The advancement of new technology has compelled modern healthcare organizations through the intelligent computing modeling to enhance efficiency in processing healthcare delivery outcomes and health care organization efficiency. This chapter focuses on the application of Fog and Edge Computing integrated with Machine Learning (ML) to solve major healthcare optimization problems. It explores the decentralized computing paradigms which support real-time analytics for various use cases such as remote patient monitoring and emergency response, which leads to lower latency and increased response times. To reduce data privacy and cybersecurity threats, measures, including encryption and an ML-based anomaly detection system, are proposed. The chapter also expounds on new and creative approaches in achieving better compatibility across various healthcare systems through the approach of applying data harmonization technique built on ML and establishes tactics for developing scalable structures based on dynamic resource management in fog and edge settings. The development of adaptive ML models for providing individualized healthcare services including accurate diagnosing and treatment planning is also investigated. Furthermore, this chapter provides a detailed summary of algorithms and frameworks such as Federated Learning, Blockchain Technology, and Edge-Fog-Cloud computing that collectively permit safe and efficient real-time healthcare solutions. Each of these technologies is illustrated through ECG anomaly, medical IoT security, and patient risk prediction use cases. The chapter also considers the modern developments in artificial intelligence approaches to data analysis in the form of Data Mining, Modeling and Optimization techniques in personalized medicine, and resources management. The value of this integrative approach is to transform the current healthcare model to secure, efficient and personalized one through novel computational models.