Mathematical modeling of diseases to inform health policy

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/ortreating 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 onthe 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.