Effective disease surveillance systems require large-scale epidemiological data to improve health outcomes and quality of care for the general population. As data may be limited within a single site, multi-site data (e.g., from a number of local/regional health systems) need to be considered. Leveraging distributed data across multiple sites for epidemiological analysis poses significant challenges. Due to the sensitive nature of epidemiological data, it is imperative to design distributed solutions that provide strong privacy protections. Current privacy solutions often assume a central site, which is responsible for aggregating the distributed data and applying privacy protection before sharing the results (e.g., aggregation via secure primitives and differential privacy for sharing aggregate results). However, identifying such a central site may be difficult in practice and relying on a central site may introduce potential vulnerabilities (e.g., single point of failure). Furthermore, to support clinical interventions and inform policy decisions in a timely manner, epidemiological analysis need to reflect dynamic changes in the data. Yet, existing distributed privacy-protecting approaches were largely designed for static data (e.g., one-time data sharing) and cannot fulfill dynamic data requirements. In this work, we propose a privacy-protecting approach that supports the sharing of dynamic epidemiological analysis and provides strong privacy protection in a decentralized manner. We apply our solution in continuous survival analysis using the Kaplan-Meier estimation model while providing differential privacy protection. Our evaluations on a real dataset containing COVID-19 cases show that our method provides highly usable results.