True, and so-called herd immunity requires 90% inoculated. Even 80% has resulted in fatal measles outbreaks.
This is an over-simplification. So-called "herd immunity" is just a common or lay term for the likelihood that the pathogen will become extinct within a given host popn. or (earlier) only infect immune members of the host popn. Worse, there are a number of "definitions" of it floating around. The best ones are a particular threshold proportion of immune individuals that should lead to a decline in incidence of infection or a pattern of immunity that should protect a population from invasion of a new infection.
A very simple model is that incidence will decline at a transition point given by 1
–1/
Ro - or maybe better, Rt. A simple analogy is to the critical point at which a nuclear chain reaction becomes self sustaining. Pathogen growth is almost exactly that: a chain reaction in an Island Biology context (hosts are the islands, and the pathogen will destroy the island and become extinct itself unless it can disperse to a new island, another host before then).
The
critical thing to realize is that R is not a constant but is a function of may other factors, e.g.
- nature of the immunity induced by the vaccine (not just the strength)
- mixing patterns in host popns.
- infection transmission in host popns.
- distribution of the vaccine and immunity in host popns.
The problem of 'freeloaders' can be a big one - Anti-Vaxers are one such group.
One of the biggest modelling problems is that host popns. are heterogeneous, so have to be divided into sub-groups with a complex of infection interactions among them. Once you have that sort of model, you then have to populate it with hard to gather and and ever-changing data...
I dunno if that made much sense, as it isn't too close to the education of the EE popn. but suffice it to say that you can't just grab a %Vaccination rate for one disease and use it for another, not can you do the same thing for one country or culture and apply it to another.