Global threshold dynamics of an SIVS model with waning vaccine-induced immunity and nonlinear incidence

• An epidemic model with nonlinear incidence rate and age structure is proposed.
• The persistence of the age structure model is proved.
• The global stability of the system is established by employing Lyapunov functional.
• Our results extend many existent results.

Vaccination is the most effective method of preventing the spread of infectious diseases. For many diseases, vaccine-induced immunity is not life long and the duration of immunity is not always fixed. In this paper, we propose an SIVS model taking the waning of vaccine-induced immunity and general nonlinear incidence into consideration. Our analysis shows that the model exhibits global threshold dynamics in the sense that if the basic reproduction number is less than 1, then the disease-free equilibrium is globally asymptotically stable implying the disease dies out; while if the basic reproduction number is larger than 1, then the endemic equilibrium is globally asymptotically stable indicating that the disease persists. This global threshold result indicates that if the vaccination coverage rate is below a critical value, then the disease always persists and only if the vaccination coverage rate is above the critical value, the disease can be eradicated.