Look at "The Questionable Contribution of Medical Measures to the Decline of Mortality in the United States in the Twentieth Century", by Mckinlay and McKinley (1977). I know it's an old paper, but it has some fascinating and, to me, very persuasive time series. Those plots show mortality from various infectious diseases over the 20th century.
Example: death rates (per 1000) from scarlet fever dropped from 0.1 in 1900 to effectively 0 in 1940. There is NO VACCINE for scarlet fever.
Example: death rates from measles (lately very much in the news) dropped from 0.12 in 1900 to 0 in 1960 (a vaccine for measles was introduced in 1960).
A similar trend exists for many other infectious diseases: huge drops in mortality PRECEDE the introduction of vaccines or antibiotics for the disease. Surely we can't credit vaccines with such a drop in death rates. I don't see how anybody could come to such a conclusion.