The probability of failing in detecting an infectious disease at entry points into a country

In a group of N individuals, carrying an infection with prevalence pi, the exact probability P of failing in detecting the infection is evaluated when a diagnostic test of sensitivity s and specificity s' is carried out on a sample of n individuals extracted without replacement from the group. Furthermore, the minimal number of individuals that must be tested if the probability P has to be lower than a fixed value is determined as a function of pi. If all n tests result negative, confidence intervals for pi are given both in the frequentistic and Bayesian approach. These results are applied to recent data for severe acute respiratory syndrome (SARS). The conclusion is that entry screening with a diagnostic test is rarely an efficacious tool for preventing importation of a disease into a country.