The stochastic simulation algorithm (SSA) has been widely used for simulating biochemical reaction networks. SSA is able to capture the inherently intrinsic noise of the biological system, which is due to the discreteness of species population and to the randomness of their reciprocal interactions. However, SSA does not consider other sources of heterogeneity in biochemical reaction systems, which are referred to as extrinsic noise. Here, we extend two simulation approaches, namely, the integration-based method and the rejection-based method, to take extrinsic noise into account by allowing the reaction propensities to vary in time and state dependent manner. For both methods, new efficient implementations are introduced and their efficiency and applicability to biological models are investigated. Our numerical results suggest that the rejection-based method performs better than the integration-based method when the extrinsic noise is considered.
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