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During the COVID-19 pandemic, machine learning models developed in high-resource hospitals achieved strong performance in predicting outcomes such as mortality, ICU admission, and mechanical ventilation, but their accuracy often degrades when applied to low-resource settings due to differences in patient populations, disease severity, clinical practices, and documentation quality. Low-resource hospitals also face limited patient volumes, incomplete labeled data, and strict privacy regulations (e.g., HIPAA and GDPR), which prevent centralized data sharing and hinder independent model development, creating a barrier to equitable AI deployment. To address this, we propose a federated transfer learning framework that adapts prognostic models from high-resource to low-resource hospitals without exchanging patient-level data. The approach transfers only aggregate statistics (e.g., feature means, variances, class-conditional distributions, and correlations) via a secure lightweight protocol, enabling target hospitals to align feature distributions using domain adaptation techniques and fine-tune models on small local datasets. The framework includes source model training, statistical aggregation, secure transmission, and target-side adaptation modules, ensuring no raw patient data leaves any institution. By relying on aggregate statistics, the method preserves privacy while mitigating domain shift and maintaining clinical utility across diverse healthcare environments. This scalable and privacy-preserving framework supports broader deployment of COVID-19 predictive models and provides a generalizable strategy for other medical conditions with heterogeneous healthcare settings.