A. Korobeinikova, P.K. Mainia, W.J. Walker. Estimation of effective vaccination rate: pertussis in New Zealand as a case study. Journal of Theoretical Biology 224 (2003) 269-275

In some cases vaccination is unreliable. For example vaccination against pertussis has comparatively high level of primary and secondary failures. To evaluate efficiency of vaccination we introduce the idea of effective vaccination rate and suggest an approach to estimate it. We consider pertussis in New Zealand as a case study. The results indicate that the level of immunity failure for pertussis is considerably higher than was anticipated.

Some other quotes from this paper:

Vaccination does not necessarily imply life-long immunity for a vaccinated person. In some cases, vaccination is ineffective and fails to provide immunity at all (the so-called "primary failure"); sometimes immunity acquired through vaccination wanes and does not provide life-long protection ("secondary failure"). For example, the New Zealand statistical data show that in the case of measles, when vaccination is known to be reliable, about one-third of those infected, whose vaccination history is known, received one dose, and about 2% received two doses of the vaccine (NZ ESR, 1997). This is especially relevant to pertussis. The vaccine against pertussis is known to be unreliable: the immunity acquired due to vaccination wanes over time (Cullen and Walker, 1997). This leads to the question of how effective is the vaccination in reality.

And at the end, in the discussion:

The obtained figures indicate that in New Zealand the effective vaccination rate against pertussis is lower than 50%, and perhaps even as low as 33% of the population. These figures contradict the medical statistics which claim that more than 80% of the newborns in New Zealand are vaccinated against pertussis (Turner et al., 2000). This contradiction is due to the mentioned unreliability of the available vaccine. The fact that the fraction of immune population obtained here is considerably lower than the fraction of vaccinated population implies a high level of vaccination failure. We believe that we can safely conclude that under the current conditions (with the present vaccine and the current vaccination practice) the effective vaccination rate against pertussis in New Zealand is considerably lower than is expected. Based on the present data it is perhaps lower than 50% of the population.

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