Detecting epidemic coupling among geographically separated populations

Abstract

The spread of infectious agents has been observed as long as their hosts have existed. The spread of infectious diseases in human populations, however, is more than an academic concern, causing millions of deaths every year, and prompting collective surveillance and intervention efforts worldwide. These surveillance data, used in conjunction with statistical methods and mathematical models, present both challenges and opportunities for advancements in scientific understanding and public health.

Early mathematical modeling of infectious diseases in humans began by assuming homogeneous contact among individuals, but has since been extended to account for many sources of non-homogeneity in human contact. Detecting the degree of epidemic mixing between geographically separated populations, in particular, remains a difficult problem. The difficulty occurs because although disease case reports have been collected by many governments for decades, case reporting is imperfect, and transmission events themselves are nearly impossible to observe.

The degree to which epidemic coupling can be detected from case reports is the central theme of this thesis. We present a careful, biologically motivated and consistent derivation of the transmission coupling (fully derived in Chapter 4). In Chapter 2 we consider the simple scenario of an epidemic spreading from one population to another, and present both numerical and analytic methodology for estimating epidemic coupling. Chapter 3 considers the problem of estimating epidemic coupling among populations undergoing recurrent epidemics, such as those of childhood diseases which have been widely observed. In Chapter 4 we present a method for estimating coupling among an arbitrary number of populations undergoing an epidemic, and apply it to estimate coupling among the parishes of London, England, during the Great Plague of 1665.