The current absence of smallpox.

Really? We have over 200 years of vaccine use in public health programmes to control contagious disease. The most effective medical treatment humanity has ever devised. That has completely eliminated some of the most transmissible and debilitating diseases on the planet. Go and read a book on the subject, it's not like it's secret arcane knowledge. Reducing transmissibility is a basic (and bloody obvious) consequence of acquired immunity. If a vaccinated individual is reinfected, then compared to an unvaccinated individual the time to eliminate the virus is greatly reduced and the window of transmissibility is greatly reduced.