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Social media (SM) based surveillance systems, combined with machine learning (ML) and deep learning (DL) techniques, have shown potential for early detection of epidemic outbreaks. This review discusses the current state of SM-based surveillance methods for early epidemic outbreaks and the role of ML and DL in enhancing their performance. Since, every year, a large amount of data related to epidemic outbreaks, particularly Twitter data is generated by SM. This paper outlines the theme of SM analysis for tracking health-related issues and detecting epidemic outbreaks in SM, along with the ML and DL techniques that have been configured for the detection of epidemic outbreaks. DL has emerged as a promising ML technique that adapts multiple layers of representations or features of the data and yields state-of-the-art extrapolation results. In recent years, along with the success of ML and DL in many other application domains, both ML and DL are also popularly used in SM analysis. This paper aims to provide an overview of epidemic outbreaks in SM and then outlines a comprehensive analysis of ML and DL approaches and their existing applications in SM analysis. Finally, this review serves the purpose of offering suggestions, ideas, and proposals, along with highlighting the ongoing challenges in the field of early outbreak detection that still need to be addressed. [ABSTRACT FROM AUTHOR]