Medical devices and related patient management systems and parameter modeling methods are provided. An exemplary method involves obtaining, by a computing device, historical measurements of a condition in a body of the patient previously provided by a sensing device, obtaining, by the computing device, historical operational context information associated with preceding operation of one or more of an infusion device and the sensing device, obtaining, by the computing device, historical values for a parameter from one or more of the infusion device and the sensing device, determining, by the computing device a patient-specific model of the parameter based on relationships between the historical measurements, the historical operational context information and the historical values, and providing, by the computing device via a network, the patient-specific model to one of the infusion device, the sensing device or a client device.