The concept of continuity in medicine refers to the delivery of care in an uninterrupted and coordinated manner and in accordance with the patient's medical needs. Many diseases and symptoms require serial observation and treatment over long periods and are interwoven with the patient's personal and social circumstances. We believe that the depth of a primary care provider's understanding of a patient is directly proportional to the total length of interaction between the patient and provider. We have reviewed the published studies in this area, and modeled continuity of care in an HMO clinic. The patients' ages, their visiting patterns, and the Length of their interactions with their doctors were synthesized stochastically. We now propose a new way of defining continuity of care, the Fundamental Continuity of Care Index (FCCI), and recommend its use. Hospitals, insurance companies, and governments should be aware of the benefits of continuity, and all physicians should commit themselves to longitudinal care for their patients.