The Fog Comuting refers to a distributed hardware and application infrastructure that offers computing, storage and networking services between terminals and traditional Cloud servers. It has the advantage of reducing service latency and improving perceived quality, as well as the benefit of total data distribution. However, the segmentation, distribution, and adaptive deployment of features on this set of devices, ranging from IoT to Cloud, pose major challenges due to the heterogeneity, hierarchical structure, and very large scale infrastructure of Fog architecture. The present work fits into this new paradigm ("Fog Computing") and proposes a generic formal model specifying a Fog architecture, consisting of a set of secure Fog nodes that act both as filters to reduce the amount of data sent to the Cloud, and as processing units close to the data collected. Besides, the multi-level collaboration requirements (IoT, Fog and Cloud), generating a new set of security issues related to identity management and resource access management, are also considered by the proposed formal model: CA-BRS (Control Agents BRS), combining agents and BRS (Bigraphical Reactive Systems). The execution and analysis of this model through the BigraphER tool made it possible to deduce important conclusions.