Reddit reviews A History of Public Health

I have two recommendations. One I've read, and the other I have on my list to read--but both seem to be what you're looking for.

My recommendation: The Sanitarians: A History of American Public Health by John Duffy. This book begins in colonial America and goes into the 1980s. Its strength is in the historical analysis of the American hygiene movement.

On my reading list: A History of Public Health by George Rosen. Johns Hopkins publishes this and they seem to keep it in print by coming out with an update every few years with some extra content. This was first written in the late 1950s. It starts with a history from Greek and Roman times, and then summarizes various epochs: 500-1500, 1500-1750, 1750-1830, 1830-1875, and 1875-1950.