The coronavirus pandemic has been declared a world health emergency by the World Health Organization, which has raised the importance of an accurate epidemiological model to predict the evolution of COVID-19. In this paper, we propose mean field evolutionary dynamics (MFEDs), inspired by optimal transport theory and mean field games on graphs, to model the evolution of COVID-19. In the MFEDs, we derive the payoff functions for different individual states from the commonly used replicator dynamics (RDs) and employ them to govern the evolution of epidemics. We also compare epidemic modeling based on MFEDs with that based on RDs through numerical experiments. Moreover, we show the efficiency of the proposed MFED-based model by fitting it to the COVID-19 statistics of Wuhan, China. Finally, we analyze the effects of one-time social distancing as well as the seasonality of COVID-19 through the post-pandemic period.
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