Parameter and State Estimation in SIRD, SEIR, and SVEIR Epidemiological Models Using Kalman Filter and Genetic Algorithm

Abstract

This study presents a comparative investigation of parameter and state estimation techniques applied to three epidemiological models: SIRD, SEIR, and SVEIR. The models are used to simulate infectious disease dynamics with increasing levels of complexity, incorporating factors such as exposure latency and vaccination. Parameter estimation is first performed using three approaches, they are Kalman Filter (KF), Extended Kalman Filter (EKF), and Genetic Algorithm (GA). The best parameter estimates from each method are then used as inputs for state estimation, which is carried out using the Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF). This forms six combinations of estimation strategies (KF-EKF, EKF-EKF, GA-EKF, KF-UKF, EKF-UKF, GA-UKF) evaluated across models. Root Mean Square Error (RMSE) is used as the evaluation metric to assess estimation accuracy. The results demonstrate that GA excels in estimating static parameters, while EKF is more effective for dynamic parameters. Hybrid combinations provide the best performance in state estimation across all models, indicating the benefit of combining global optimization and recursive filtering. These findings can support public health policy by informing the selection of appropriate modeling and estimation techniques to accurately predict epidemic trends, optimize vaccination strategies, and allocate medical resources more effectively during outbreaks. All experiments are conducted on synthetically generated epidemic data to ensure controlled evaluation and generalizability across models.