Researchers propose a hybrid, data-driven approach that combines two methods—Sparse Identification of Nonlinear Dynamics (SINDy) and the Ensemble Kalman Filter (EnKF)—to learn how Chikungunya virus (CHIKV) spreads when real surveillance data are noisy, incomplete, or only partially observed. Their numerical experiments show the combined method improves short-term prediction accuracy and can reconstruct unobserved parts of an outbreak trajectory better than using SINDy alone.

As a starting point the team wrote a detailed compartmental model that tracks 10 population groups over time: seven human states (susceptible, vaccinated, exposed, symptomatically infectious, asymptomatically infectious, treated, recovered) and three mosquito states (susceptible, exposed, infectious). This mechanistic model provides a concrete benchmark for testing data-driven recovery. SINDy is then used to try to discover the governing equations from time series of those states. SINDy works by building a large library of candidate functions and using a sparsity-promoting regression to pick a few terms that explain the dynamics.

SINDy can recover the right equations when the data are clean. But the method is sensitive to noise because it needs numerical estimates of time derivatives; calculating derivatives amplifies measurement noise and can lead SINDy to keep spurious terms or discard true ones. Its performance also depends on the chosen candidate library and the sparsity threshold, which are hard to tune without ground truth.

To address that fragility the authors embed SINDy inside an Ensemble Kalman Filter. The EnKF is a sequential data-assimilation tool that propagates an ensemble of possible system states and updates them when observations arrive. This update uses the ensemble spread to estimate covariances and thus filters measurement noise. In the hybrid setup the EnKF uses the SINDy-derived model to forecast, then assimilates noisy observations to correct forecasts and infer unobserved state variables. The paper reports that this coupling gives better state reconstruction and prediction under partial observability, a common constraint in real epidemiological surveillance.