Abstract
We introduce an extended SEIR infectious disease model with data assimilation for the study of the spread of COVID-19. In this framework, undetected asymptomatic and pre-symptomatic cases are taken into account, and the impact of their uncertain proportion is fully investigated. The standard SEIR model does not consider these populations, while their role in the propagation of the disease is acknowledged. An ensemble Kalman filter is implemented to assimilate reliable observations of three compartments in the model. The system tracks the evolution of the effective reproduction number and estimates the unobservable subpopulations. The analysis is carried out for three main prefectures of Japan and for the entire country of Japan. For these four communities, our estimated effective reproduction numbers are more stable than the corresponding ones estimated by a different method (Toyokeizai). We also perform sensitivity tests for different values of some uncertain medical parameters, like the relative infectivity of symptomatic/asymptomatic cases. The regional analysis results suggest the decreasing efficiency of the states of emergency.