Global Stability of a Multi-group SVEIR Epidemiological Model with the Vaccination Age and Infection Age

Although many studies have proposed different multi-group epidemic models, few models considering that the vaccinated class may lose their protective properties at different rates have been developed. In this paper, we formulate a new multi-group SVEIR epidemic model that incorporates both the vaccination age of vaccinated individuals and the infection age of infectious individuals. We show that the basic reproduction number plays an important role in determining the long-term dynamics, that is, if , then the disease-free equilibrium is globally asymptotically stable while if , an endemic equilibrium uniquely exists and is globally asymptotically stable by using a graph-theoretic approach to the method of Lyapunov functionals. Mathematical results suggest that vaccination is shown to be helpful for disease control by decreasing the basic reproduction number, either enhancing the vaccination rate or lengthening the duration of vaccination protection.