The 𝜏-leaping algorithm is closely related to the Poisson process. From the theory of the Poisson process, it is established that if the interarrival times of events follow an exponential distribution with rate parameter 𝜆, and the intervals are mutually independent, the process can be classified as a Poisson process. Furthermore, the number of events occurring within any given time interval t follows a Poisson distribution with a mean of 𝜆𝑡 However, the SSA algorithm is not a Poisson process, as the parameter ∑ 𝑁 𝑎 𝑖 of the exponential distribution must be recalculated and updated after each event. Gillespie demonstrated that under the Leap Condition, by selecting an appropriate time interval 𝜏, the process can be approximated as a Poisson process, allowing for "leaps" and thus significantly improving simulation efficiency.