  Intuitively, sampling is likely to be more efficient for prevalence
estimation, if the cases (or positives) have a relatively higher representation
in the sample than in the population. In case the virus is transmitted via
personal contacts, contact tracing of the observed cases (but not noncases), to
be referred to as \emph{adaptive network tracing}, can generate a higher yield
of cases than random sampling from the population. The efficacy of relevant
designs for cross-sectional and change estimation is investigated. The
availability of these designs allows one unite tracing for combating the
epidemic and sampling for estimating the prevalence in a single endeavour.
