Which model is the hospital utilizing when seeking assistance from other organizations after a sudden increase in patients with an uncommon illness?

The correct answer is the open systems model, which effectively describes the hospital's approach as it responds to a sudden increase in patients with an uncommon illness by seeking assistance from other organizations. In healthcare, the open systems model emphasizes the importance of interaction and exchange with external environments, recognizing that hospitals do not exist in isolation.

By collaborating and seeking resources or support from other organizations, the hospital acknowledges that its operational and clinical effectiveness is enhanced by engaging with external entities. This model allows for adaptability and responsiveness to changing patient needs and external pressures, which is critical in public health situations, such as the emergence of an uncommon illness.

This approach contrasts with the static systems model, which does not accommodate changes or input from outside influences, and the closed systems model, which is characterized by minimal interaction with external environments. The network systems model also represents a collaboration but is usually more structured around formal organizations or partnerships, rather than the immediate and flexible response illustrated in this scenario.

Thus, the open systems model underscores the hospital's ability to leverage external resources and knowledge to manage sudden health challenges effectively.