An important epidemiological question for highly skewed partnership distributions is whether their variance is finite5,6. As the reproduction number of a pathogen increases linearly with the variance in the level of sexual activity7,8, populations with infinite variance lack epidemic thresholds. In these populations, a sexually transmitted infection could persist regardless of its transmissibility, and interventions such as vaccines or barrier contraceptives would be ineffective for eradicating it.

Liljeros et al. estimate the scaling exponent for Sweden by fitting a line to the apparently linear region of the upper tail of the logged sexual-contact distribution. This approach is not statistically appropriate, for several reasons9. Inference on the basis of the distribution's extreme upper tail yields wildly increasing confidence intervals because there is little empirical information in this region (Fig. 1). Estimates based on partial lifetime contacts (as in Fig. 2b of ref. 3) are a source of further difficulties, including temporal confounding and censoring.

Figure 1: Interval estimates of the scaling parameter, ρ, for the generalized Yule probability mass function for Swedish males and females.
figure 1

Data show the sensitivity of the 95% bootstrap confidence intervals to the upper tail of the partnership distribution, defined as k > kmin, where k is the number of sexual partners in the previous 12 months. For both males and females, the best-fitting model has kmin = 1. By contrast, Liljeros et al.3 used kmin = 5 for males and kmin = 4 for females. For these values, our estimates of parameter uncertainty are six times greater than the intervals reported by Liljeros et al.3.

We take a more principled statistical approach, using a stochastic mechanism for the underlying preferential-attachment process. This yields a Yule distribution10, and infinite variance when the single scaling parameter ρ≤3. (Details of the Yule model and the statistical estimation procedure are presented elsewhere9.) We generalize the simple Yule model to allow for a mixture of distributions — a process for the lower tail, and a preferential-attachment-type process for the upper tail. Assuming the Yule form, we can estimate the model parameter using maximum likelihood, and base our model selection on the bayesian information criterion9.

The 95% bootstrap confidence-interval estimates of the scaling parameters fall above the infinite-variance range (females, 3.60–5.21; males, 3.01–3.63). Our results are similar when we analyse two further data sets from Uganda and the United States (both based on representative samples with substantially higher response rates than in the Swedish survey). Thus, there seems to be consistent evidence that sexual-contact distributions are characterized by finite variance9.

Our findings suggest that sexual-contact distributions, although strongly right-skewed, are characterized by finite variance. This implies that interventions aimed at reducing transmissibility have the potential to reduce the reproductive number of sexually transmitted infections below the epidemic threshold.

To justify using “radically different” prevention strategies for sexually transmitted infections, strong evidence is needed that current strategies will be ineffective. Results based on unverified mathematical assumptions about network structure do not come close to meeting this standard11. Such data provide no new insight for epidemiology7,8, and conclusions drawn from them could jeopardize campaigns to eliminate sexually transmitted infections worldwide.

It has been suggested in the media that 'eliminating' highly promiscuous nodes could be more effective than reducing their probability of transmission, but this overlooks the remarkable progress in preventing mother-to-child infection, the difficulty in identifying highly active individuals, and the growing evidence of the importance of other behavioural patterns, such as differential assortative mixing1 and concurrency12,13. The high stakes in the battle against HIV and AIDS call for a broad perspective.