Healthcare applications with the Internet of Things (IoT) are often safety-critical, thus, require extensive testing. Such applications are often connected to smart medical devices from various vendors. System-level testing of such applications requires test infrastructures physically integrating medical devices, which is time and monetary-wise expensive. Moreover, applications continuously evolve, e.g., introducing new devices and users and updating software. Nevertheless, a test infrastructure enabling testing with a few devices is insufficient for testing healthcare IoT systems, hence compromising their dependability. In this paper, we propose a model-based approach for the creation and operation of digital twins (DTs) of medicine dispensers as a replacement for physical devices to support the automated testing of IoT applications at scale. We evaluate our approach with an industrial IoT system with medicine dispensers in the context of Oslo City and its industrial partners, providing healthcare services to its residents. We study the fidelity of DTs in terms of their functional similarities with their physical counterparts: medicine dispensers. Results show that the DTs behave more than 92% similar to the physical medicine dispensers, providing a faithful replacement for the dispenser.