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In this article, we construct an age-structured model for COVID-19 withvaccination and analyze it from multiple perspectives. We derive the uniquedisease-free equilibrium point and the basic reproduction number $\mathscr{R}_0 $, then we show that the disease-free equilibrium is locallyasymptotically stable when $ \mathscr{R}_0 < 1 $, while is unstable when $\mathscr{R}_0 > 1 $. We also work out endemic equilibrium points and reveal thestability. We use sensitivity analysis to explore how parameters influence $\mathscr{R}_0 $. Sensitivity analysis helps us develop more targeted strategiesto control epidemics. Finally, this model is used to discuss the cases inShijiazhuang, Hebei Province at the beginning of 2021. We compare reportedcases with the simulation to evaluate the measures taken by Shijiazhuanggovernment. Our study shows how age structure, vaccination and drasticcontainment measures can affect the epidemic.

An age-structured epidemic model with vaccination