Before revision:  Lastly, we compute the number of detectable cases if one were to test the whole local outbreak at a single point in time. In a growing epidemic, most individuals have been infected recently, which can strongly limit the detection of infected individuals when there is a delay between an infection and its potential detection. Overall, our analysis provides new analytical estimates about the epidemic size at identification of a first disease-related case. This piece of information is important to inform policy makers during the early stages of an epidemic outbreak .
After revision:  Lastly, we compute the detection rate of infected individuals during a single mass testing effort. For example, in a COVID-19-parameterized model with an effective reproduction number R=1.1, a fraction 1.3\% of a population needs to be randomly tested each day for cluster size to not exceed 30 infected individuals. These results improve our theoretical understanding of early epidemics and are useful for the study and control of local infectious disease clusters .