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Rule-based models have been successfully used to represent different aspectsof the COVID-19 pandemic, including age, testing, hospitalisation, lockdowns,immunity, infectivity, behaviour, mobility and vaccination of individuals.These rule-based approaches are motivated by chemical reaction rules which aretraditionally solved numerically with the standard Gillespie algorithm proposedin the context of molecular dynamics. When applying reaction system type ofapproaches to epidemiology, generalisations of the Gillespie algorithm arerequired due to the time-dependency of the problems. In this article, wepresent different generalisations of the standard Gillespie algorithm whichaddress discrete subtypes (e.g., incorporating the age structure of thepopulation), time-discrete updates (e.g., incorporating daily imposed change ofrates for lockdowns) and deterministic delays (e.g., given waiting time until aspecific change in types such as release from isolation occurs). Thesealgorithms are complemented by relevant examples in the context of the COVID-19pandemic and numerical results.

Generalised Gillespie Algorithms for Simulations in a Rule-Based Epidemiological Model Framework