Global stability of an SVEIR epidemic model with ages of vaccination and latency

The vaccination period (i.e., the time period retaining acquired immunity following vaccination) and the latent period are two important factors affecting disease dynamics. Classical compartmental disease models unrealistically assume that these periods are exponentially distributed. In this paper, these two ages are assumed to have arbitrary distributions that are represented by age-specific rates leaving the vaccinated and the exposed classes, resulting in an SVEIR model with population dynamics. We investigate the global behavior of this model, and derive its basic reproduction number. The basic reproduction number completely determines the global dynamics of the model, i.e., the disease-free equilibrium is globally asymptotically stable and the disease always dies out when the basic reproduction number is less than unity; whereas when the basic reproduction number is larger than unity, there exists a unique endemic equilibrium which is globally asymptotically stable and the disease persists at this endemic equilibrium if it initially exists. The contributions of the vaccine-wane rate to the basic reproduction number and the level of the endemic equilibrium are displayed.