19 citations · 36 across the 9 of their papers we have counts for
6 papers · 1 filter
Asymptotic properties of a general model of immune status
Katarzyna Pichór, Ryszard Rudnicki
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 pe…
Dynamics of antibody levels: asymptotic properties
Katarzyna Pichór, Ryszard Rudnicki
We study properties of a piecewise deterministic Markov process modeling the changes in concentration of specific antibodies. The evolution of densities of the process is described…
Applications of stochastic semigroups to cell cycle models
Katarzyna Pichór, Ryszard Rudnicki
We consider a generational and continuous-time two-phase model of the cell cycle. The first model is given by a stochastic operator, and the second by a piecewise deterministic Mar…
Piecewise deterministic Markov processes in biological models
Ryszard Rudnicki, Marta Tyran-Kaminska
We present a short introduction into the framework of piecewise deterministic Markov processes. We illustrate the abstract mathematical setting with a series of examples related to…
On a stochastic gene expression with pre-mRNA, mRNA and protein contribution
Ryszard Rudnicki, Andrzej Tomski
In this paper we develop a model of stochastic gene expression, which is an extension of the model investigated in the paper [T. Lipniacki, P. Paszek, A. Marciniak-Czochra, A.R. Br…
Model of phenotypic evolution in hermaphroditic populations
Ryszard Rudnicki, Paweł Zwoleński
We consider an individual based model of phenotypic evolution in hermaphroditic populations which includes random and assortative mating of individuals. By increasing the number of…