Algorithmic discovery of dynamic models from infectious disease data

Theoretical models are typically developed through a deductive process where a researcher formulates a system of dynamic equations from hypothesized mechanisms. Recent advances in algorithmic methods can discover dynamic models inductively–directly from data. Most previous research has tested these methods by rediscovering models from synthetic data generated by the already known model. Here we apply Sparse Identification of Nonlinear Dynamics (SINDy) to discover mechanistic equations for disease dynamics from case notification data for measles, chickenpox, and rubella. The discovered models provide a good qualitative fit to the observed dynamics for all three diseases, However, the SINDy chickenpox model appears to overfit the empirical data, and recovering qualitatively correct rubella dynamics requires using power spectral density in the goodness-of-fit criterion. When SINDy uses a library of second-order functions, the discovered models tend to include mass action incidence and a seasonally varying transmission rate–a common feature of existing epidemiological models for childhood infectious diseases. We also find that the SINDy measles model is capable of out-of-sample prediction of a dynamical regime shift in measles case notification data. These results demonstrate the potential for algorithmic model discovery to enrich scientific understanding by providing a complementary approach to developing theoretical models.