Modeling Heterogeneity in Infectious Disease Systems for Inference and Monitoring
Nonhomogeneity in infectious disease spread can be described most directly via a population that is heterogeneous at the individual level. Spatial and network-based individual level models (ILMs) of Deardon et al. (2010) are two classes of models that describe such a population, and that have been successfully applied to human, animal, and plant diseases. ILMs allow the use of covariate information at the individual level (e.g. spatial location, number of contacts, etc.); the cost for this level of detail, however, is the computational time they take to be fitted to data. This thesis considers of a selection of topics on inference and surveillance for such models. One general theme is the reduction in computational burden associated with IBMs via aggregation and mathematical approximations. First, we consider a spatial ILM adapted to a system with two competing pathogens. A data-intensive model is first proposed for inference within a Bayesian MCMC framework, and then approximated by a faster model that utilizes aggregated data. The second topic develops an inference methodology for a network model that has a given degree distribution. Following results from Volz (2008) and Miller (2011), we develop an analytic likelihood for count data, and fit this to single and multi-season epidemics. Thirdly, we employ the same network model to test various surveillance systems. Using simulation, we derive distributional results for alarms meant to determine the start of seasonal epidemics, and compare their performance. All of our methods are tested on simulated data, and in addition, we use real influenza data sets to illustrate the methods related to network models.