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Lie group analysis is arguably the most systematic vehicle for finding exact solutions of differential equations. Using this approach one has at one's disposal a variety of algorithms that make the solution process of many differential equations algorithmic. Vital properties of a given differential equation can often be inferred from the symmetries admitted by the equation. However, Lie group analysis has not enjoyed wide-spread application to systems of first-order ordinary differential equations. This is because such systems typically admit an infinite number of Lie point symmetries, and there is no systematic way to find even a single nontrivial one-dimensional Lie symmetry algebra. In the few applications available, the approach has been to circumvent the problem by transforming a given system of first-order ordinary differential equations into one in which at least one of the equations is of order two or greater. It is therefore fair to say that the full power of Lie group analysis has not been sufficiently harnessed in the solution of systems of first-order ordinary differential equations. In this dissertation we review some applications of Lie group analysis to systems of first order ordinary differential equations. We shed light on the integration procedure for first-order systems of ordinary differential equations admitting a solvable Lie algebra. We do this via instructive examples drawn from mathematical epidemiology models. In particular we revisit the work of Nucci and Torrisi [54] and improve the exposition of the Lie-symmetry-inspired solution of a mathematical model which describes a HIV transmission. To aid implementation of the integration strategy for systems of ordinary differential equations, we have developed ad-hoc routines for finding particular types of admitted symmetries and checking if a given symmetry is indeed admitted by a system of ordinary differential equations.

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The central theme of this dissertation is the development of a new approach to conceptualize and quantify dependence structures of capture-recapture data for closed populations, with specific emphasis on epidemiological applications. We introduce a measure of source dependence: the Coefficient of Incremental Dependence (CID). Properties of this and the related Coefficient of Source Dependence (CSD) of Vandal, Walker, and Pearson (2005) are presented, in particular their relationships to the conditional independence structures that can be modelled by hierarchical joint log-linear models (HJLLM). From these measures, we develop a new class of marginal log-linear models (MLLM), which we compare and contrast to HJLLMs. / We demonstrate that MLLMs serve to extend the universe of dependence structures of capture-recapture data that can be modelled and easily interpreted. Furthermore, the CIDs and CSDs enable us to meaningfully interpret the parameters of joint log-linear models previously excluded from the analysis of capture-recapture data for reasons of non-interpretability of model parameters. / In order to explore the challenges and features of MLLMs, we show how to produce inference from them under both a maximum likelihood and a Bayesian paradigm. The proposed modelling approach performs well and provides new insight into the fundamental nature of epidemiological capture-recapture data.

Capture-recapture methods are used to estimate population size from overlapping, incomplete sources of information. With three or more sources, dependence between sources may be modelled using log-linear models. We propose a Coefficient of Incremental Dependence Criterion (CIDC) for selecting an estimate of population size among all possible estimates that result from hierarchical log-linear models. A penalty for the number of parameters in the model was selected via simulation for the three-source and four-source settings. The performance of the proposed criterion was compared to the Akaike Information Criterion (AIC) through simulation. The CIDC was found to modestly outperform the AIC for data generated from a population size of approximately 100, with AIC performing consistently better for larger population sizes. Modifications to the criterion such as incorporating the estimated population size and the type of source interaction present should be investigated, along with the mathematical properties of the CIDC.

Susceptibles-infectives-removals (SIR) and its derivatives are the classic mathematical models for the study of infectious diseases in epidemiology. In order to model and simulate epidemics of an infectious disease, a global stochastic field simulation paradigm (GSFS) is proposed, which incorporates geographic and demographic based interactions. The interaction measure between regions is a function of population density and geographical distance, and has been extended to include demographic and migratory constraints. The progression of diseases using GSFS is analyzed, and similar behavior to the SIR model is exhibited by GSFS, using the geographic information systems (GIS) gravity model for interactions. The limitations of the SIR and similar models of homogeneous population with uniform mixing are addressed by the GSFS model. The GSFS model is oriented to heterogeneous population, and can incorporate interactions based on geography, demography, environment and migration patterns. The progression of diseases can be modeled at higher levels of fidelity using the GSFS model, and facilitates optimal deployment of public health resources for prevention, control and surveillance of infectious diseases.

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No description available.

