Detection of minimal epidemics

Epidemiologists seeking epidemics of events in time, and attempting to distinguish real epidemics from random clusters, need to calculate the random probability of n or more events occurring within a time window of duration w, and for any position of the window as it scans continuously across the period of observation. Exact algebraic solutions have been proposed by other workers, but, over a wide range of important values, systematic arithmetic evaluation is beyond the capacity of existing computers. This paper proposes an approximate test which is quick and simple and which achieves the same purpose. An example of its application is given.