The hybrid cloud model is the most suitable for the scenario described. It allows an organization to maintain a private cloud (or on-premises infrastructure) for sensitive, critical, or regulated data and application workloads, ensuring privacy and control, while also using public cloud services for less sensitive tasks. This model combines the benefits of both public and private clouds, providing the flexibility to use each where it makes the most sense, maintaining compliance with regulatory requirements, and scaling resources as needed.

The public cloud wouldn't offer the same levels of control and isolation required for sensitive healthcare data, potentially not meeting strict regulatory compliance. The private cloud alone, while providing control and security, lacks the flexibility and cost-effectiveness of the public cloud for elastic scaling. Multi-cloud involves using multiple cloud computing services in a single architecture, which may be more complex than necessary for this scenario and does not inherently provide the tight integration between public and private resources that a hybrid model does.