Reply to McBryde

Tothe Editor—We appreciate the letter by McBryde [1], and we agree that conventional modelling equations may be too optimistic and underestimate the risk presented by the clustering of susceptible individuals in a largely vaccinated population. Mathematical modelling of infectious diseases is recognized to be a valuable tool for public health decision making, and any efforts to predict and determine where and how clusters of susceptible individuals in a population might be reached can be of great importance. In many disease models, the rate of transmission from infectious to susceptible hosts is represented by the probability of transmission, and an understanding of the different variables involved is desirable [2].

Formulating a model for disease prediction requires that the model be as accurate as possible. Accuracy generally improves with increasing complexity and the inclusion of more heterogeneities and relevant biological details. Understanding how such heterogeneities influence transmission is necessary to determine which individuals in a population are most at risk and the most-effective means of targeting control [3]. If an unvaccinated individual is more likely to be in contact with other unvaccinated individuals than would be expected by chance, clusters of susceptible individuals will form and thus constitute a subpopulation in which the disease can spread and cause local outbreaks. In particular, the effect of clustering on outbreak probability is greatest when the vaccination coverage is close to the level required to provide herd immunity under the assumption of random mixing [4].

A crucial question is: what proportion of the population must be vaccinated to fight the disease as efficiently as possible? However, the answer is complicated when vaccination is heterogeneous among different population groups, because the estimability of a summary vaccine-efficacy parameter depends on whether the different groups are identifiable and on the nature of the heterogeneity (whether it is host- or vaccine-related) [5]. Undoubtedly, the structure of social links (i.e., travel, immigration, opinion groups, or others) also determines the possibility of infection and plays a key role in the dynamics of an epidemic disease; it should therefore constitute an additional factor in the definition of a vaccination strategy [6].

In the measles outbreak that occurred in Catalonia (a population with high vaccination coverage) from August 2006 through June 2007, 187 (55.2%) of 339 cases occurred in nonvaccinated subjects that were aged ⩽15 months [7]. This suggests that other issues must be taken into account, including a reduction of the timespan anticipated for the loss of effective protection from maternal antibodies in children, which may be attributable to the nature of these antibodies. Changes in the nature of maternal antibodies may be attributable to vaccine-induction (rather than being induced by wild measles virus infection), the increasing mean age of mothers at first childbirth, or the reduced exposure of young adults to natural immunity boosters [8].

Finally, it is important to keep in mind that the risk of importation of disease by travel or immigration is high in a globalized world. This makes it very important to improve the vaccine coverage in some specific population groups and strengthen surveillance systems, to avoid vaccine-preventable disease outbreaks that might disturb the well-being of a population and postpone the consecution of disease elimination.

acknowledgments

Potential conflicts of interest. All authors: no conflicts.