Parameter estimation in a stochastic SEIHR model of COVID-19 using the EnKF: A case study based on real-world data

In this study, we estimate unknown constant parameters, transmission states, and the stochastic basic reproduction number R0∗ of the COVID-19 pandemic by developing a stochastic data assimilation framework based on the ensemble Kalman filter (EnKF) combined with the Milstein discretisation scheme for a nonlinear stochastic SEIHR (Susceptible-Exposed-Infected-Hospitalised-Recovered) model. The filter’s performance is first assessed on simulated data to evaluate its accuracy under controlled conditions, and then applied to real epidemiological data from France, Italy, and Germany over a 364-day period, from 2 January to 31 December 2022. This period captures a critical phase marked by the gradual easing of non-pharmaceutical interventions and the rollout of vaccination campaigns. The results show that the EnKF effectively estimates unknown parameters, key epidemiological states, and the stochastic basic reproduction number in all three countries, providing insights into the temporal evolution of the epidemic. In particular, the filter yields accurate estimates for the exposed (E), infected (I), and hospitalised (H) compartments. However, estimates for the susceptible compartment (S) exhibit higher root mean square error (RMSE) in both simulated and real data, indicating reduced reliability across contexts. Overall, the proposed Milstein-EnKF framework remains a robust and practical tool for estimating unknown parameters and predicting COVID-19 dynamics within a nonlinear stochastic modelling framework.