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Public health emergencies reveal critical weaknesses in healthcare supply chains, especially when PPE demand outpaces procurement and distribution capacity, making predictive analytics an important tool for forecasting demand and improving allocation during crises. This systematic review evaluates predictive analytics models for PPE demand forecasting and distribution optimization during public health emergencies, focusing on model types, data sources, validation approaches, performance metrics, equity considerations, and implementation readiness. Following PRISMA 2020 guidelines, searches were conducted in PubMed, Web of Science, Scopus, IEEE Xplore, and Google Scholar for studies published between 2017 and 2025, yielding 2,847 records, of which 35 met inclusion criteria. Included studies comprised time series and statistical models (34%), machine learning and hybrid approaches (29%), optimization methods (26%), and simulation or digital twin frameworks (11%), with limited evidence of real-world deployment. Overall, findings indicate that predictive analytics can enhance PPE supply chain resilience by improving demand forecasting, allocation decisions, and scenario testing, but widespread adoption is limited by poor data interoperability, insufficient prospective validation, weak equity integration, and limited operational integration into healthcare decision systems.