Global dynamics for an age-structured epidemic model with media impact and incomplete vaccination

•A novel age-structured epidemic model with media impact and incomplete vaccination is studied.•Media-induced nonlinear incidence, age-dependent vaccination and latency are contained.•Uniform persistence and global stability of the system are established.•Our results can be extended to the SVEIR model with general nonlinear infectious force function of monotonicity and concavity.

Some studies show that the efficacy of vaccines may decline and the vaccine-induced immunity wanes with time elapsed since vaccination (e.g., BCG, HBV vaccines). Meanwhile, the use of media can effectively contain the emerging epidemics. In our work, an SVEIR epidemic model with media impact, age-dependent vaccination and latency is proposed, where the efficacy of vaccines depends on the time since vaccination. Uniform persistence and the sharp threshold dynamics are established, that is, the vaccination reproduction number completely determines the global dynamics of the model system. Our main results established can be extended to the SVEIR model with the general nonlinear infectious force function of monotonicity and concavity.