  This chapter surveys univariate and multivariate methods for infectious
disease outbreak detection. The setting considered is a prospective one: data
arrives sequentially as part of the surveillance systems maintained by public
health authorities, and the task is to determine whether to 'sound the alarm'
or not, given the recent history of data. The chapter begins by describing two
popular detection methods for univariate time series data: the EARS algorithm
of the CDC, and the Farrington algorithm more popular at European public health
institutions. This is followed by a discussion of methods that extend some of
the univariate methods to a multivariate setting. This may enable the detection
of outbreaks whose signal is only weakly present in any single data stream
considered on its own. The chapter ends with a longer discussion of methods for
outbreak detection in spatio-temporal data. These methods are not only tasked
with determining if and when an outbreak started to emerge, but also where. In
particular, the scan statistics methodology for outbreak cluster detection in
discrete-time area-referenced data is discussed, as well as similar methods for
continuous-time, continuous-space data. As a running example to illustrate the
methods covered in the chapter, a dataset on invasive meningococcal disease in
Germany in the years 2002-2008 is used. This data and the methods covered are
available through the R packages surveillance and scanstatistics.
