This paper presents a modular software design for the construction of computational modeling technology that will help implement precision medicine. In analogy to a common industrial strategy used for preventive maintenance of engineered products, medical digital twins are computational models of disease processes calibrated to individual patients using multiple heterogeneous data streams. They have the potential to help improve diagnosis, prognosis, and personalized treatment for a wide range of medical conditions. Their large-scale development relies on both mechanistic and data-driven techniques and requires the integration and ongoing update of multiple component models developed across many different laboratories. Distributed model building and integration requires an open-source modular software platform for the integration and simulation of models that is scalable and supports a decentralized, community-based model building process. This paper presents such a platform, including a case study in an animal model of a respiratory fungal infection.