Home Plan For Duke Plan for Duke The 2021 Open Enrollment Season Has Ended View Our Accepted Health Insurance Plans Starting on January 1, 2021, Duke will begin accepting Bright Health and Cigna Connect Individual Family Plan insurance plans. View our list of accepted insurance plans. Visit Healthcare.gov for more information. Medicare Open Enrollment Open enrollment for Medicare ran from October 15 through December 7, 2020. Learn more about Medicare Advantage plans that have Duke Health doctors and locations in their networks.