The epidemiologic settings in which network descriptions have the longest history of use involve sexually transmitted infections (STIs), such as gonorrhea or the human immunodeficiency virus (HIV).8-14 Here there are natural, well-defined, network structures (sexual partnership networks) which have long been exploited by public health bodies in their attempts to track and control outbreaks of STIs. Network models have more recently been employed to describe the spread of a wider range of infections such as measles, SARS or foot and mouth disease (FMD).15-18 Increased interest in bioterrorism has also spurred much research, with the spread of smallpox coming under particular scrutiny.19'20
The network structure appropriate for a given setting not only depends on the structure of the population, but on the infection itself. Within the same population, the network would be quite different for infections spread by sexual contact or by more casual contact. Even in the latter case, considerable differences would arise between infections that require prolonged close contact in order for transmission to occur and ones for which a brief encounter would be sufficient.
The contrast between networks describing sexual partnerships and more general social contact networks is particularly pronounced. It is instructive to look at some of these differences as they highlight many important aspects of network structure. The number of sexual partnerships is dwarfed by the number of social contacts in a population. An STI has far fewer chances to spread than an infection such as the common cold. Furthermore, since most individuals are monogamous (i.e. have only one sexual partner over a given time period), a large part of a sexual network consists of isolated pairs of individuals. Sexual networks often exhibit a high variance in the number of partners that different individuals have over a given time period.1'21'22 Most individuals have just one partner, while a few individuals (such as sex workers) have a large number of partners.
In many cases, epidemiologic networks can be described by undirected graphs. Although transmission of infection is a directional event (from an infectious individual to a susceptible), the probability of transmission along an edge would often be the same if the placement of the two individuals (susceptible and infective) were reversed. Sexual transmission networks provide an example where this might not be the case, since the male to female transmission probability can differ from the female to male probability. In this setting a directional network may be more appropriate, with two directed edges between the partners having unequal transmission probabilities.23
Transmission networks are dynamic structures: individuals' groups of contacts change over time. This is perhaps most pronounced in the case of sexual partnership networks. Partnership dynamics (the break up of existing partnerships and the formation of new partnerships) plays a major role in the spread of infection through the large part of the network that consists of isolated pairs.8'9'14 Considering a monogamous pair of individuals, infection can be readily transmitted between an infected individual and their susceptible partner, but further transmissions can only occur if the pair breaks up and the individuals find new susceptible partners.
The changing pattern of social contacts can have a major impact on transmission in more general settings. The classic example is provided by childhood infections, such as measles.24 Schools are important sites for the transmission of such infections: the congregation of children leads to much higher transmission rates during school terms than vacations. (This seasonal variation in transmission leads to large seasonal variations in disease incidence: the resulting multi-annual oscillations have been widely studied in the literature.)
The importance of the dynamic aspect of network structure depends on the timescale over which disease dynamics are of interest. For rapidly spreading infections, it is often assumed that a static network description will suffice. This leads to a considerable simplification, for both numerical simulation and mathematical analysis of transmission. As a consequence, much of the recent work has focused on static network settings.
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