Because of the relatively simplistic nature of the models developed in this paper, several caveats should be made regarding the results. The first is that vaccination campaigns are unlikely to achieve a constant level of uptake over time; a more realistic assumption is that vaccination initially begins slowly due to logistical issues, builds to a plateau, but may finally decline if the epidemic begins to wane during the period of the vaccination programme and there is less incentive for individuals to be vaccinated. Associated with this is the fact that not all individuals are prepared to be vaccinated, and in particular parents in the UK are often anxious about vaccinating children; therefore, the optimal targeting of vaccination is unlikely to be possible and it may simply be better to vaccinate any individuals who wish to be vaccinated. The second issue, which applies to figures 2 and 3, is that it may not always be possible to identify or target relevant risk groups. For example, there may be considerable overlap between the age groups used in figure 3 , and the groups at risk of severe symptoms defined in figure 2 ; this was undoubtedly the case in 2009 (as well as previous pandemics), where age was often a key contributing factor to both the risk of infection and the risk of complications. Throughout, we have assumed a perfect vaccine, which offers 100 per cent protection to all those vaccinated. In practice, this is never realized, all vaccines fail to some degree; however, there are two ways in which this failure can be modelled. The first is an all or nothing approach in which a fraction of all vaccinations fails to generate any protection, while the remaining offers full protection; in this case, the results of our model natural extrapolate based on considering the numbers protected. The second approachis to consider 'leaky' vaccines that offer partial protection reducing either susceptibility or onward transmission; given the relatively low reproductive ratios considered within this paper, we believe that our results are likely to generalize to this case. A further issue related to figure 2 is the ethics of vaccinating the epidemiologically important groups in order to protect the group with severe health risks. While for influenza the vaccine has little associated risk and therefore it may be argued that the health benefits to the epidemiologically important (but healthy) groups outweigh the dangers, the same may not be true for other pathogens and the associated vaccine. Additionally, we have generally used deterministic models and hence assumed that vaccine would be used to mitigate the impact of infection rather than to prevent an epidemic occurring. This is particularly pertinent to the metapopulation model (figure 4) when we neglect the possibility of using vaccine to eradicate infection in the early stages and prevent its spread to the remainder of the country as exemplified in Ferguson et al. [11] . We feel this is a reasonable assumption given that most novel infections will be seeded continually by imports from abroad, and vaccine is unlikely to be available at the start of the epidemic. Finally, throughout we have assumed that there is a strong public demand for vaccine. Clearly, demand will vary both with disease severity and public perception of the infection; for example, the relatively mild nature of the 2009 pandemic meant that demand and uptake of the vaccine was low. However, if the infection has severe health implications, and therefore there is a clear need to optimize control measures, then demand for vaccination is likely to be substantial. The models in this paper, and therefore the results generated, are not designed to replace very detailed simulations parametrized to match epidemiological data from a given outbreak; however, they do provide a high degree of generality that is difficult to obtain with more case-specific simulations and hence provide a rapid assessment of conflicting methods of targeting vaccination. Often public-health action has to be taken in the absence of critical information: levels of prior immunity in the population affect the transmission patterns, but it takes time to develop the appropriate serological test; parameters such as casefatality ratios or the probability of hospitalization are difficult to estimate in real time as an epidemic progresses; and although clinical trials can measure the theoretical vaccine efficacy, vaccine effectiveness in practice can only be determined once the vaccination programme has begun. Given this range of uncertainties, models can be best used to assist policy-makers by examining a range of scenarios ahead of time; so decisions can be taken based on the range of scenarios that are consistent with the available data at the time that the decision has to be taken. Simple models often allow us to partition parameter space into clearly defined regions where a particular strategy is optimal; and while precise parameters may be difficult to estimate early in an epidemic, there may be sufficient evidence to suggest that the infection parameters lie within one of these prescribed regions. As such, the simple models developed here provide useful policy guidance before or during the early stages of an epidemic before there are sufficient data to parametrize more detailed simulations. Networks and the Epidemiology of Infectious Disease The science of networks has revolutionised research into the dynamics of interacting elements. It could be argued that epidemiology in particular has embraced the potential of network theory more than any other discipline. Here we review the growing body of research concerning the spread of infectious diseases on networks, focusing on the interplay between network theory and epidemiology. The review is split into four main sections, which examine: the types of network relevant to epidemiology; the multitude of ways these networks can be characterised; the statistical methods that can be applied to infer the epidemiological parameters on a realised network; and finally simulation and analytical methods to determine epidemic dynamics on a given network. Given the breadth of areas covered and the ever-expanding number of publications, a comprehensive review of all work is impossible. Instead, we provide a personalised overview into the areas of network epidemiology that have seen the greatest progress in recent years or have the greatest potential to provide novel insights. As such, considerable importance is placed on analytical approaches and statistical methods which are both rapidly expanding fields. Throughout this review we restrict our attention to epidemiological issues. The science of networks has revolutionised research into the dynamics of interacting elements. The associated techniques have had a huge impact in a range of fields, from computer science to neurology, from social science to statistical physics. However, it could be argued that epidemiology has embraced the potential of network theory more than any other discipline. There is an extremely close relationship between epidemiology and network theory that dates back to the mid-1980s [1, 2] . This is because the connections between individuals (or groups of individuals) that allow an infectious disease to propagate naturally define a network, while the network that is generated provides insights into the epidemiological dynamics. In particular, an understanding of the structure of the transmission network allows us to improve predictions of the likely distribution of infection and the early growth of infection (following invasion), as well as allowing the simulation of the full dynamics. However the interplay between networks and epidemiology goes further; because the network defines potential transmission routes, knowledge of its structure can be used as part of disease control. For example, contact tracing aims to identify likely transmission network connections from known infected cases and hence treat or contain their contacts thereby reducing the spread of infection. Contact tracing is a highly effective public health measure as it uses the underlying transmission dynamics to target control efforts and does not rely on a detailed understanding of the etiology of the infection. It is clear, therefore, that the study of networks and how they relate to the propagation of infectious diseases is a vital tool to understanding disease spread and, therefore, informing disease control.