denim: An R package for deterministic compartmental models with flexible dwell-time distributions

Compartmental models are widely used for dynamical systems where states are discrete, such as in infectious disease epidemiology with the so-called Susceptible-Infectious-Recovered (SIR) framework. For mathematical simplicity, rates of transition between compartments are generally assumed to be independent of the dwell time (or secondary timescale in survival analysis): they are either constant or dependent on the epidemiological time (or primary timescale in survival analysis) only, either directly (e.g. environmental or behavioural forcings in epidemiological models) or indirectly through dependence on other variables of the system (e.g. the force of infection in epidemiological models). In some domains of application, this memoryless assumption leads to distributions of dwelling times that are incompatible with those observed in data (e.g. infectious periods for childhood diseases), which can lead to serious problems since the model predictions are highly sensitive to the exact shape of these distributions. Here, we propose a deterministic, continuous-variable, numerical modelling approach that allows full flexibility on the dwell-time distributions. The accompanying denim package provides a user-friendly interface to implement our proposed method through a dedicated language for model definition. The package is open source and available on CRAN. As more detailed data on the clinical process of infections become available, the denim package will be extremely useful for building more realistic epidemiological models that provide more accurate projections.