Dynamics and Interactions: An Analysis of Childhood Diseases in London, 1897-1906

Abstract

Objective. The overarching goal of this thesis is to analyze the disease-induced mortality in London 1897-1906 for measles, smallpox, whooping cough (pertussis), typhoid (enteric) fever, diphtheria, and scarlet fever. More specifically, it seeks to understand trends in epidemics for individual diseases over the ten-year period, as well as to analyze the interactions between diseases. Finally, this thesis uses mathematical modeling to study the impact of a smallpox outbreak on measles dynamics and the subsequent outcome of this perturbation. Introduction. Infectious diseases have historically been a major contributor to global mortality. Using mathematical modeling and analysis to study such diseases is essential to understanding the disease dynamics and the implications for human populations even today. The introduction provides a comprehensive overview of each of the six different diseases, of the study site London in the late 19th and early 20th centuries, and of mathematical modeling of diseases. Methodology. The dataset used is from the Registrar General’s Weekly Report for London. These historical datasets are comprised of mortality figures and include other demographic information such as population size and births. The primary statistical analyses conducted to study disease interactions were cross-correlation analysis and wavelet spectral analyses. To model the impact of a smallpox outbreak on regular measles dynamics, a two-strain SIR model was adapted and applied to the London dataset. Results. Time series plots of overall mortality and specific disease-induced mortality were produced and reveal annual epidemics for measles, whooping cough, diphtheria, and typhoid fever. Further breakdown of London into regions shows varying birth rates and thus varying frequency of outbreaks for measles, most notably biennial outbreaks in the west region. Cross-correlation analysis of measles and whooping cough show that in the west region the two diseases are out of phase by 49 weeks. The two-strain SIR model depicts a clear disruption of measles dynamics by the smallpox outbreak, resulting in higher and more frequent measles epidemics post-smallpox outbreak, though this does not match the dynamics found in the actual dataset. Discussion. There were significant differences among the different regions in London in regards to measles dynamics. The biennial measles epidemics experienced in the west region may be attributed to the notably lower birth rate compared to the other regions and London as a whole. The out of phase correlations between measles and whooping cough in the west region is consistent with previous analyses of the two diseases. The smallpox outbreak on measles dynamics was successfully modeled. By analyzing the average age of infection during the smallpox outbreak, the susceptible populations for measles and smallpox during this outbreak were found to be different, explaining why the outcome of the model does not reflect the data. This model has significant implications from both the ecological and public health perspectives as these perturbations in regular dynamics will happen both organically or artificially in nature.