Mathematical modelling is an effective tool for studying infectious disease epidemics. Stochastic models have been increasingly used in recent studies due to their ability to quantify uncertainty. Chapter 2 of my dissertation discusses the building of stochastic compartment models to analyze time series, infectious disease data, and applying Bayesian method to estimate the parameters. With an emphasis on modeling disease transmissibility, population-level, time series data of influenza morbidity and mortality from 1918 pandemic influenza in Baltimore, MD and Newark, NJ is analyzed. We find evidence that the transmissibility of influenza varies with time over the period September 1918 to November 1918 in these two locations with an increasing then decreasing transmissibility in Baltimore and a strictly decreasing transmissibility in Newark.
In contrast to the traditional population level models, simulation-based computational models that feature the "micro" structure of population have been developed to capture fine-grained disease dynamics and control strategies. These "agent-based models" (ABMs) general require a large number of input parameters, with empirical data insufficient to provide estimates for all of them (in statistical terms, nonidentifiability). Availability of prior information on different model levels make statistical inference a challenging task, for computational infectious disease models and for more general ABMs. Prior information at various model levels is combined and used to update information on the input parameters. The standard Bayesian approach to this updating induces changes in the ABM stochastic structure. Chapter 3 of my dissertation reports on Optimal Constrained Bayesian Updating method to address these issues including retaining the original ABM structure. Subject to retaining the ABM structure, the approach produces an updated distribution on inputs as close as possible to the standard Bayesian solution.
A disease natural history estimation example is presented in Chapter 4 to illustrate the optimal constrained Bayesian updating method.
Chapter 5 summarizes and discusses future works.
|School:||The Johns Hopkins University|
|School Location:||United States -- Maryland|
|Source:||DAI-B 68/11, Dissertation Abstracts International|
|Subjects:||Biostatistics, Public health|
|Keywords:||Bayesian updating, Infectious diseases, Stochastic model inference|
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