Lyapunov functional and global asymptotic stability for an infection-age model

Abstract

We study an infection-age model of disease transmission, where both the infectiousness and the removal rate may depend on the infection age. In order to study persistence, the system is described using integrated semigroups. If the basic reproduction number R ₀ < 1, then the disease-free equilibrium is globally asymptotically stable. For R ₀ > 1, a Lyapunov functional is used to show that the unique endemic equilibrium is globally stable amongst solutions for which disease transmission occurs.

Keywords:

• Lyapunov functional
• structured population
• global stability
• age of infection
• integrated semigroup

AMS Subject Classifications::

• 34K20
• 92D30