Recognition and Forecasting of Time-Varying Parameters in SIRD Models: The L-TPENN Method for Processing Missing Vertical Data
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.