Time-varying Individual-level Infectious Disease Models
Individual-level models (ILMs) of infectious disease spread are a system of statistical models which can be used to model infectious disease transmission through a population in discrete-time. These models allow researchers to incorporate risk factors at the individual level; thus they are suited for modeling epidemics spatially. Individuals, here, may refer to people, animals, or plants, or aggregated units such as animals on a farm or students in a school. ILMs are usually fitted to data within a Bayesian statistical framework using Markov chain Monte Carlo (MCMC) methods. Ideally, covariate data and the infection status of individuals over time would be used to obtain parameter estimates for the ILMs. However, owing to various practical reasons, there are often situations in which the collection of infectious disease data at the individual level is infeasible. Instead, infectious disease data is collected at a regional level (e.g. a level which actually consists of spatially aggregated sets of individual units), such as health units or census regions. Therefore, it is reasonable to assume that the infectivity of such aggregated units varies as the status of infectiousness (i.e. the number/proportion of infectious individuals) within the aggregated unit changes. In the thesis, ILMs are extended to allow for time-varying susceptibility, infectivity and contact functions. A series of time-varying infectivity ILMs (TVI-ILMs) are then developed for the problem of modeling disease spread at the regional level. A method of carrying out model comparison and assessment based on the use of probability scoring rules is also developed and explored. Finally, the TVI-ILMs are extended to allow for infectivity curves that are dependent on regional-level covariates. Models and methods are tested on a combination of simulated epidemic data, and data from the 2009 H1N1 influenza pandemic collected in Southern Ontario.