Dynamical properties in an SVEIR epidemic model with age-dependent vaccination, latency, infection, and relapse

An SVEIR epidemic model with continuous age-dependent vaccination, latency, infection, and disease relapse is proposed and analyzed in this paper. The dynamical behaviors including the derivation of basic reproduction number R0, the existence and the stability of steady states, and the uniform persistence of the model are investigated. The results indicate that if R0 <= 1, the disease-free steady state is globally asymptotically stable, and the disease dies out, whereas if R0>1, the disease is uniformly persistent, and the endemic steady state is also globally asymptotically stable, and the disease remains at the endemic level. The research shows the global dynamics of the model are sharply determined by its basic reproduction number R0. Finally, numerical examples support our main theoretical results.