CROSS-SCALE POPULATION DYNAMICS OF ACUTE IMMUNIZING PATHOGENS: MEASLES AS A CASE STUDY

Abstract

A key task in ecology is clarifying how population- and community-level processes emerge from individual-level interactions. An important component of this theme lies in understanding whether, and at what scale, population dynamics can be described by simple, low-dimensional models. This scale-dependent problem is inherently challenging as it requires both data across many levels, and the development of new modeling and inference methods that can encompass a range of behaviors. With their rich data sets and important public health applications, infectious diseases of humans provide a particularly useful case study for analyzing these cross-scale dynamics. At the scale of large cities, outbreaks can be analyzed using the mass-action assumption in the Susceptible-Infected-Recovered model, in which the number of individuals who will become infected in the next time step is proportional to the total number currently infected as well as those currently susceptible. Mass-action is a reasonable assumption at large population levels given the high transmissibility of childhood infectious diseases, and such models have proven extremely useful in dissecting infectious disease dynamics. However, at finer grains (e.g., foci of seasonal aggregation such as primary schools), social structures (e.g., towns or classrooms) begin to manifest themselves in more heterogeneous epidemics which often deviate away from the population-level patterns. Understanding the impact of these subscale heterogeneities on population dynamics remains a key question in cross-scale dynamics in ecology. Recent digitization efforts have made available new data sources that now allow for analysis at multiple population scales.

In my dissertation work, I have approached this problem by confronting detailed historic data of childhood infectious diseases with a family of ecological models and inference methods. Chapter 1 begins with a general introduction to infectious disease dynamics, mathematical modeling, and inference techniques. In Chapter 2, I analyzed the finest-scale contained in this thesis: infections in primary schools. I find significantly higher transmission in the school-setting than population-level data suggests, indicating key signatures of heterogeneity at the subscales. Chapter 3, in contrast, examines the impact of secular changes in demography and external shifts on long-term aggregation population dynamics using measles in London, 1897-1991, as a case study. Fitting a simple mass-action model to this near-century of data illuminates long-term predictability and the role of intrinsic and extrinsic drivers. In particular, although demographic changes explain the majority of the dynamics, key events such as school closures during the 1918 pandemic shape the patterns of infection for decades. Chapter 4 further examines sub-scale heterogeneity. Although the aggregate London dynamics (1897-1906) exhibit a clear annual pattern, the nine inner regions of London display both annual and biennial epidemic trends. Disentangling these dynamics, I illustrate how tension between regional coupling and variation in seasonality explain the observed heterogeneity. In tandem, these three chapters examine three primary scales of population-level transmission in historic London. They each find signatures of heterogeneity that would be hidden without examining subscales, highlighting the crucial role of cross-scale dynamics in population ecology. Finally, in Chapter 5 I present an R software package I developed to infer epidemiologically-relevant parameters from long-course time series data. Chapter 6 concludes the dissertation with a general discussion of future directions.