We investigate the age structured data for the COVID-19 outbreak in Japan. We consider epidemic mathematical model with unreported infectious patient with and without age structure. In particular, we build a new mathematical model which allows to take into account differences in the response of patients to the disease according to their age. This model also allows for a heterogeneous response of the population to the social distancing measures taken by the local government. We fit this model to the observed data and obtain a snapshot of the effective transmissions occurring inside the population at different times, which indicates where and among whom the disease propagates after the start of the public measures.