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The τ-leaping methods are very known solutions for accelerating the Gillespie's Stochastic Simulation Algorithm in the simulation of well-stirred chemically reacting systems. In this paper, we propose a new variant of the stochastic simulation algorithm, that we call SSAL, which lays in the middle between the Gillespie's Direct Method and a τ-leaping. Essentially, SSAL works as a standard Direct Method. However, it uses the typical Leap Condition to incrementally build leaps, avoiding at the same time the risk of getting into negative populations. We compare SSAL with one of the most known and efficient τ-leaping methods, named Modified τ-leaping. We provide for both of them a detailed theoretical asymptotic analysis and some experimental tests upon three realistic biological models.

SSALeaping: efficient leap condition based direct method variant for the stochastic simulation of chemical reacting system