  Rule-based models have been successfully used to represent different aspects
of 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 are
traditionally solved numerically with the standard Gillespie algorithm proposed
in the context of molecular dynamics. When applying reaction system type of
approaches to epidemiology, generalisations of the Gillespie algorithm are
required due to the time-dependency of the problems. In this article, we
present different generalisations of the standard Gillespie algorithm which
address discrete subtypes (e.g., incorporating the age structure of the
population), time-discrete updates (e.g., incorporating daily imposed change of
rates for lockdowns) and deterministic delays (e.g., given waiting time until a
specific change in types such as release from isolation occurs). These
algorithms are complemented by relevant examples in the context of the COVID-19
pandemic and numerical results.
