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

TL;DR

This paper introduces generalized Gillespie algorithms tailored for rule-based epidemiological models, enabling more accurate simulations of COVID-19 dynamics with features like age structure, time-dependent rates, and delays.

Contribution

It presents novel extensions of the Gillespie algorithm to handle time-dependent, discrete, and delay features in epidemiological modeling frameworks.

Findings

Algorithms successfully model COVID-19 scenarios with age and delay considerations

Numerical results demonstrate improved simulation accuracy

Applicable to complex, real-world epidemiological data

Abstract

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.