Gillespie algorithm and diffusion approximation based on Monte Carlo simulation for innovation diffusion: A comparative study

Abstract

Abstract Monte Carlo simulations have been utilized to make a comparative study between diffusion approximation (DA) and the Gillespie algorithm and its dependence on population in the information diffusion model. Diffusion approximation is one of the widely used approximation methods which have been applied in queuing systems, biological systems and other fields. The Gillespie algorithm, on the other hand, is used for simulating stochastic systems. In this article, the validity of diffusion approximation has been studied in relation to the Gillespie algorithm for varying population sizes. It is found that diffusion approximation results in large fluctuations which render forecasting unreliable particularly for a small population. The relative fluctuations in relation to diffusion approximation, as well as to the Gillespie algorithm have been analyzed. To carry out the study, a nonlinear stochastic model of innovation diffusion in a finite population has been considered. The nonlinearity of the problem necessitates use of approximation methods to understand the dynamics of the system. A stochastic differential equation (SDE) has been used to model the innovation diffusion process, and corresponding sample paths have been generated using Monte Carlo simulation methods.