On the Statistical Properties of Epidemics on Networks

Abstract

One major aim of statistics is to systematically study outcomes of interest in a population by observing the properties of a sample of that population. Some outcomes, such as the total number of people infected in an epidemic, can depend on properties of the whole population, such as the structure of contacts among the individuals, or contact network. A network is a collection of individuals as well as the pairwise connections between them. This dissertation explores how the effects of network structure on infectious outcomes yield challenges for statistical analysis, and suggests strategies to address them.

In Section I, we consider an intervention to reduce the spread of an epidemic on a collection of individuals in partially-connected networks, and show how network structure and mixing across networks can reduce the probability of observing true intervention effects, or statistical power. In Section II, we show how accounting for estimated properties of an epidemic contact network can improve statistical power, and that this improvement depends on the properties of the whole network as well as the epidemic spreading through them. Finally, in Section III, we derive the conditions under which a particular kind of network - the Degree-Corrected Stochastic Blockmodel - is susceptible to extensive epidemic spread, enabling statistical analysts to estimate when and to what extent the challenges and corrections explored here require consideration. We will conclude with a discussion of how the estimates and derivations in the final two sections can be used as adjustment covariates when assessing the effect of treatment on epidemic spread.