Compositional modelling of immune response and virus transmission dynamics.

Transmission models for infectious diseases are typically formulated in terms of dynamics between individuals or groups with processes such as disease progression or recovery for each individual captured phenomenologically, without reference to underlying biological processes. Furthermore, the construction of these models is often monolithic: they do not allow one to readily modify the processes involved or include the new ones, or to combine models at different scales. We show how to construct a simple model of immune response to a respiratory virus and a model of transmission using an easily modifiable set of rules allowing further refining and merging the two models together. The immune response model reproduces the expected response curve of PCR testing for COVID-19 and implies a long-tailed distribution of infectiousness reflective of individual heterogeneity. This immune response model, when combined with a transmission model, reproduces the previously reported shift in the population distribution of viral loads along an epidemic trajectory. This article is part of the theme issue 'Technical challenges of modelling real-life epidemics and examples of overcoming these'.

Rule-based epidemic models.

Rule-based models generalise reaction-based models with reagents that have internal state and may be bound together to form complexes, as in chemistry. An important class of system that would be intractable if expressed as reactions or ordinary differential equations can be efficiently simulated when expressed as rules. In this paper we demonstrate the utility of the rule-based approach for epidemiological modelling presenting a suite of seven models illustrating the spread of infectious disease under different scenarios: wearing masks, infection via fomites and prevention by hand-washing, the concept of vector-borne diseases, testing and contact tracing interventions, disease propagation within motif-structured populations with shared environments such as schools, and superspreading events. Rule-based models allow to combine transparent modelling approach with scalability and compositionality and therefore can facilitate the study of aspects of infectious disease propagation in a richer context than would otherwise be feasible.