Since December 2019,the COVID-19 epidemic has repeatedly hit countries around the world due to various factors such as trade,national policies and the natural environment.To closely monitor the emergence of new COVID-19 clusters and ensure high prediction accuracy,we develop a new prediction framework for studying the spread of epidemic on networks based on partial differential equations (PDEs),which captures epidemic diffusion along the edges of a network driven by population flow data.In this paper,we focus on the effect of the population movement on the spread of COVID-19 in several cities from different geographic regions in China for describing the transmission characteristics of COVID-19.Experiment results show that the PDE model obtains relatively good prediction results compared with several typical mathematical models.Furthermore,we study the effectiveness of intervention measures,such as traffic lockdowns and social distancing,which provides a new approach for quantifying the effectiveness of the government policies toward controlling COVID-19 via the adaptive parameters of the model.To our knowledge,this work is the first attempt to apply the PDE model on networks with Baidu Migration Data for COVID-19 prediction.