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The concept of continuity in medicine is fundamental and it refers to the delivery of medical care to a patient by a care provider in an uninterrupted and coordinated manner and in accordance with the medical care needs of the patient. This paper models continuity for a representative staff model health maintenance organization (HMO) clinic in suburban Arizona and simulates patient visits that are stochastically generated through utilizing representative numbers of patient visits and care providers. It focuses on individual-based continuity delivered by a primary care provider, i.e., a general practitioner. In the simulation, the visit patterns of patients, their ages, and the length of the interaction episodes are synthesized stochastically. The distributions reflect both the patient visit profile, by age, inherent in the 90000+ patient electronic records collected at the CIGNA HMO clinic at Chandler, AZ, over a three-year period, and the population distribution inherent in the CIGNA records. This paper proposes a new definition of continuity, fundamental continuity of care index (FCCI), and argues that, fundamentally, a primary care provider's depth of understanding of the patient is directly proportional to the total length of interaction between the patient and the primary care provider.