A rule-based epidemiological framework for modelling and simulation in the context of the covid-19 pandemic

Motivated by chemical reaction rules, we introduce a rule-based epidemiological framework for the mathematical modelling of the COVID-19 pandemic which lies the foundations for further study of this class of models. Here we stress that we do not have a specific model in mind, but a whole collection of models which can be transformed into each other, or represent different aspects of the pandemic. Each single model is based on a mathematical formulation that we call a rule-based system. They have several advantages, for example that they can be both interpreted both stochastically and deterministically without changing the model structure. Rule-based systems should be easier to communicate to non-specialists, when compared to differential equations. Due to their combinatorial nature, the rule-based model framework we propose is ideal for systematic mathematical modelling, systematic links to statistics, data analysis in general and machine learning. Most importantly, the framework can be used inside a Bayesian model selection algorithm, which can extend unsupervised machine learning technology to gain mechanistic insight through mathematical models. We first introduce the Bayesian model selection algorithm and give an introduction to rule-based systems. We propose precursor models, all consistent with our rule-based framework and relevant for the COVID-19 pandemic. We complement the models with numerical results and, for some of them, we include analytical results such as the calculation of the number of new infections generated by an infected person during their infectious period. We conclude the article with an in depth discussion of the role of mathematical modelling through the COVID-19 pandemic.