Severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2; COVID-19) has rapidly transmitted between people. Mathematical modeling of infectious diseases is emphasized to inform policy responses by capturing the ongoing pattern of COVID-19. We introduce epidemic model with the additional states such as a vaccinated and isolated state to closer to reality. A data-driven epidemic model based on the Markov chain would be a desirable approach to overcome the challenges that infer the latent states. To this aim, we take advantage of the reported data and underlying Markov chain dynamics. To verify our model, we set initial values of each states and estimated the state values by fitting COVID-19 dataset of South Korea. Throughout the investigation, it is confirmed that the proposed models can successfully estimate all states.