This paper provides a comprehensive survey of recent advancements in leveraging machine learning techniques, particularly Transformer models, for predicting human mobility patterns during epidemics. Understanding how people move during epidemics is essential for modeling the spread of diseases and devising effective response strategies. Forecasting population movement is crucial for informing epidemiological models and facilitating effective response planning in public health emergencies. Predicting mobility patterns can enable authorities to better anticipate the geographical and temporal spread of diseases, allocate resources more efficiently, and implement targeted interventions. We review a range of approaches utilizing both pretrained language models like BERT and Large Language Models (LLMs) tailored specifically for mobility prediction tasks. These models have demonstrated significant potential in capturing complex spatio-temporal dependencies and contextual patterns in textual data.