Chen et al, Measles antibody: reevaluation of protective titers http://www.ncbi.nlm.nih.gov/pubmed/2230231
reported on data from a measles outbreak that came just after a school blood drive. So they had before and after titer information on the students. They observed that 7 out of 8 donors with titers below 120 got clinical measles, compared with none having titer above 120. So a titer of 120 appears to protect against getting clinical measles. However, 70% of donors with titers between 120 and 1050 reported symptoms without getting the rash, as did 30% of donors with titers above 1050, and about 70% of patients in the 120-1050 group
also had their titers go up by a factor of more than 4, indicating that they had had a measles virus infection, even though short of clinical measles.

So the conclusion: below 120, vulnerable to measles. Above 120, won’t get clinical measles, but may get ill without rash and become contagious for measles. Below 1050, 70% chance of getting ill and becoming contagious for measles. Above 1050, less than 30%.

Le Baron et al, Persistence of measles antibodies after 2 doses of measles vaccine in a postelimination environment
http://archpedi.jamanetwork.com/article.aspx?articleid=569784
studied how long titers persist in kids after their last booster. The results are plain in their Figure 3. They report that around 95% of recipients of the MMR have a titer over the 120 that Chen et al predict should prevent one from getting clinical measles for at least 10 years. (After that the percentage vulnerable starts rising rapidly.) That’s the good news.

The bad news is, they report that 2 years after their last booster, more than a third of kids will have titers below 1050, the region where, according to Chen et al, such kids will have a 70% chance of becoming ill and contagious if exposed, although they won’t show the rash. And 30% of kids with titers not far above that, and there are many of those, may also become ill and contagious. As each year passes from the MMR, still more kids fall into the camp vulnerable to illness and contagion, although not yet clinical measles. In a fully vaccinated population, even if most people are protected from clinical measles, most will be subject to infection by and transmission of measles virus.

This is why, I expect, you see constant epidemics in near 100% vaccinated populations, and herd immunity is a marketing slogan of the vaccine industry. For example, New York State boasts a 97% compliance rate for MMR in kindergarten http://www.cdc.gov/mmwr/preview/mmwrhtml/mm6133a2.htm .
Yet they have measles outbreaks every year or two, including a measles outbreak starting with a fully vaccinated index case http://news.sciencemag.org/health/2014/04/measles-outbreak-traced-fully-vaccinated-patient-first-time
and a measles outbreak with 90% of the patients vaccinated http://www.thedailysheeple.com/new-york-measles-outbreak-90-vaccinated_032014.

In fact, it seems very likely that the pool of vaccinated carriers may well be keeping measles from being eradicated. As we saw in the NY case (although she apparently had a rash), a vaccinated carrier may not recognize they have measles or may not be quarantined, preventing the disease from being eradicated. Measles may travel from vaccinee to vaccinee, not getting the characteristic rash or being recognized, until finally it lights into an unvaccinated individual or one whose titer has faded below 120, and is declared measles.
If we persist in vaccinating, the disease may never go away, whereas it might well be that if we simply stopped vaccinating, the disease would vanish from the means that have likely eradicated most of the other diseases that have gone away: quarantine and better nutrition.

Update: There’s other evidence on this. Maybe I’ll post on it later. For example, vaccinated baboons (but not naturally immune baboons) when exposed to pertussis carried the virus and could spread it for 35 days. Seemingly, as titers fade, the problems of original antigenic sin may mean the carriers take very long times to clear the virus if exposed.
http://www.scientificamerican.com/article/baboon-study-reveals-new-shortcoming-of-pertussis-vaccine/?utm_source=twitterfeed&utm_medium=twitter

For which diseases do we see more continuing outbreaks:
Typhoid, Scarlet Fever, Bubonic Plague, Scurvy — all once major killers, hardly anybody in the population vaccinated against any of them, or
Measles, Mumps, Chicken Pox, Whooping Cough– nearly 100% vaccinated population, potentially providing a population of virus carriers.

Note added, found a more recent paper that confirms Le Baron on a larger group. According to this http://www.ncbi.nlm.nih.gov/pubmed/21539880
only 23% of people have a PRMN titer of over 1050, 7.4 years after their last MMR booster

Note added: New paper indicates pertussis is spreading through asymptomatic transmission of vaxed individuals.
http://www.biomedcentral.com/1741-7015/13/146