Preliminary list of abstracts

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On hybrid models for discrete stochastic reaction systems
Keywords: chemical master equation; model reduction; error estimates
Wed, 10:45--11:10
  • Jahnke, Tobias (Department of Mathematics, Karlsruhe Institute of Technology, Germany)

Many processes in biology, chemistry and physics can be regarded as reaction systems in which different species interact via a number of reaction channels. In the approach of deterministic reaction kinetics, such systems are modelled by ordinary differential equations which describe how the concentrations of the species change in time. This model is simple and computationally cheap, but fails if the influence of stochastic noise cannot be ignored, and if certain species have to be represented in terms of integer particle numbers instead of real-valued concentrations.

In stochastic reaction kinetics, the system is considered as a Markov jump process on a high-dimensional, discrete state space. The goal is to compute the associated time-dependent probability distribution which evolves according to the chemical master equation. Due to the curse of dimensionality, however, solving this equation is computationally expensive or even impossible in most applications.

This dilemma has motivated the derivation of hybrid models which combine the accurate but computationally costly stochastic description and the simple but coarse deterministic description for different parts of the system. A particularly appealing hybrid model has recently been proposed by Andreas Hellander and Per Lötstedt. In this talk, we discuss the properties of the Hellander-Lötstedt model, present bounds for the modelling error, and sketch an extension which allows to overcome certain limitations.