  Prior research primarily examined differentially-private continual releases
against data streams, where entries were immutable after insertion. However,
most data is dynamic and housed in databases. Addressing this literature gap,
this article presents a methodology for achieving differential privacy for
continual releases in dynamic databases, where entries can be inserted,
modified, and deleted. A dynamic database is represented as a changelog,
allowing the application of differential privacy techniques for data streams to
dynamic databases. To ensure differential privacy in continual releases, this
article demonstrates the necessity of constraints on mutations in dynamic
databases and proposes two common constraints. Additionally, it explores the
differential privacy of two fundamental types of continual releases: Disjoint
Continual Releases (DCR) and Sliding-window Continual Releases (SWCR). The
article also highlights how DCR and SWCR can benefit from a hierarchical
algorithm for better privacy budget utilization. Furthermore, it reveals that
the changelog representation can be extended to dynamic entries, achieving
local differential privacy for continual releases. Lastly, the article
introduces a novel approach to implement continual release of randomized
responses.
