The outbreak of the coronavirus pandemic since the end of 2019 has been declared as a world health emergency by the World Health organization, which raised the importance of an accurate mathematical epidemiological dynamic model to predict the evolution of COVID-19. Replicator dynamics (RDs) are exclusively applied to many epidemic models, but they fail to satisfy the Nash stationarity and can only describe a unidirectional population flow between different states. In this paper, we proposed mean field evolutionary dynamics (MFEDs), inspired by the optimal transport theory and mean field games on graphs, to model epidemic dynamics. We compare the MFEDs with RDs theoretically. In particular, we also show the efficiency of MFEDs by modeling the evolution of COVID-19 in Wuhan, China. Furthermore, we analyze the effect of one-time social distancing as well as the seasonality of COVID-19 through the post-pandemic period.