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. 2015 Oct 20;5:15468. doi: 10.1038/srep15468

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(a) Variation of the vaccine coverage. (b) Variation of the basic reproductive number. (c) Variation of the relative hazard of re-infection. (1) Low prevalence regardless presence of vaccination. (2) High prevalence with no vaccination whereas prevalence is still low in presence of vaccination. (3) High prevalence regardless presence of vaccination. (d) Variation of the relative infectiousness for vaccinated individuals. (a,b) The vertical dashed lines indicate a threshold in the parameter value after/before which a vaccination program would be totally effective (i.e. herd immunity). Direct effectiveness is not measurable in such settings, as the attack rate in vaccinated and unvaccinated individuals is zero.