Global stability of vaccine-age/staged-structured epidemic models with nonlinear incidence

Abstract

We consider two classes of infinitely dimensional epidemic models with nonlinear incidence, where one assumes that the rate of a vaccinated individual losing immunity depends on the vaccine-age and another assumes that, before the vaccine begins to wane, there is a period during which the vaccinated individuals have complete immunity against the infection. The first model is given by a coupled ordinary-hyperbolic differential system and the second class is described by a delay differential system. We calculate their respective basic reproduction numbers, and show they characterize the global dynamics by constructing the appropriate Lyapunov functionals.

Keywords

• nonlinear incidence
• vaccination
• basic reproduction number
• steady state
• global stability
• lyapunov functional