Modified delay chemical master equation and two simulation methods to approximate its solution
Communications in Statistics: Simulation and Computation, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Publication Date: 2026
- Doi Number: 10.1080/03610918.2026.2668037
- Journal Name: Communications in Statistics: Simulation and Computation
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, MathSciNet, zbMATH
- Keywords: Delay chemical master equation, Delay differential equations, Delay-modified Runge-Kutta method, Delay-modified stochastic simulation algorithm, Modified delay chemical master equation, Stochastic simulation algorithm
- Hacettepe University Affiliated: Yes
Abstract
Biochemical reaction networks (BRNs) with time delays are described by Delay Chemical Master Equations (DCMEs), which represent the time evolution of the system’s probability distribution. In this paper, a Modified Delay Chemical Master Equation (MDCME) is presented to approximate the dynamics of such BRNs. The modification strategy is to use the mean of delayed propensities, which in turn, transforms the corresponding DCME into a system of Delay Differential Equations (DDEs). Two simulation-based algorithms are proposed to approximate the solution of the MDCME. The first is called Delay-Modified Runge-Kutta Method (DMRKM), which is based on the Runge-Kutta methods for DDEs and obtains a numerical approximation to the probability distribution governed by the MDCME. The second, named the Delay-Modified Stochastic Simulation Algorithm (DMSSA), extends the classical stochastic simulation algorithm (SSA) by incorporating delayed mean propensities and reduces to SSA when delays vanish. We validate the efficiency and accuracy of the proposed algorithms on three benchmark BRNs.