Jens Malmros: Respondent-driven Sampling and an Unusual Epidemic

Respondent-driven sampling (RDS) is frequently used when sampling from hidden populations. In RDS, sampled individuals pass on participation coupons to at most \(c\) of their acquaintances in the community (\(c=3\) being a common choice), who then in turn pass on to their acquaintances if they choose to participate, and so on. The process of distributing coupons is shown to behave like a new Reed-Frost (R-F) type network epidemic, in which ``becoming infected'' corresponds to ``receiving a coupon''. We calculate \(R_0\), the probability of a major ``outbreak'', and the relative size of a major outbreak for \(c<\infty\) in the limit of infinite population size and compare to the standard R-F epidemic. Our results indicate that \(c\) often should be chosen larger than in current practice.