A Measles Epidemic Threshold in a Highly Vaccinated Population

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Abstract
Mass vaccination against measles has successfully lowered the incidence of the disease and has changed the epidemic pattern from a roughly biennial cycle to an irregular sequence of outbreaks. A possible explanation for this sequence of outbreaks is that the vaccinated population is protected by solid herd immunity. If so, we would expect to see the fraction of susceptible individuals remaining below an epidemic threshold. An alternative explanation is the occurrence of occasional localised lapses in herd immunity that allow for major outbreaks in areas with a low vaccine coverage. In that case, we would expect the fraction of susceptible individuals to exceed an epidemic threshold before outbreaks occur. These two explanations for the irregular sequence of measles outbreaks can be tested against observations of both the fraction of susceptible individuals and infection attack rates. We have estimated both the fraction of susceptible individuals at the start of each epidemic year and the infection attack rates for each epidemic year in the Netherlands over a 28-y period. During this period the vaccine coverage averaged 93%, and there was no sustained measles transmission. Several measles outbreaks occurred in communities with low vaccine coverage, and these ended without intervention. We show that there is a clear threshold value for the fraction of susceptible individuals, below which only minor outbreaks occurred, and above which both minor and major outbreaks occurred. A precise, quantitative relationship exists between the fraction of susceptible individuals in excess of this threshold and the infection attack rate during the major outbreaks. In populations with a high but heterogeneous vaccine coverage, measles transmission can be interrupted without establishing solid herd immunity. When infection is reintroduced, a major outbreak can occur in the communities with low vaccine coverage. During such a major outbreak, each additional susceptible individual in excess of the threshold is associated with almost two additional infections. This quantitative relationship offers potential for anticipating both the likelihood and size of future major outbreaks when measles transmission has been interrupted.