19 citations · 36 across the 9 of their papers we have counts for
11 papers
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…
Cell cycle length and long-time behaviour of an age-size model
Katarzyna Pichór, Ryszard Rudnicki
We consider an age-size structured cell population model based on the cell cycle length. The model is described by a first order partial differential equation with initial-boundary…
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…
Replicator dynamics for the game theoretic selection models based on state
Krzysztof Argasinski, Ryszard Rudnicki
The paper contains the attempt to integration of the classical evolutionary game theory based on replicator dynamics and the state based approach of Houston and Mcnamara. In the ne…
Beyond classical Hamilton's Rule. State distribution asymmetry and the dynamics of altruism
Krzysztof Argasinski, Ryszard Rudnicki
This paper analyzes the relationships between demographic and state-based evolutionary games and Hamilton's rule. It is shown that the classical Hamilton's rule (counterfactual met…
Invariant density & time asymptotics for collisionless kinetic equations with partly diffuse boundary operators
Bertrand Lods, Mustapha Mokhtar-Kharroubi, Ryszard Rudnicki
This paper deals with collisionless transport equations in bounded open domains with boundary , orthogonally invariant v…
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…
Does a population with the highest turnover coefficient win competition?
Ryszard Rudnicki
We consider a discrete time competition model. Populations compete for common limited resources but they have different fertilities and mortalities rates. We compare dynamical prop…
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…