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Naoki Masuda and Christian L. Vestergaard explain algorithms for simulating systems whose individual agents change state through discrete events in continuous time. Their tutorial introduces the Gillespie approach and relates its mathematical assumptions to interactions within populations and networks.
The opening material develops the stochastic processes needed to understand the classic algorithms. Subsequent sections show why continuous-time simulation can be preferable to simpler discrete-time models, especially when event timing affects the results. Worked explanations and diagrams connect the formal methods with models of interacting agents.
The later discussion surveys extensions that make simulations faster or allow event processes to depart from the independent Poisson assumptions of the basic method. By distinguishing exact simulation from approximations and clarifying the conditions under which particular methods apply, the book provides a technical guide for readers working with complex systems, numerical models and network dynamics.
Naoki Masuda; Christian L. Vestergaard. Gillespie Algorithms for Stochastic Multiagent Dynamics in Populations and Networks. Cambridge University Press, 2022. https://doi.org/10.1017/9781009239158. Licensed CC BY-NC-ND 4.0; the unchanged original edition and its required notices are retained.