Respondent-driven sampling (RDS) is a commonly used substitute for random
sampling when studying hidden populations, such as injective drug users or men
who have sex with men, for which no sampling frame is known. The method works
like a snowball sample but can, given that some assumptions are met, generate
unbiased population estimates. One key assumption, not likely to be met, is
that the acquaintance network in which the recruitment process takes place is
undirected, meaning that all recruiters should have the potential to be
recruited by the person they recruit.
Researchers in many scientific fields make inferences from individuals to
larger groups. For many groups however, there is no list of members from which
to take a random sample. Respondent-driven sampling (RDS) is a relatively new
sampling methodology that circumvents this difficulty by using the social
networks of the groups under study. The RDS method has been shown to provide
unbiased estimates of population proportions given certain conditions. The
method is now widely used in the study of HIV-related high-risk populations
globally.
This paper is a survey paper on stochastic epidemic models. A simple
stochastic epidemic model is defined and exact and asymptotic model properties
(relying on a large community) are presented. The purpose of modelling is
illustrated by studying effects of vaccination and also in terms of inference
procedures for important parameters, such as the basic reproduction number and
the critical vaccination coverage. Several generalizations towards realism,
e.g. multitype and household epidemic models, are also presented, as is a model
for endemic diseases.