Amelia Elizabeth Dyer
Born Amelia Hobley in 1837, she was one of the most prolific and least remembered serial killers in history, She was involved in a Victorian practice known as “baby farming.” Over a period of 30 years, as a trained nurse, she offered to adopt or place unwanted children with other families for a fee. Except, those kids never made it to a loving family; they were strangled and dumped in the Thames river.
She was arrested a few times for neglect, or placed in a mental hospital, but she always made it out and continued with her activities. By the time she was arrested, it was estimated that she had killed over 400 babies.
You forgot Harold Shipman, probably the world's most prolific serial killer and a doctor.