The Challenges of Surveying Heavy-tail Distributions for Use in Infectious Disease Dynamics

Sexual networks often have heavy-tails, where a small number of exceptional individuals in a population have many more sexual partners than the average (e.g., more than five standard deviations). Heavy-tails pose challenges when surveying this group, as these exceptional individuals are uncommon in the population (and so hard to detect), but have disproportionate impact on epidemiological questions, such as those related to the spread of sexually transmitted diseases. In essence, omitting these individuals is a severe error. In this modeling study, we use prior estimates of the distribution of sexual partners amongst men who have sex with men to explore the implication of different sample sizes on survey estimates. We find that even large surveys consistently fail to capture the variance of the sexual network. Surveys of heavy-tailed sexual networks should be designed with this high variance in mind so as not to underestimate the disease dynamics. The failure to adequately capture the variance within a heavy-tailed network has strong implications for infectious disease dynamics and modeling as disease dynamics are often driven by the heavy-tail.