Numerical methods for stochastic simulations: application to contagion processes

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Abstract
Approximate numerical methods are one of the most used strategies to extract information from many-interacting-agents systems. In particular, the binomial method is of extended use to deal with epidemic, ecological and biological models, since unbiased methods like the Gillespie algorithm can become unpractical due to high CPU time usage required. However, authors have criticized the use of this approximation and there is no clear consensus about whether unbiased methods or the binomial approach is the best option. In this work, we derive new scaling relations for the errors in the binomial method. This finding allow us to build rules to compute the optimal values of both the discretization time and number of realizations needed to compute averages with the binomial method with a target precision and minimum CPU-time usage. Furthermore, we also present another rule to discern whether the unbiased method or the binomial approach is more efficient. Ultimately, we will show that the choice of the method should depend on the desired precision for the estimation of averages.

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