The Application of Gillespie Algorithm in Spreading

. The contagion models of disease-spread which predict the epidemics grow with time goes by have been widely researched in social networks. The discrete-time simulation method, Monte Carlo Simulation where time is discretized into uniform steps and transition rates between states are replaced by transition probabilities, are mostly applied when simulating the models. In this paper, we propose a continuous-time approach, the Gillespie algorithm, which can be used for fast simulation of stochastic processes, is event-driven rather than using equally-spaced time steps. We show how the method can be adapted to the epidemic models, mainly in the susceptible-infected model and susceptible-infected-susceptible model, and confirm the accuracy of the method with numerical simulations. Based on the accuracy of the method, we make some changes in epidemic models to make the models more applicable.