2000 character limit reached
Asymptotic properties of a general model of immune status (2212.13147v1)
Published 26 Dec 2022 in math.PR
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 that this system generates a stochastic semigroup and we study the long-time behaviour of this semigroup. In particular we prove a theorem on its asymptotic stability.