Abstract
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.
Highlights
Theoretical models are typically developed through a deductive process where a researcher formulates a system of dynamic equations from hypothesized mechanisms
To test whether models discovered by Sparse Identification of Nonlinear Dynamics (SINDy) can predict real-world dynamics, we studied the ability of the second-order SINDy baseline measles model (Fig. 3) to make out-of-sample prediction of regime shifts in measles dynamics
Model discovery generates models inductively from data, using minimal prior knowledge about the system. This differs from the deductive approach that currently dominates model development in most fields, including theoretical epidemiology
Summary
Theoretical models are typically developed through a deductive process where a researcher formulates a system of dynamic equations from hypothesized mechanisms. We 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. Since Isaac Newton’s Principia mathematica, research have been devoted to creating models that accurately describe and predict the behaviour of these systems[2] These models are typically arrived at through a deductive process by hypothesizing mechanisms, formulating dynamic mathematical models that represent those mechanisms, and testing them against data. The simplest method to obtain a model that explains the data well minimizes the residual squared error between the predicted response and the data (OLS) This tends to create very complicated models with high descriptive value.
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