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Respondent-driven sampling and an unusual epidemic

Part of: Mathematical sociology

Published online by Cambridge University Press:  21 June 2016

J. Malmros ,
F. Liljeros  and
T. Britton
J. Malmros*
Affiliation:
Stockholm University
F. Liljeros*
Affiliation:
Stockholm University
T. Britton*
Affiliation:
Stockholm University
*
* Postal address: Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden.
*** Postal address: Department of Sociology, Stockholm University, SE-106 91 Stockholm, Sweden. Email address: [email protected]
* Postal address: Department of Mathematics, Stockholm University, SE-106 91 Stockholm, Sweden.
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Abstract

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). If these individuals choose to participate, they in turn pass coupons on to their acquaintances, and so on. The process of recruiting is shown to behave like a new Reed–Frost-type network epidemic, in which 'becoming infected' corresponds to study participation. We calculate R0, the probability of a major 'outbreak', and the relative size of a major outbreak for c < ∞ in the limit of infinite population size and compare to the standard Reed–Frost epidemic. Our results indicate that c should often be chosen larger than in current practice.

Keywords

Stochastic epidemic modelrespondent-driven samplingconfiguration modelReed–Frost

MSC classification

Primary: 92D30: Epidemiology
Secondary: 91D30: Social networks
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 2 , June 2016 , pp. 518 - 530
Copyright
Copyright © Applied Probability Trust 2016 

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