NIRG: Rule-based epidemic models

Epidemic models for pathogens transmitted from human to human are, naturally, concerned with the interaction between individuals that leads to transmission. This is clearly a major simplification; there are many processes at work, from the feedack loop of epidemics on behaviour and interventions, to resource constraints limiting the production of prophylaxis and availability of diagnostic tests, to the response of the immune system to the pathogen and pharmaceuticals. Epidemic models do not normally include an account of these highly influential processes. Instead, only the assumed effect of these processes is sometimes included. This strongly limits the scope of epidemic models.

By contrast, in molecular biology, it is typical to consider a much larger class of possible interactions. There exist methods as well as mature software for expressing and simulating systems with many interactions. We have successfully shown that these techniques can be fruitfully applied directly to epidemics, including in a multi- scale setting incorporating immune response and, with suitable extensions, to detailed epidemic reconstruction in a complex community setting.

We will build on this success in order to consolidate this capability within the infectious disease modelling community. We will improve accessibility of the tools that we used in our pioneering work, facilitating adoption of our epidemic modelling methods more widely. We will foster a community of practice by conducting a series of case studies to establish documented and standardisable approaches to bringing our advanced techniques to bear on pressing current and future questions relevant to reducing the public health burden of infectious disease.

Epidemics in the context of a complex system characterised by many types of interaction. Interactions leading to infection are the primary focus of epidemic modelling, but there are many others leading to, intra alia, changing behaviour, allocation of resources, and immune response. These are difficult to capture in most epidemic modelling formalisms. If we could capture these processes, we could
better understand the dynamics of epidemics and better target public health interventions.

We build on work in molecular biology where models with different interactions are the norm. In that setting, the relevant questions are often about what the relevant interactions are, or what models make sense. From its rigorous foundations (Danos and Laneve 2004, Behr et al. 2016, Behr and Sobocinski 2020, Danos et al. 2020), rule-based modelling (Boutillier et al. 2018, Maus et al. 2011, Harris et al. 2016) allows us to rapidly explore the landscape of possible models by leveraging modularity and composition.

We have successfully applied this methodology to epidemics. We presented a diverse collection of seven simple models (Waites et al. 2021b). We showed how a multi-scale model of immune-response and epidemics can reproduce empirically observed viral load distributions for COVID-19 (Waites et al. 2021a). We also showed how to reconstruct an epidemic in a multiple transmission process setting (Waites et al. 2021c).

While it is evident that rule-based modelling is a very powerful tool for understanding epidemics, our work has also revealed some limitations in the modelling formalism. With an amount of effort commensurate to the size of this grant, we could support epidemics on networks, more accurate multi-scale models, and better integration into workflows typical of working modellers, and show that this works through a series of case studies.