The recent COVID-19 pandemic has led to an increasing interest in the modeling and analysis of infectious diseases. Our social behaviors in the daily lives have been significantly affected by the pandemic. In this paper, we propose a federated evolutionary game-theoretic framework to study the coupling of herd behaviors changes and epidemics spreading. Our framework extends the classical degree-based mean-field epidemic model over complex networks by integrating it with the evolutionary game dynamics. The statistically equivalent individuals in a population choose their social activity intensities based on the fitness or the payoffs that depend on the state of the epidemics. Meanwhile, the spread of infectious diseases over the complex network is reciprocally influenced by the players' social activities. We address the challenge of federated dynamics by breaking the analysis into the studies of the stationary properties of the epidemic for given herd behavior and the structural properties of the game for a given epidemic process. We use numerical experiments to show that our framework enables the prediction of the historical COVID-19 statistics.