Agent-based Monte Carlo simulations for reaction-diffusion models, population dynamics, and epidemic spreading

Abstract

We provide an overview of Monte Carlo algorithms based on Markovian stochastic dynamics of interacting and reacting many-particle systems not in thermal equilibrium. These agent-based simulations are an effective way of introducing students to current research without requiring much prior knowledge or experience. By starting from the direct visualization of the data, students can gain immediate insight into emerging macroscopic features of a complex system and subsequently apply more sophisticated data analysis to quantitatively characterize its rich dynamical properties, both in the stationary and transient regimes. We utilize simulations of reaction-diffusion systems, stochastic models for population dynamics and epidemic spreading, to exemplify how interdisciplinary computational research can be effectively utilized in bottom-up undergraduate and graduate education through learning by doing. We also give helpful hints for the practical implementation of Monte Carlo algorithms, provide sample codes, explain some typical data analysis tools, and describe various potential error sources and pitfalls and tips for avoiding them.

60 pages, 17 figures, final version, editorially edited and condensed, to appear in American Journal of Physics (2025)

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