Many measures can be deployed in an attempt to control the spread of infection, such as isolation, quarantine and drug treatments. In this section, we shall focus on the use of vaccination. We may consider the effect of a perfect vaccine as preventing vaccinated nodes from acquiring and transmitting infection, essentially removing them from the network. In reality, vaccines are not perfect: not everyone gains protection against the infection, and the protection gained may only be partial.
For well-mixed models of the form (8.2-8.4), there is a critical vaccination fraction, pc, given by pc =1 - 1/Ro (8.8)
such that vaccination of this fraction (or greater) of the population will guarantee eradication of the infection if it already exists, or prevent the infection from causing an outbreak in a naive population. This result makes the intuitive point that it is more difficult to eradicate a highly infectious disease than a less infectious one.
Given its impact upon the spread of infection, it is hardly surprising that network structure can have a major impact upon control of infection. Considerable attention has been directed towards the effects of heterogeneity. Anderson and May showed that uniform vaccination, in which individuals are vaccinated without regard to the heterogeneity, is always less effective than targeted vaccination and that the optimal vaccination strategy in-
volves vaccinating those at highest risk.1 In the case of sexually transmitted infections, this means that control measures should be directed towards the core group rather than the general population. This makes sense, particularly if the core group is responsible for the maintenance of the infection, and forms the basis of many public health policies.
Anderson and May's results were recently rediscovered in the context of vaccination of scale-free networks.42 It was found that uniform vaccination was a completely ineffective approach since a randomly chosen individual in a scale-free network is likely to have a small number of neighbors. Removal of such individuals does little to affect the structure of the network. In contrast, removal of highly connected individuals, by targeting vaccinations, has a major impact and quickly leads to a situation in which the infection cannot spread.
One issue with targeted vaccination is that it requires the identification of individuals that are highly connected (or have some other high risk factor). This requires more effort than a simple uniform vaccination strategy. One intriguing approach43 makes use of the fact, discussed above, that in most instances, randomly chosen neighbors of individuals have a higher connectivity than do randomly chosen individuals. A control strategy based on vaccinating randomly chosen neighbors of randomly chosen individuals can be shown to be more effective than uniform vaccination.43 Of course, the potential benefit of this approach should be weighed up against the added complexity of its implementation.
Control measures can utilize local spatial structure, particularly during the early stages of an epidemic. If transmission is mainly local in nature, effort can be concentrated in and around any foci of infection.16'17'20 As an example, ring vaccination targets the area surrounding a geographically localized outbreak, much in the same way as fire-fighters might use fire breaks to contain a forest fire. Such approaches formed the cornerstone of control efforts during the 2001 outbreak of foot and mouth disease in the British livestock population.16'17 Local control strategies become more difficult to employ as the infection becomes more widely disseminated in a given region.
The small world effect has a major impact on the use of local control strategies unless one can guarantee that long-range transmission events cannot occur. This was possible in the foot and mouth case as one of the earliest reactions of the UK authorities was to impose a ban on the movement of animals between farms. In a human setting, long-range travel such as transcontinental and intercontinental flights have reduced the entire planet to a small world, and so reliance on local control measures would appear to be unwise unless accompanied by stringent controls on travel.
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