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The need for accurate tourism demand forecasting is widely recognized. The unreliability of traditional methods makes tourism demand forecasting still challenging. Using deep learning approaches, this study aims to adapt Long Short-Term Memory (LSTM), Bidirectional LSTM (Bi-LSTM), and Gated Recurrent Unit networks (GRU), which are straightforward and efficient, to improve Taiwan’s tourism demand forecasting. The networks are able to seize the dependence of visitor arrival time series data. The Adam optimization algorithm with adaptive learning rate is used to optimize the basic setup of the models. The results show that the proposed models outperform previous studies undertaken during the Severe Acute Respiratory Syndrome (SARS) events of 2002–2003. This article also examines the effects of the current COVID-19 outbreak to tourist arrivals to Taiwan. The results show that the use of the LSTM network and its variants can perform satisfactorily for tourism demand forecasting.