This study proposes a novel interpretable framework to forecast the daily tourism volume of Jiuzhaigou Valley, Huangshan Mountain, and Siguniang Mountain in China under the impact of COVID-19 by using multivariate time-series data, particularly historical tourism volume data, COVID-19 data, the Baidu index, and weather data. For the first time, epidemic-related search engine data is introduced for tourism demand forecasting. A new method named the composition leading search index-variational mode decomposition is proposed to process search engine data. Meanwhile, to overcome the problem of insufficient interpretability of existing tourism demand forecasting, a new model of DE-TFT interpretable tourism demand forecasting is proposed in this study, in which the hyperparameters of temporal fusion transformers (TFT) are optimized intelligently and efficiently based on the differential evolution algorithm. TFT is an attention-based deep learning model that combines high-performance forecasting with interpretable analysis of temporal dynamics, displaying excellent performance in forecasting research. The TFT model produces an interpretable tourism demand forecast output, including the importance ranking of different input variables and attention analysis at different time steps. Besides, the validity of the proposed forecasting framework is verified based on three cases. Interpretable experimental results show that the epidemic-related search engine data can well reflect the concerns of tourists about tourism during the COVID-19 epidemic.