Applications of stochastic semigroups to cell cycle models

TL;DR

This paper explores stochastic semigroups and Markov processes to model the cell cycle, analyzing their long-term behavior and establishing connections between different modeling approaches.

Contribution

It introduces a stochastic semigroup framework for cell cycle models and compares it with a Markov process approach, providing new insights into their stability and dynamics.

Findings

Proved theorems on asymptotic stability of the models

Established conditions for sweeping behavior

Analyzed relations between the two modeling approaches

Abstract

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 Markov process. In the second case we also introduce a stochastic semigroup which describes the evolution of densities of the process. We study long-time behaviour of these models. In particular we prove theorems on asymptotic stability and sweeping. We also show the relations between both models.