We calculated results for 2 reproduction number values, 31 and 16, which belong to a range that is high when compared with published estimates of the basic reproduction number of measles (R0
≈8–18) (1–4). This comparison indicates that our results are rather conservative with regard to how quickly the intervention should be implemented. However, it must be noted that our results apply to schools in Europe for which BVRs were average (>80%) before the outbreak (8
When we considered institutions with smaller populations than that considered in our study, timing for vaccination remained roughly the same. This finding is explained by the association between the time to react effectively and the generation interval of infection, which is the average time it will take for a newly infected person to infect someone else. The generation interval will depend mostly on the within-host disease development, as long as children have enough contacts to transmit the disease, even in schools with ≈300 children (25
We considered our contact structure to be homogeneous mixing. More intricate contact networks, such as those considering clustering in the different classrooms of the school, popularity of some children, and household contacts with siblings attending the same school, might better resemble reality. Some network structures, contact rates, and superspreading events can influence the speed and growth of an epidemic (29
). However, our baseline simulations had peak incidence during weeks 6–11 (16th and 84th percentiles, respectively), mode 7 weeks, for the R0
≈31 scenario; and weeks 6–14, mode 8 weeks, for the R0
≈16 scenario. These data are consistent with the real outbreak described by Wichmann et al. (27
), indicating that the rate of disease spread in our simulations was similar to that in the real outbreak.
At the moment of vaccination, a person might already be infected but not yet symptomatic or might become infected soon after vaccination, before immunity has had time to develop. We assume that in these cases the disease progresses in the same way it does in nonvaccinated persons. However, there is evidence that vaccinating during the incubation period might mitigate the symptoms of measles infection (30
). The vaccine might act as postexposure prophylaxis, potentially reducing the infectiousness of the vaccinated persons.
In many schools in Europe a BVR >80% can be found, but in communities with rather low BVRs (e.g., because of religious or philosophic beliefs), measles virus spreads much quicker. For example, in an outbreak originating in an anthroposophic community in Austria during 2008, with a BVR of 0.6%, of the 123 cases in the anthroposophic school of that community, 96% occurred during the first 4 weeks of the outbreak (31
), indicating that most cases were either second or third generation (the index case is considered the first generation). An outbreak-response vaccination campaign during such a rapidly spreading outbreak would be effective in a school setting only if implemented within 1 average generation interval (≈9 days) to avoid third-generation infection, which is logistically difficult and requires 100% compliance. However, because school outbreaks are often part of larger community outbreaks, vaccination activities focused on susceptible persons should be promoted in the broader community at any time to prevent further spread of the disease, independent from the time of a school outbreak.
In our study, we assumed 100% compliance to the vaccination strategy. But high compliance to a vaccination campaign cannot be expected in regions with low BVRs associated with religious or philosophical beliefs that are opposed to vaccination. The compliance needed for an intervention to be effective should ensure herd immunity (≈95% vaccinated children). Other complementary measures can be implemented to control measles outbreaks at schools when no vaccination compliance is expected. For example, a measure such as the temporary exclusion of students who lack documented vaccination or whose parents do not agree to vaccination of their children might have a limited effect on preventing further spread of measles by itself (20
). However, a combination of timely vaccination of all susceptible students at school who agree to be vaccinated and temporary exclusion of those who do not would be the most effective way to control a measles outbreak in a school.
In conclusion, we computed the possible outcomes of a measles outbreak in a school according to the vaccination delay, assuming that all potentially susceptible children in the school were vaccinated on the same day. We found that it is possible to reduce the number of cases during a measles outbreak in a school by applying a schoolwide vaccination strategy within a realistic time frame. Subsequently, because disease tends to spread in schools during the early stages of a city outbreak, reducing the effects of school outbreaks should help reduce the extent of the outbreak in the larger community. We also showed that BVRs that are high (>80%) but not high enough to achieve herd immunity (≈95%) keep the number of susceptible persons low, reduce the size of an outbreak, and reduce the speed at which the disease spreads, thereby increasing the time frame for mounting an effective intervention.