Herd immunity can be achieved via survival of enough of the population or induced immunity via inoculation with a weakened strain, a close variant or another means of causing antibodies.
Smallpox was eradicated with herd immunity by an inoculation that was only 95% effective in inducing antibodies in the human host. Smallpox was not eradicated with natural survival herd immunity and never would have been ONLY induced immunity via inoculation eradicated smallpox. Pfizer and moderna both have data to support 95% effectiveness this is high enough for eradication just like smallpox.
I gave the old scientific definition which is when the majority of people are surviving a disease.
Otherwise, how did humanity survive all the illnesses from the beginning of time to the invention of vaccines?
It is the immune systems of the survivable which determine herd immunity, not vaccinations.
I am doing some research for a Big 10 University I work with. When did we achieve herd immunity for the Flu, RSV, Swine Flu, Rhinovirus, other coronaviruses?