  Early detection of disease outbreaks is of paramount importance to
implementing intervention strategies to mitigate the severity and duration of
the outbreak. We build methodology that utilizes the characteristic profile of
disease outbreaks to reduce the time to detection and false positive rate. We
model daily counts through a Poisson distribution with additive background plus
outbreak components. The outbreak component has a parametric form with unknown
underlying parameters. A mixture likelihood ratio scan statistic is developed
to maximize parameters over a window in time. This provides an alert statistic
with early time to detection and low false positive rate. The methodology is
demonstrated on three simulated data sets meant to represent E. coli,
Cryptosporidium, and Influenza outbreaks.
