Middle East respiratory syndrome (MERS) has been widespread at a global scale since 2012. Clinical symptoms of MERS tend to be non-specific, and it is frequently difficult to differentiate it from other febrile infectious diseases such as influenza. In the present study, we construct a probabilistic model that helps diagnose infections among imported cases. First, a mathematical formulation of infection dynamics among imported cases is conducted using McKendrick von Foerster equation, deriving the time from immigration to illness onset among imported cases. Second, a Bayesian approach is employed to estimate the conditional probability of MERS (or influenza) given the specific time from immigration to onset. We show that the illness onset within 2 days from immigration is suggestive of influenza. Two exceptions to suspect MERS even for those with illness onset within 2 days since immigration are (i) when we observe substantial community transmissions of MERS and (ii) when the cases are at high risk of MERS. This modeling framework is expected to greatly improve diagnostic activities at travel clinics.