For some diseases, it is reported that immunity acquired by natural infection and vaccination subsequently wanes. It is also likely that an individual's immune period is extended owing to boosting immunity by re-exposure to an infection. We here study an age-dependent epidemic model, incorporating boosting immunity, which is a nonlinear version of the Aron epidemic model (1983), and is recently reformulated by Inaba (2017). We study the mathematical model, paying attention to the number and stability of the endemic equilibrium. This is a collaboration work with Liu Yang (Northeast Normal University).