The epidemic of infectious diseases has brought harm to society, so the study of the epidemic trend of viruses has been widely concerned by researchers. In this paper, by analyzing the current research status at home and abroad, the prediction models of infectious diseases are classified, and the principle and application of each model are introduced respectively. It mainly includes differential equation model, mainly introduces SIR, SEIR model, time series model ARIMA model and BP neural network model, compares the advantages and disadvantages of each model, helps readers quickly understand the main tasks and common methods of current model research. Finally, the methods and progress of infectious disease research models are summarized, the existing problems are analyzed, and the future research directions are prospected.