  Contact tracing is an effective method to control emerging diseases. Since
the 1980's, mathematical modelers are developing a consistent theory for
contact tracing, with the aim to find effective and efficient implementations
of contact tracing, and to assess the effects of contact tracing on the spread
of an infectious disease. Despite the progress made in the area, there remain
important open questions. In addition, technological developments, especially
in the field of molecular biology (genetic sequencing of pathogens) and modern
communication (digital contact tracing), have posed new challenges for the
modeling community. In the present paper, we discuss modeling approaches for
contact tracing and identify some of the current challenges for the field.
