How robust is a healthcare system? How does a patient navigate the system and what is the cost (e.g., number of medical services required or number of times the medical provider had to be changed to get access to the required medical services) incurred from the first symptoms to getting cured? How will it fare in the wake to a sudden epidemic or a disaster? How are all of these affected by administrative decisions such as allocating/diminishing resources in various areas or centralising services? These are the questions motivating our study on a formal prototype model for a healthcare system. We propose that a healthcare system can be understood as a distributed system with independent nodes (healthcare providers) computing according to their own resources and constraints, with tasks (patient needs) being allocated between the nodes. The questions about the healthcare system become in this context questions about resource availability and distribution between the nodes. We construct in this paper an Event-B model capturing the basic functionality of a simplified healthcare system: patients with different types of medical needs being allocated to suitable medical providers, and navigating between different providers for their turn for multi-step treatments.