Ecology of infectious diseases with contact networks and percolation theory

In this era of globalization and bioterrorism, infectious diseases have become an increasing threat that can have a devastating impact on human life. Most pathogens (a virus, bacterium or other microorganism that causes disease) require close contact between an infected host and a new susceptible host for successful transmission. The nature and structure of contacts among individual hosts is thus of extreme importance to the spread of disease. Traditional epidemiological models are based on a compartmentalization of individual hosts according to their disease status (e.g. susceptible, infected, recovered). The dynamics of the hosts through the different compartments is described by a differential equation system and is solvable due to the strong assumption of homogeneous mixing. This assumption is inappropriate for most communities which have heterogeneous contact patterns, and thus the traditional approach can prove to be limited. Heterogeneity among hosts can be modeled via contact networks (graphs where nodes represent individuals and edges represent contacts which can potentially cause disease), which provide an individual-level description of contact patterns. The use of the analytical methods of percolation theory to understand disease spread on arbitrary contact networks is known as contact network epidemiology.;In this dissertation, I extend the mathematical and computational methods of contact network epidemiology to provide a better understanding of the spread and control of disease in human populations. I quantify the impact of the underlying contact structure of a host population on the spread of infectious disease and compare the merits of an individual-based approach to the traditional one. Then I focus specifically on networks with the non-random structure of clustering and investigate the impact of this structure on epidemic dynamics. I also consider the evolution of contact structure due to patterns of immunity caused by previous epidemics and the ways this impacts future disease dynamics. Additionally, I introduce a novel analytical approach to incorporate previous immunity (both partial and complete) into our individual-based models. Finally, I use the developed methods and the theoretical results of this study, to design and test in-silico control measures to prevent the spread of influenza and other human diseases.;The mathematical methods that I have developed in this thesis are unique because they enable explicit models of complex host population structures which are mathematically tractable. This work extends the methodological toolkit of mathematical epidemiology, and has provided both general insights into infectious disease ecology and practical public health recommendations.