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. ### Competing Interest Statement The authors have declared no competing interest. ### Funding Statement MD and CM receive support administered through the US Centers for Disease Control and Prevention's Epidemiology and Laboratory Capacity for the Prevention and Control of Infectious Diseases Cooperative Agreement (CK19-1904) for Strengthening the US Response to Resistant Gonorrhea. ### Author Declarations I confirm all relevant ethical guidelines have been followed, and any necessary IRB and/or ethics committee approvals have been obtained. Yes I confirm that all necessary patient/participant consent has been obtained and the appropriate institutional forms have been archived, and that any patient/participant/sample identifiers included were not known to anyone (e.g., hospital staff, patients or participants themselves) outside the research group so cannot be used to identify individuals. Yes I understand that all clinical trials and any other prospective interventional studies must be registered with an ICMJE-approved registry, such as ClinicalTrials.gov. I confirm that any such study reported in the manuscript has been registered and the trial registration ID is provided (note: if posting a prospective study registered retrospectively, please provide a statement in the trial ID field explaining why the study was not registered in advance). Yes I have followed all appropriate research reporting guidelines, such as any relevant EQUATOR Network research reporting checklist(s) and other pertinent material, if applicable. Yes All data and code are stored in a publicly available GitHub repository .