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We develop a simulation method for Markov Jump processes with finite time steps based in a quasilinear approximation of the process and in multinomial random deviates. The second order approximation to the generating function, Error$=O(dt^{2})$, is developed in detailand an algorithm is presented. The algorithm is implemented for a Susceptible-Infected-Recovered-Susceptible (SIRS) epidemic model a
