Statistical Methods for Complex Infectious Disease Systems

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Studies of infectious diseases are increasingly important in Canada and around the world. Outbreaks of diseases such as COVID-19, Ebola, SARS, or foot-and-mouth disease pose direct threats to public health and agriculture industries, and/or have serious economic effects. To quickly control such disease outbreaks, it is important to understand how the disease spreads over time and what factors lead some individuals to become infected and some not. To address these issues, several individual-level mathematical models for infectious disease transmission have been developed. These models have intuitive and flexible characteristics and have been shown to accurately describe the patterns of disease spread dynamics over time and space. The parameter estimation of such models is in general carried out in a Bayesian framework, using techniques such as Markov chain Monte Carlo (MCMC), which explores the posterior distribution. The Bayesian approach offers many advantages, such as the easy incorporation of missing data information as latent variables. However, the parameter estimation from these models in a Bayesian framework are computationally intensive, requiring substantial computer time to carry out. This is especially apparent in cases with large amounts of data, a substantial proportion of missing data, or inaccuracies in the data that we wish to account for. All of these cases typically apply with infectious disease data sets. To decide how best to control an infectious disease during the course of an outbreak, results are needed quickly and updates needed often as new data are available. The purpose of this research program is therefore to: i)develop individual-level models that more accurately and reliably model disease transmission as it occurs in real settings; ii)improve the computationally intensive statistical inference process to make it more efficient, for example using Gaussian process emulation and epidemic classification techniques; iii)apply new models to data collected about various infectious diseases to answer biologically interesting questions about those diseases; iv)use computer simulation and inference to determine what sort of infectious disease data should be collected in the future to provide information most efficiently about the infection process. This proposal emphasizes that statisticians play an important role in solving problems in the analysis of large scale infectious disease data. It will also provide opportunities for training highly qualified personnel at all levels. This training has three components: methodology, computation, and analysis of real life data. The outcomes of this research program are expected to aid stakeholders in health care services, and to aid in making proper decisions based on quick and correct statistical inferences in other areas of applications such plant and animal disease.