Piecewise deterministic Markov processes in biological models

TL;DR

This paper introduces piecewise deterministic Markov processes (PDMPs) and demonstrates their application to various biological models, highlighting their mathematical properties and relevance to biological phenomena.

Contribution

It provides an accessible introduction to PDMPs and applies general asymptotic results to specific biological examples, showcasing their modeling utility.

Findings

PDMPs effectively model biological dispersal and cell dynamics

Asymptotic properties of PDMPs are established for biological systems

Applications include gene expression and neural activity modeling

Abstract

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 dispersal of biological systems, cell cycle models, gene expression, physiologically structured populations, as well as neural activity. General results concerning asymptotic properties of stochastic semigroups induced by such Markov processes are applied to specific examples.