Algorithmic discovery of dynamic models from infectious disease data.

Area of Science:

• Epidemiology
• Computational Biology
• Dynamical Systems Theory

Background:

• Traditional theoretical models are deductively derived from hypothesized mechanisms.
• Algorithmic approaches enable inductive dynamic model discovery directly from empirical data.
• Prior studies primarily validated these methods using synthetic data.

Purpose of the Study:

• To apply Sparse Identification of Nonlinear Dynamics (SINDy) for discovering mechanistic equations governing disease dynamics.
• To analyze the efficacy of SINDy using real-world case notification data for measles, chickenpox, and rubella.
• To evaluate the discovered models' qualitative fit, predictive capabilities, and common epidemiological features.

Main Methods:

• Utilized the Sparse Identification of Nonlinear Dynamics (SINDy) algorithm.
• Applied SINDy to measles, chickenpox, and rubella case notification data.
• Incorporated power spectral density into the goodness-of-fit for rubella model refinement.
• Employed a library of second-order functions within the SINDy framework.

Main Results:

• SINDy models exhibited a good qualitative fit for all three diseases.
• The chickenpox model showed signs of overfitting; rubella model recovery required spectral density analysis.
• Discovered models frequently included mass action incidence and seasonal transmission rates.
• The SINDy measles model accurately predicted a dynamical regime shift in out-of-sample data.

Conclusions:

• Algorithmic model discovery, exemplified by SINDy, offers a powerful complementary approach to traditional deductive modeling in epidemiology.
• SINDy can uncover key epidemiological features like seasonal transmission and predict disease dynamics, including regime shifts.
• This data-driven approach enhances scientific understanding and enriches theoretical model development.