Topographic spreading analysis of an empirical sex workers’ network

Abstract

The problem of epidemic spreading over networks has received considerable attention in recent years, due both to its intrinsic intellectual challenge and to its practical importance. A good recent summary of such work may be found in Newman (8), while (9) gives an outstanding example of a non-trivial prediction which is obtained from explicitly modeling the network in the epidemic spreading. In the language of mathematicians and computer scientists, a network of nodes connected by edges is called a graph. Most work on epidemic spreading over networks focuses on whole-graph properties, such as the percentage of infected nodes at long time. Two of us have, in contrast, focused on understanding the spread of an infection over time and space (the network) (61; 63; 62). This work involves decomposing any given network into subgraphs called regions (61). Regions are precisely defined as disjoint subgraphs which may be viewed as coarse-grained units of infection—in that, once one node in a region is infected, the progress of the infection over the remainder of the region is relatively fast and predictable (63). We note that this approach is based on the ‘Susceptible-Infected’ (SI) model of infection, in which nodes, once infected, are never cured. This model is reasonable for some infections, such as HIV—which is one of the diseases studied here. We also study gonorrhea and chlamydia, for which a more appropriate model is Susceptible-Infected-Susceptible (SIS) (67) (since nodes can be cured); we discuss the limitations of our approach for these cases below.