Statistical methods in infectious disease modeling: agent-based models, computations, and selection biases

Abstract

Understanding the dynamics of an infectious disease is important, since it helps to prevent known infectious disease outbreaks and to recognize and control emerging threats. To put more simply, it can save lives. To draw conclusions about infectious diseases given observations is challenging, not only because the transmission dynamics are complex, but also because even some of the most detailed and informative datasets have missing information, due to latency period, asymptomatic infections, and expensive data collection. To address these challenges in inference, this dissertation investigates statistical methods in infectious disease modeling, and a key contribution is a framework for likelihood-based inference in agent-based epidemic models, accompanied by computational tools. We present a generative model suitable for understanding the initial period of an outbreak, when the number of cases are still increasing exponentially. We utilize a parametric model to illustrate sample selection biases in the literature and to conclude an alarming epidemic doubling time of 2 to 2.5 days during the early coronavirus disease 2019 (COVID- 19) outbreak in Wuhan. We also demonstrate age- and gender-specific differences in the distribution of the disease latency period in the population. We motivate the development of agent-based models of disease transmission with individual heterogeneity and social network structure. Since infectious disease processes are often observed only after some aggregation, despite growing popularity and increasing number of applications of agent-based models, with notable examples such as Ebola, malaria, and COVID-19, the inverse problem of reconstructing individual behavior from aggregated data remains challenging due to its computational complexity. We design improved particle filters, where each particle corresponds to a specific configuration of the population of agents, that take either the next or all future observations into account when proposing population configurations. We illustrate that orders of magnitude improvements are possible over bootstrap particle filters and provide theoretical support for the approximations employed to make the algorithms practical. The methodologies are illustrated on a smallpox outbreak dataset and are applied to evaluate vaccine efficacy.