The stability analysis of an SVEIR model with continuous age-structure in the exposed and infectious classes

In this paper, an Susceptible-Vaccines-Exposed-Infectious-Recovered model with continuous age-structure in the exposed and infectious classes is investigated. These two ages are assumed to have arbitrary distributions that are represented by age-specific rates leaving the exposed and the infectious classes. We investigate the global dynamics of this model in the sense of basic reproduction number via constructing Lyapunov functions. The asymptotic smoothness of solutions and uniform persistence of the system is shown from reformulating the system as a system of Volterra integral equations.