In India, hospitals have existed from ancient times. Even in 6th century BC, during the time of Buddha, there were a number of the hospitals to look after the handicapped and the poor. The outstanding hospitals in India at that time were those built by King Ashoka (273–232 BC). Books written by Arabian and European travellers (around AD 600) reveal that the study of medicine in India was in its bloom. The zeal of the native vaidyas for the investigation of the Indian flora slackened for want of encouragement. The invasion of foreigners in the 10 th century AD brought with them their own physicians called Hakims.
(PDF) Historical Development of Health Care in India (researchgate.net)
Dr. Kapoor, in the first reply to the query, focuses on the development of health care in India. I am not aware that there is a general pattern to the development of health systems, but perhaps one would be discernable if there were a scholarly study of the development of health systems in multiple countries. The key description of the development of the medical profession and health care system in the United States is Paul Starr's 1983 book, "The Social Transformation of American Medicine: The Rise of a Sovereign Profession and the Making of a Vast Industry."
Sri Lanka has evidences of an ancient buddhist hospital belonging to 853-857 AD in Mihinthale and considered as the oldest hospital in the world. Sri Lanka inherited most of the socio cultural practices from the India so the evaluation should have happened there.