The best example
A very noteworthy study was published in 2013, looking at baboons, which are susceptible and manifest whooping cough like humans do. In the study by Warfel, baboons who were either vaccinated or not vaccinated were later exposed to pertussis bacteria, something that cannot be done experimentally in humans (due to ethical considerations), but which yields very important data. Expectedly, the baboons that had never been infected got the cough and remained colonized with bacteria for a maximum of 38 days. Baboons that were previously vaccinated and immune vaccine-style, became colonized upon later exposure for a longer time than the naïve baboons; 42 days. However unvaccinated baboons that recovered naturally and were later exposed to the bacteria did not become colonized at all – zero days.
So, who is providing better herd immunity in the face of bacterial exposure? Vaccinated individuals who presume they are immune, yet remain asymptomatically colonized for 42 days spreading bacteria? Unvaccinated kids who get infected and remain colonized for 38 days? Or the naturally convalesced who are not able to be colonized and therefore do not spread bacteria at all upon re-exposure? Better still: natural convalescence makes for decades longer, solid immunity than vaccination.
http://www.pnas.org/content/111/2/787.abstract
You should read the article you're referencing. They're comparing two different types of vaccines and showing that an older one works better. You're cherry picking from the vaccine that didn't perform as well. The paper itself demonstrates that both vaccines have benefits and concludes with a pro-vaccine sentiment:
Benefits who?
Paul Offit ?
When something happens to you it is all risk no benefits .
Truth is an experience