Asymptotic Properties of a General Model of Immune Status

Abstract

We consider a model of dynamics of the immune system. The model is based on three factors: occasional boosting and continuous waning of immunity and a general description of the period between subsequent boosting events. The antibody concentration changes according to a non-Markovian process. The density of the distribution of this concentration satisfies some partial differential equation with an integral boundary condition. We check whether this system generates a stochastic semigroup and we study the long-time behavior of this semigroup. In particular we prove a theorem on its asymptotic stability.