A hybrid, data-driven model framework that combines Sparse Identification of Nonlinear Dynamics (SINDy) with the Ensemble Kalman Filter (EnKF) for sequential data assimilation improves prediction accuracy and provides a good reconstruction of unobserved trajectories under partial observability, a common constraint in real-world epidemiological surveillance.
Abstract
Current mechanistic models for the transmission dynamics of the Chikungunya virus (CHIKV) rely on uncertain parameters or partially observed data. This limitation challenges the use of theoretical models for understanding and forecasting disease spread. Here we present a hybrid, data-driven model framework that combines Sparse Identification of Nonlinear Dynamics (SINDy) with the Ensemble Kalman Filter (EnKF) for sequential data assimilation. Our numerical experiments show that this approach improves prediction accuracy and provides a good reconstruction of unobserved trajectories under partial observability, a common constraint in real-world epidemiological surveillance. SINDy can be applied to epidemic trajectories, recovering the underlying equations in noise-free conditions. However, standalone SINDy is highly sensitive to noise, leading to spurious terms and poor performance. Hence, we embed the identification procedure within an EnKF framework, which assimilates noisy observations to correct forecast states from the SINDy-derived model and to infer unobserved state variables.
This work introduces Generative Neural Inference for Epidemics (GENIE), a spatio-temporal ML-based framework for high-resolution forecasting of the burden of respiratory pathogens and demonstrates superior performance across a range of measures.
Laura M Guzman-Rincon, George R.E. Bradley, Joel Kandiah et al.· 0 citations
Outbreaks and epidemics of infectious diseases have continuously driven the iterative development of epidemiological models. However, in reality, epidemic data often contains missing values due to delayed updates and incomplete reporting, which weakens the model's ability to characterize the transmission process and increases the difficulty of prediction. Therefore, this study proposes a loss-constrained time-varying parameter estimation neural network (L-TPENN), which directly incorporates the structural information of missing data into the objective loss function, enabling the model to handle the uncertainty caused by missing data during training. This method combines the powerful solution capabilities of Physics-Informed Neural Network under differential equation constraints with the advantages of Gated Recurrent Unit in capturing dynamic data features and handling missing data. By introducing a masking mechanism at the GRU input layer, the model can utilize the data's inherent temporal structure to execute adaptive estimation without dependence on traditional missing value imputation steps, thereby fundamentally enhancing the robustness of the estimation process. Numerical simulations show that L-TPENN achieves superior fitting performance compared to Quantile Regression Bidirectional Gated Recurrent Unit, Hybrid Grey Genetic Algorithm-based Maximum Likelihood Method and Iterated imputation estimation. Empirical analysis section, experimental results based on real pandemic data from Minnesota, demonstrate that this method can accurately fit and forecast real-world data, In furtherance of this, to make effective estimates of the time-varying parameters within the model.
Xiang-Lei Li, Jun Wang, Yue-Cai Han· Journal of Data and Dynamic...· 0 citations
Experiments with synthetic data and COVID-19 surveillance data show that SUC–PINN recovers plausible hidden infection trajectories, yields stable parameter estimates, and provides accurate short-term forecasts, support SUC–PINN as a practical computational approach for inverse modeling and prediction in partially observed epidemic dynamics.
U. M. Rifanti, N. Susyanto, Ratinan Boonklurb· Advances in Complex Systems· 0 citations
Accurate forecasts of seasonal influenza are imperative to successfully manage public health resources. However, epidemiological time series data often show significant spiky volatility along with heavy-tailed distributions that do not satisfy the normality assumption required by traditional linear models. This paper proposes a new model called Robust Laplace-ARDL, which uses a Double Exponential (Laplace) distribution instead of the standard normal distribution to accommodate heavy-tailed distributions. Using 792 weekly observations (2005–2020) and benchmarking against a Long Short-term Memory (LSTM) model, the Laplace-ARDL
(
p
=
5
)
model reduces the mean square error (MSE) by
33.5
\%
compared to the LSTM model. This paper provides empirical evidence that it is vital to solve the leptokurtic distribution in infection data for obtaining stable forecasts.
Gokul Thanigaivasan, Ratha Jeyalakshmi T, R. Mani et al.· Model Assisted Statistics an...· 0 citations
In this study, five distinct COVID-19 models developed in different countries, each designed to reflect the prevailing epidemiological condition at the time of formulation, are examined. The models are reformulated while still maintaining their original compartmental structure, using their common transmissions from one compartment to the other. Modified Patankar–Runge–Kutta (MPRK) methods are then applied to approximate the solutions of the resulting system of nonlinear ordinary differential equations (ODEs) representing each model to produce unconditionally positive approximations and to preserve the conservative part of the ODEs. In particular, we incorporate the numerical solution into a cost function to improve the estimates for the non-autonomous model hyperparameters. In a first step we obtain piecewise constant parameters that fit real data. Later we perform a WENO reconstruction in a post-process to approximate the true time-dependent coefficients inside the ODEs. As a proof-of-concept, we apply our approach to improve the parameters of a paper concerned with modeling COVID-19 in Ghana, where we can make 5-day predictions within a 10% error range.
Thomas Izgin-Melnikov, Andreas Meister, Isaac Azure· Journal of Mathematics in In...· 0 citations
Infectious diseases exhibit complex and rapidly evolving transmission dynamics, requiring modeling approaches that can accurately capture these mechanisms. The SIRS-D compartmental model provides a suitable framework, as it incorporates temporary immunity and disease-induced mortality within the epidemic process. Accurate parameter estimation is essential for quantifying the transmission rate, recovery rate, waning immunity rate, and mortality rate, which collectively govern the system behavior. Among existing estimation methods, Physics-Informed Neural Networks (PINNs) offer significant advantages by integrating observational data with the underlying structure of differential equations, thereby preserving physical consistency while maintaining robustness under imperfect data conditions. In this study, PINNs are employed to estimate the parameters of the SIRS-D model using synthetic data generated through the fourth-order Runge–Kutta (RK4) method to ensure stable and consistent numerical solutions. To better represent real-world measurement conditions, 5% noise is added to the synthetic data, introducing realistic variability into the training process. The results demonstrate that PINNs successfully reconstruct the trajectories of S(t), I(t), R(t), and D(t) with low prediction errors. The model achieves MAE values of 0.0065 (S), 0.0067 (I), 0.0208 (R), and 0.0043 (D), with corresponding RMSE values of 0.0090, 0.0074, 0.0253, and 0.0058. Moreover, the estimated parameters closely match the true values, yielding ????????=0.5031, ????=0.0996, ????=0.0095, and ????=0.0149, demonstrating strong parameter identification capability. These findings confirm that PINNs constitute a reliable and accurate framework for analyzing infectious disease dynamics and offer promising potential for extension to more complex epidemiological models and real-world datasets.
Fitri Cahyani, Abdurakhman Abdurakhman, Chyntia Meininda Anjanni· The eurasia proceedings of s...· 0 citations
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