Asymptotic properties of a general model of immune status

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.Comment: 25 pages, 2 figure

Stability of Markov Semigroups and Applications to Parabolic Systems

AbstractA new theorem for asymptotic stability of Markov semigroups is proved. This result is applied to semigroups generated by parabolic systems describing the evolution of densities of two-state diffusion processes

Stochastic semigroups and their applications to biological models

Some recent results concerning generation and asymptotic properties of stochastic semigroups are presented. The general results are applied to biological models described by piecewise deterministic Markov processes: birth-death processes, the evolution of the genome, genes expression and physiologically structured models

Asymptotic stability of a partial differential equation with an integral perturbation

We study the asymptotic behaviour of the Markov semigroup generated by an integro-partial differential equation. We give new sufficient conditions for asymptotic stability of this semigroup