This document introduces ADPS (Asynchronous Distributed Publish Subscribe), a PubSub-based communication model tailored for a hierarchical architecture distributed on Edge, Fog, and Cloud layers. The primary challenge addressed by this model is establishing runtime connections between subscribers and data providers, enabling communication across various segments. ADPS is implemented within a Smart Cities healthcare application, monitoring vital statistics via IoT devices. Furthermore, this work will cover the specifications of message formats, topic definitions, message delivery reliability and latency effects, broker configurations, control data exchange among nodes, and the dynamic behaviour of topology due to user movement and structural changes with node additions at the Edge and Fog levels. Test results from the model’s most demanding scenarios showed latency variations of approximately 200ms, 300ms, and 400ms with quality of service levels 0, 1, and 2 from the initial Fog node to the Cloud.