  In recent days different types of surveillance data are becoming available
for public health reasons. In most cases several variables are monitored and
events of different types are reported. As the amount of surveillance data
increases, statistical methods that can effectively address multivariate
surveillance scenarios are demanded. Even though research activity in this
field is increasing rapidly in recent years, only a few approaches have
simultaneously addressed the integer-valued property of the data and its
correlation (both time correlation and cross correlation) structure. In this
paper, we suggest a multivariate integer-valued autoregressive model that
allows for both serial and cross correlation between the series and can easily
accommodate overdispersion and covariate information. Moreover, its structure
implies a natural decomposition into an endemic and an epidemic component, a
common distinction in dynamic models for infectious disease counts. Detection
of disease outbreaks is achieved through the comparison of surveillance data
with one-step-ahead predictions obtained after fitting the suggested model to a
set of clean historical data. The performance of the suggested model is
illustrated on a trivariate series of syndromic surveillance data collected
during Athens 2004 Olympic Games.
