Online

Allen, Andrea Joan

Complex Systems and Data Science

2022

M.S.

Mathematical models of infectious disease are important tools for understanding large-scale patterns of how a disease spreads through a population. Predictions of trends from disease models help guide public health prevention and mitigation measures. Most simple disease models assume that the population is randomly mixed, but real-world populations exhibit heterogeneous patterns in the way people interact. These differences in population structure can be represented by networks. Networks can then be incorporated into disease models by using various interdisciplinary concepts and tools. Yet even network disease models often overlook that populations change over time. In this thesis, two models of infectious disease are presented, for the purpose of analyzing how the spread of the disease evolves over time, particularly when the population is also changing.To model a changing population, a sequence of different networks can each be associated with a length of time each is active for. Although, how to construct these networks from real contact data, from things like wearable sensors, is a nontrivial problem. We present a method to ascertain if temporal data can be aggregated into a single network, or not. This method underlies an algorithm for compressing real data into a time-varying sequence of networks, creating a system still tractable enough to use existing network analysis tools. We show how fine-grained temporal contact data can be compressed into just a handful of ordered, static networks while preserving the most significant temporal trends of the dynamic population. Not only do populations change over time, but there is also inherent randomness involved in the spread of disease between individuals. To account for this, the underlying random process can be used as the basis for the disease model. Here, one particular model is presented that uses a random, or stochastic, framework to predict the temporal evolution of the spread of disease by tracking generations of infected individuals over time. We show that often the distribution of cumulative infections is heavy tailed, implying that deterministic models of spread, which present average point estimates, do not account for underlying uncertainty. The two models presented in this thesis address the heterogeneity of the temporal dynamics of infectious disease spread through a population. These models also contribute to a body of work focused on designing models that can leverage real data about population structure and contact patterns to produce more accurate predictions and insights.