Hybrid stochastic algorithms for simulating delayed biochemical reaction networks with monomolecular subsystems

Biochemical reaction networks (BRNs) often exhibit stochastic dynamics due to molecular discreteness and may include time delays arising from lagged biochemical processes. The delayed chemical master equation (DCME) provides a probabilistic framework for modelling such systems, which can be simulated using the Delay Stochastic Simulation Algorithm (DSSA) or the Purely Delayed Algorithm (PDA). In this work, we propose two hybrid simulation algorithms–MHDSSA and MHPDA–for BRNs involving both delayed reactions and monomolecular reactions. These algorithms combine the analytical solution of the monomolecular subsystem with DSSA and PDA, respectively, and are integrated using a sequential splitting approach inspired by delay differential equations (DDEs). The performance and efficiency of the proposed methods are evaluated through numerical experiments on BRNs of varying sizes. Results demonstrate significant computational speedup and accuracy preservation, particularly in systems dominated by monomolecular dynamics.