases. In general, the transmission of vector-borne diseases can be considered as falling into two categories, i.e. direct transmission and environmental transmission. Two representative vector-borne diseases, namely; malaria which represents all directly transmitted vector-borne diseases and schistosomiasis which represents all environmentally transmitted vector-borne diseases were studied. Based on existing mathematical modelling science base, we established a new multiscale modelling framework that can be used to evaluate the effectiveness of vector-borne diseases treatment and preventive interventions. The multiscale models consisted of systems of nonlinear ordinary differential equations which were studied for the provision of solutions to the underlying problem of the disease transmission dynamics. Relying on the fact that there is still serious lack of knowledge pertaining to mathematical techniques for the representation and construction of multiscale models of vector-bone diseases, we have developed some grand ideas to placate this gap. The central idea in multiscale modelling is to divide a modelling problem such as a vector-bone disease system into a family of sub-models that exist at different scales and then attempt to study the problem at these scales while simultaneously linking the sub-models across these scales. For malaria, we formulated the multiscale models by integrating four submodels which are: (i) a sub-model for the mosquito-to-human transmission of malaria parasite, (ii) a sub-model for the human-to-mosquito transmission of malaria parasite, (iii) a within-mosquito malaria parasite population dynamics sub-model and (iv) a within-human malaria parasite population dynamics sub-model. For schistosomiasis, we integrated the two subsystems (within-host and between-host sub-models) by identifying the within-host and between-host variables and parameters associated with the environmental dynamics of the pathogen and then designed a feedback of the variables and parameters across the within-host and between-host sub-models. Using a combination of analytical and computational tools we adequately accounted for the influence of the sub-models in the different multiscale models. The multiscale models were then used to evaluate the effectiveness of the control and prevention interventions that operate at different scales of a vector-bone disease system. Although the results obtained in this study are specific to malaria and schistosomiasis, the multiscale modelling frameworks developed are robust enough to be applicable to other vector-borne diseases. / NRF

Cette thèse est consacrée à la modélisation mathématique de la coagulation sanguine et de la formation de thrombus dans des conditions normales et pathologiques. La coagulation sanguine est un mécanisme défensif qui empêche la perte de sang suite à la rupture des tissus endothéliaux. C'est un processus complexe qui est règlementé par différents mécanismes mécaniques et biochimiques. La formation du caillot sanguin a lieu dans l'écoulement sanguin. Dans ce contexte, l'écoulement à faible taux de cisaillement stimule la croissance du caillot tandis que la circulation sanguine à fort taux de cisaillement la limite. Les désordres qui affectent le système de coagulation du sang peuvent provoquer différentes anomalies telles que la thrombose (coagulation exagérée) ou les saignements (insuffisance de coagulation). Dans la première partie de la thèse, nous présentons un modèle mathématique de coagulation sanguine. Le modèle capture la dynamique essentielle de la croissance du caillot dans le plasma et le flux sanguin quiescent. Ce modèle peut être réduit à un modèle qui consiste en une équation de génération de thrombine et qui donne approximativement les mêmes résultats. Nous avons utilisé des simulations numériques en plus de l'analyse mathématique pour montrer l'existence de différents régimes de coagulation sanguine. Nous spécifions les conditions pour ces régimes sur différents paramètres pathophysiologiques du modèle. Ensuite, nous quantifions les effets de divers mécanismes sur la croissance du caillot comme le flux sanguin et l'agrégation plaquettaire. La partie suivante de la thèse étudie certaines des anomalies du système de coagulation sanguine. Nous commençons par étudier le développement de la thrombose chez les patients présentant une carence en antihrombine ou l'une des maladies inflammatoires. Nous déterminons le seuil de l'antithrombine qui provoque la thrombose et nous quantifions l'effet des cytokines inflammatoires sur le processus de coagulation. Puis, nous étudions la compensation de la perte du sang après un saignement en utilisant un modèle multi-échelles qui décrit en particulier l'érythropoïèse et la production de l'hémoglobine. Ensuite, nous évaluons le risque de thrombose chez les patients atteints de cancer (le myélome multiple en particulier) et le VIH en combinant les résultats du modèle de coagulation sanguine avec les produits des modèles hybrides (discret-continues) multi-échelles des systèmes physiologiques correspondants. Finalement, quelques applications cliniques possibles de la modélisation de la coagulation sanguine sont présentées. En combinant le modèle de formation du caillot avec les modèles pharmacocinétiques pharmacodynamiques (PK-PD) des médicaments anticoagulants, nous quantifions l'action de ces traitements et nous prédisons leur effet sur des patients individuels / This thesis is devoted to the mathematical modelling of blood coagulation and clot formation under flow in normal and pathological conditions. Blood coagulation is a defensive mechanism that prevents the loss of blood upon the rupture of endothelial tissues. It is a complex process that is regulated by different mechanical and biochemical mechanisms. The formation of the blood clot takes place in blood flow. In this context, low-shear flow stimulates clot growth while high-shear blood circulation limits it. The disorders that affect the blood clotting system can provoke different abnormalities such thrombosis (exaggerated clotting) or bleeding (insufficient clotting). In the first part of the thesis, we introduce a mathematical model of blood coagulation. The model captures the essential dynamics of clot growth in quiescent plasma and blood flow. The model can be reduced to a one equation model of thrombin generation that gives approximately the same results. We used both numerical simulations and mathematical investigation to show the existence of different regimes of blood coagulation. We specify the conditions of these regimes on various pathophysiological parameters of the model. Then, we quantify the effects of various mechanisms on clot growth such as blood flow and platelet aggregation. The next part of the thesis studies some of the abnormalities of the blood clotting system. We begin by investigating the development of thrombosis in patients with antihrombin deficiency and inflammatory diseases. We determine the thrombosis threshold on antithrombin and quantify the effect of inflammatory cytokines on the coagulation process. Next, we study the recovery from blood loss following bleeding using a multiscale model which focuses on erythropoiesis and hemoglobin production. Then, we evaluate the risk of thrombosis in patients with cancer (multiple myeloma in particular) and HIV by combining the blood coagulation model results with the output of hybrid multiscale models of the corresponding physiological system. Finally, possible clinical applications of the blood coagulation modelling are provided. By combining clot formation model with pharmacokinetics-pharmacodynamics (PK-PD) models of anticoagulant drugs, we quantify the action of these treatments and predict their effect on individual patients