We propose a model for the COVID-19 epidemic where the population is partitioned into classes corresponding to ages (that remain constant during the epidemic). The main feature is to take into account the infection age of the infected population. This allows to better simulate the infection propagation that crucially depend on the infection age. We discuss how to compute the coefficients from data available in the future, and introduce a confinement variable as control. The cost function is a compromise between confinement cost, hospitalization peak and the death toll. Our numerical experiments allow to evaluate the interest of confinement varying with age classes.