Technical Abstract: The early detection of an invading epidemic is crucial for successful disease control. Although models have been used extensively to test control strategies following the first detection of an epidemic, few studies have addressed the issue of how to achieve early detection in the first place. Moreover, sampling theory has made great progress in understanding how to estimate the incidence or spatial distribution of an epidemic but how to sample for early detection has been largely ignored. Using a simple epidemic model we demonstrate a method to calculate the incidence of an epidemic when it is discovered for the first time (given a monitoring program taking samples at regular intervals). We use the method to explore how the intensity and frequency of sampling influences early detection. In particular, we find that for epidemics characterized by high population growth rates it is most effective to spread sampling resources evenly in time. In addition we derive a useful approximation to our method which results in a simple equation capturing the relation between monitoring and epidemic dynamics. Not only does this provide valuable new insight but it provides a simple rule of thumb for the design of monitoring programs in practice.