Each month, Dr. Richard Dupee and his office staff work their way through a sizeable list of patients. They put out emails and calls to men in their 40s with slightly high blood pressure that warrants re-checking. They track down 55-year-olds who are avoiding colonoscopies, diabetics who require eye exams, and patients with chronic lung disease who need breathing tests. “You bring in every one of your patients and you watch them like a hawk,’’ said Dupee, an internist and geriatrician in Wellesley. Dupee, 66, is an early adopter of a new strategy for providing medical care that is expected to expand rapidly throughout Massachusetts, and that promises to transform the relationship between primary care doctors and their patients.