Modeling dynamic and network heterogeneities in the spread of sexually transmitted diseases

Abstract

A wide range of communicable human diseases can be considered as spreading through a network of possible transmission routes. The implied network structure is vital in determining disease dynamics, especially when the average number of connections per individual is small as is the case for many sexually transmitted diseases (STDs). Here we develop an intuitive mathematical framework to deal with the heterogeneities implicit within contact networks and those that arise because of the infection process. These models are compared with full stochastic simulations and show excellent agreement across a wide range of parameters. We show how such models can be used to estimate parameters of epidemiological importance, and how they can be extended to examine the effectiveness of various control strategies, in particular screening programs and contact tracing.spatial correlations ͉ pair-wise models ͉ mixing matrix ͉ core groups ͉ contact tracing S exually transmitted diseases (STDs) are an important and increasing public-health problem throughout the world, causing widespread mortality and morbidity and having immense social and economic consequences (1-4). The progress and dynamics of these infections within a population must be understood so that treatment and interventions can be most effectively targeted. Here we present a mechanism to predict the spread of infection through a network of contacts. This work bridges the gap between full simulations, which are difficult to parameterize, and risk-structured mean-field models, which ignore the strong effects attributable to partnerships.The localized spread of infectious diseases has been successfully captured with a variety of spatial models (5-10). Such approaches recognize that the predominantly local nature of disease transmission leads to a high degree of spatial segregation and means that the population is not uniformly well mixed. An alternative and often more realistic strategy is to consider the spread of infection across a network of contacts. This approach is necessary for STDs because proximity in space is no longer the determining risk factor for transmission. The resulting sexual mixing network contains all of the information on potential pathways of infection and as such has proved vital in understanding STD spread (11-18).The sexual mixing network focuses on one of the central issues of epidemiology: who can acquire infection from whom (19)(20)(21)(22). Such networks represent each individual within a population as a node, with connecting edges denoting relationships that could lead to the transmission of infection (Fig. 1). For many of the common airborne infections it may be difficult to define which contacts form an edge (23); for STDs, however, edges are more precisely defined and correspond to sexual partnerships. We note that the network is disease dependent, with STD networks contained within the networks of more readily transmitted infections.The initial spread and long-term behavior of any infectious disease are determined by both its epidemiologi...

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