In this dissertation we present mathematical models that help answer health policy questions relating to HIV and Hepatitis C (HCV), and analyze bias in Markov models of disease progression. We begin by developing a Markov decision process model that examines the timing of testing and treatment for diseases with asymptomatic periods such as HCV. We explicitly consider secondary infections, false positives and negatives, and behavioral modification from information from test results. We derive sufficient conditions for testing and/or treating in a dynamic environment, i.e., when unscheduled patients arrive. We also develop a detailed simulation model for general testing and/or treating for HCV. A key finding is that the current policy recommendations on testing for HCV may be too restrictive, and that it is cost-effective to test the overall population if done at the appropriate times. The Markov models used in the study of HCV motivated the next topic where we examine bias in Markov models of diseases. We examine models in which the progression of the disease varies with severity and find sufficient conditions for bias to exist in models that do not allow for transition probabilities to change with disease severity. We apply the results to HCV and find that the bias is significant depending on the method used to aggregate the disease data. We close with a discussion on a specific question in HIV policy where we develop a Bernoulli process transmission model in which, for a given individual, each risky person-to-person contact is treated as an independent Bernoulli trial. Using the model and data from the Urban Men's Health Study, we estimate the affect that interventions at venues, namely bathhouses, in which high-risk behavior takes place would have on HIV transmission.

For explanation and prediction of the evolution of infectious diseases in populations, researchers often use simplified mathematical models for simulation. We believe that the results from these models are often questionable when the epidemic dynamics becomes more complex, and that developing more realistic models is intractable. In this dissertation we propose to simulate infectious disease propagation using dynamic and complex networks. We present the Simulator of Epidemic Evolution using Complex Networks (SEECN), an expressive and high-performance framework that combines algorithms for graph generation and various operators for modeling temporal dynamics. For graph generation we use the Kronecker algorithm, derive its underlying statistical structure and exploit it for a variety of purposes. Then the epidemic is evolved over the network by simulating the dynamics of the population and the epidemic simultaneously, where each type of dynamics is performed by a separate operator. All dynamics operators can be fully and independently parameterized, facilitating incremental model development and enabling different influences to be toggled for differential analysis. As a prototype, we simulate two relatively complex models for the HIV epidemic and find a remarkable fit to reported data for AIDS incidence and prevalence. Our most important conclusion is that the mere dynamics of the HIV epidemic is sufficient to produce rather complex trends in the incidence and prevalence statistics, e.g. without the introduction of particularly effective treatments at specific times. We show that this invalidates assumptions and conclusions made previously in the literature, and argue that simulations used for explanation and prediction of trends should incorporate more realistic models for both the population and the epidemic than is currently done. In addition, we substantiate a previously predicted paradox that the availability of Highly Active Anti-Retroviral Treatment likely causes an increased HIV incidence.

Prions are self-perpetuating and, in most cases, aggregation-prone protein isoforms that transmit neurodegenerative diseases in mammals and control heritable traits in yeast. Prion conversion requires a very high level of identity of the interacting protein sequences. Decreased transmission of the prion state between divergent proteins is termed "species barrier" and was thought to occur due to the inability of divergent prion proteins to co-aggregate. Species barrier can be overcome in cross-species infections, for example from "mad cows" to humans. We studied the counterparts of yeast prion protein Sup35, originated from three different species of the Saccharomyces sensu stricto group and exhibiting the range of prion domain divergence that overlaps with the range of divergence observed among distant mammalian species. Heterologous Sup35 proteins co-aggregated in S. cerevisiae cells. However, in vivo cross-species prion conversion was decreased and in vitro polymerization was cross-inhibited in at least some heterologous combinations, thus demonstrating the existence of prion species barrier. Our data suggests that species-specificity of prion transmission is controlled at the level of conformational transition rather than co-aggregation. We have shown the Sup35 prion domain is sufficient for the species barrier among the S. sensu stricto species, and constructed SUP35 chimeric prion domains, combining the subregions of various origins Our data demonstrated in different cross-species combinations, different modules of prion domain play a crucial role in the controlling of species-specificity of prion transmission. One essential amino acid position has been identified in S. cerevisiae and S. paradoxus system. Our data support a model suggesting that identity of the short amyloidogenic sequences is crucial for the species barrier. Sup35 originated from three different species of the S. sensu stricto group were capable of forming a prion in S. cerevisiae. However, it was not known whether they are capable of generating and maintaining the prion state in the homologous cell environment. We have constructed the S. paradoxus and S. bayanus strains with appropriate markers, and we were able to demonstrate de novo [PSI+] formation in S. paradoxus but not in S. bayanus. Our data show that [PSI+] formation is not a unique property of S. cerevisiae.

More than 25 years have passed since the first cases of HIV/AIDS were reported and a decade since highly active antiretroviral therapy (HAART) was introduced as part of the continuum of care for people living with HIV/AIDS (PLWHA). The introduction of HAART as a continuum of care for PLWHA positively changed the characteristics of HIV/AIDS epidemic, contributing for significant declines of HIV/AIDS-related morbidity and mortality rates. Thus, a new era began with HAART, often referred as the “HAART era”. However, HAART also brought with it new challenges and issues for researchers working in the field of HIV/AIDS. This thesis comprises several studies that were designed to gain understanding of some issues on prevention and management of HIV/AIDS that emerged in the current HAART era. The review of the literature points out for many emergent issues in HAART era, but only some issues were researched and presented in this thesis.

Thesis (M.A.)--Naval Postgraduate School, 2008. / Description based on title page of source document ( viewed on April 23, 2008). Includes bibliographical references (p. 95-100).

Thesis (Ph.D.)--University of Wollongong, School of Biological Sciences. / Typescript. Includes bibliographical references: leaf 269-331.

Thesis (M.P.H.M. (Primary Health Care Management))--Mahidol University, 2007. / LICL has E-Thesis 0023 ; please contact computer services.

Thesis (MEng (Electronic engineering))-University of Pretoria, 2008. / Includes bibliographical references.

Thesis (M.A.) -- University of Texas Southwestern Medical Center at Dallas, 2004. / Vita. Bibliography: 71-73.

Published also as thesis (Ph. D.) Columbia university. / Bibliography: p. 102-103.