 
Summary: A modified next reaction method for simulating chemical systems
with time dependent propensities and delays
David F. Andersona
Department of Mathematics, University of WisconsinMadison, Madison, Wisconsin 53706, USA
Received 20 June 2007; accepted 26 September 2007; published online 6 December 2007;
publisher error corrected 28 January 2008
Chemical reaction systems with a low to moderate number of molecules are typically modeled as
discrete jump Markov processes. These systems are oftentimes simulated with methods that produce
statistically exact sample paths such as the Gillespie algorithm or the next reaction method. In this
paper we make explicit use of the fact that the initiation times of the reactions can be represented
as the firing times of independent, unit rate Poisson processes with internal times given by integrated
propensity functions. Using this representation we derive a modified next reaction method and, in a
way that achieves efficiency over existing approaches for exact simulation, extend it to systems with
time dependent propensities as well as to systems with delays. © 2007 American Institute of
Physics. DOI: 10.1063/1.2799998
I. INTRODUCTION
Due to advances in the knowledge of cellular systems,
where there are low to moderate numbers of molecules of
certain species, there has been a renewed interest in model
ing chemical systems as discrete and stochastic as opposed to