This thesis examines the effect of hepatitis C virus infection (HCV) on health-related quality of life (HRQOL) to define burden of disease at individual and population levels. A systematic review of HCV HRQOL studies was undertaken with translation of Short Form-36 (SF-36) Health Survey data into community-weighted health state utilities using three different methods. Derived estimates of health utilities were 0.87 for HCV treatment-induced sustained virological response (SVR); 0.81 for pre-cirrhosis; 0.76 for compensated cirrhosis; 0.69 for decompensated cirrhosis; 0.67 for hepatocellular carcinoma (HCC); and 0.77 for liver transplant. The HCV health state utilities varied considerably from expert estimates, with relatively lower estimates for early liver disease and higher estimates for advanced liver disease, but were comparable to direct patient-elicited utilities. A study utilising data from population-based health surveys incorporating HCV screening among prisoners at Australian correctional centres in 1996 and 2001 showed no measurable effect of HCV on HRQOL, including that attributable to HCV viraemia. Compared to uninfected Australian norms, prisoners had lower HRQOL irrespective of HCV status. Several non-HCV factors such as age, co-morbidity, severity of depressive symptoms, and medical care utilization influenced HRQOL. A prospective study of health outcomes among HCV monoinfected and HIV/HCV coinfected individuals conducted at Sydney tertiary level hepatitis clinics between 2003 and 2005 found similar cognitive function, mood, and HRQOL patterns in these two HCV groups in the context of pegylated interferon (PEG-IFN) alfa-2a and ribavirin therapy. The HCV groups had similar levels of pre-treatment HRQOL impairment, further on-treatment deterioration, and posttreatment improvements. SVR was associated with significant HRQOL improvements, but mental HRQOL improvement was also seen in individuals not achieving an SVR. The impact of HCV treatment uptake on HCV-related burden of disease at a population level in Australia was examined using a mathematical model. The model estimated that in 2004, there were ~181,500 cases of chronic HCV infection, 7,020 with HCV-related cirrhosis, and annual incidence of 238 cases of HCV-related liver failure and 70 cases of HCV-related HCC. Compared to no treatment, current treatment levels (~1% of HCV-infected individuals per annum) would reduce projected HCV-related cirrhosis and advanced liver disease numbers by ~30% at 2020 and a gain of ~122,200 Quality-Adjusted Life Years (QALYs). Even with a five-fold increase from current treatment levels, advanced liver disease numbers will continue to increase through 2020 but will be reduced by ~55% and a gain of ~483,200 QALYs.

Made available in DSpace on 2015-12-10T14:23:17Z (GMT). No. of bitstreams: 0 Previous issue date: 2015-02-12. Added 1 bitstream(s) on 2015-12-10T14:27:58Z : No. of bitstreams: 1 000853296.pdf: 525856 bytes, checksum: 95f5500e6558ce1f31d89b02936acd5e (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Apresenta-se um modelo de equações diferenciais ordinárias que descreve a transmissão de dengue em uma população humana e de mosquitos quando há circulação de dois sorotipos de vírus. Resultados analíticos e numéricos para os pontos de equilíbrio deste modelo, e o estudo da estabilidade dos mesmos são obtidos. Faz-se uma aproximação de estado quase-estacionário para a população de mosquito, com o objetivo de estudar e comparar a dinâmica da transmissão da dengue em redes de diferentes topologias. O modelo de transmissão através de redes complexas considera diferentes graus de conectividade entre os indivíduos da população e por isso representa melhor as interações sociais. Observa-se que a dinâmica da transmissão da dengue depende fortemente da topologia da rede e do número médio de conexões, portanto medidas de controle da doença devem ter um impacto diferente dada a diversidade das conexões entre os indivíduos de uma população / We present a model of ordinary differential equations to describe the dengue transmission in a human and a mosquito populations when there are two serotypes of circulating virus. Analytic and numeric results to the equilibruim points of this model, and the study of the stability of this points were obtained. We assume the quasi-steady state approach to the mosquito population, in order to study and compare the dynamics of transmission of two serotypes of dengue virus in networks with different topologies. We consider the transmission model through complex networks with different degrees of conectivity among the individuals and, thus, it provides a better representation of the social interations. We observe that the transmission dynamics of dengue depends strongly on the network topology and the mean number of conections, thus the control measures must have a different impact given the diversity of conections among the individuals on the population / FAPESP: 2013/01552-7