Implementing a vaccination campaign during an outbreak can effectively reduce the outbreak size.

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Assess measles vaccination and the prognosis of measles infection

Distinguish the maximum amount of time permissible to initiate an outbreak response vaccination in order to prevent a large outbreak of measles

Distinguish the maximum amount of time permissible to initiate an outbreak response vaccination in order to significantly affect the rate of measles infection at all

Analyze the peak incidence rates of measles infection during a school outbreak

Disclosures: Axel Antonio Bonačić-Marinović, PhD; Corien Swaan, MD; Ole Wichmann, MD; Jim van Steenbergen, MD, PhD; and Mirjam Kretzschmar, PhD, have disclosed no relevant financial relationships.

Despite high vaccination coverage in most European countries, large community outbreaks of measles do occur, normally clustered around schools and resulting from suboptimal vaccination coverage. To determine whether or when it is worth implementing outbreak-response vaccination campaigns in schools, we used stochastic outbreak models to reproduce a public school outbreak in Germany, where no vaccination campaign was implemented. We assumed 2 scenarios covering the baseline vaccination ratio range (91.3%–94.3%) estimated for that school and computed outbreaks assuming various vaccination delays. In one scenario, reacting (i.e., implementing outbreak-response vaccination campaigns) within 12–24 days avoided large outbreaks and reacting within 50 days reduced outbreak size. In the other scenario, reacting within 6–14 days avoided large outbreaks and reacting within 40 days reduced the outbreak size. These are realistic time frames for implementing school outbreak response vaccination campaigns. High baseline vaccination ratios extended the time needed for effective response.

Measles is a highly contagious disease that causes illness and death in developing and industrialized countries. Measles has an estimated basic reproduction number (R_{0}) range of 12–40 (

In 2002, the WHO Region of the Americas was declared free from endemic measles transmission, which was achieved by implementing immunization programs with very high vaccination coverage (>95%). This goal has not been achieved in the WHO European region, for which the target year for measles elimination was 2010. Measles is so highly contagious that the average vaccination coverage in Europe (80%–95%) (

The only means of protection against measles are prior infection or vaccination. Several studies have focused on the effectiveness of mass outbreak-response vaccination campaigns for controlling measles outbreaks in settings where incidence and morbidity and mortality rates are high. Although some studies suggest that mass outbreak-response vaccination campaigns will not stop measles epidemics because of the rapid spread of the disease (

A delay from detection of an outbreak to implementation of an outbreak-response vaccination campaign to onset of an effective immune response of those vaccinated is inevitable. Because measles is highly contagious, many children might become infected during that delay. Thus, whether vaccinating children against measles during a school outbreak would substantially affect the outcome of a newly forming epidemic is in doubt (

We based our stochastic model design on a combined compartmental and individual-based approach (

Schematic diagram of stochastic outbreak models to estimate the expected size of a measles outbreak in a school, depending on the delay between detection and implementation of a complete school outbreak-response vaccination campaign. Susceptible persons (susceptibles) become affected if they are infected and become vaccinated after vaccination is implemented. Vaccinated persons (vaccinated) can also be infected but with lower probability than susceptible persons. Those who become affected are followed individually, each with their own transmission and clinical time lines.

Model parameter | Notation | Value/distribution | Reference |
---|---|---|---|

Duration of incubation period (from distribution) | D_{inc} | Log normal (2.3,0.2); 7–14 d after infection, mode 10 d. | ( |

Duration of latent period (distribution) | D_{lat} | (D_{inc} − 4) + normal (0.7); latent period ends ≈4 d before symptom onset. | ( |

Duration of infectious period (from distribution) | D_{inf} | (D_{inc} + 4 − D_{lat}) + normal (0.7); infectious period ends ≈4 d after symptom onset. | ( |

Duration of symptomatic period (from distribution) | D_{symp} | D_{lat} + D_{inf} − Dinc; assumes that symptomatic period ends at same time as infectious period. | ( |

Duration of period to build up immunity after vaccination (from distribution) | D_{imm} | 13.2 + normal (3.0); approximates measles-specific IgM positivity rates of 2% and 61% after 1 and 2 weeks of vaccination, respectively. | ( |

Number of daily contacts per person (from distribution) | n_{cont} | 20 + NegBin (0.155,2.2). | ( |

Infection probability of a susceptible person after contact with an infectious person | P_{inf} | 0.12 in the R_{0}≈16 scenario; 0.2348 in the R_{0}≈31 scenario. | This article (Model Calibration) |

Vaccination effectiveness | VE_{S} | 0.9975. | ( |

Infection probability of a vaccinated person after contact with an infectious person | P_{inf,vac} | P_{inf} (1 − VE_{S} ); 3 × 10^{–4} in the R_{0}≈16 scenario; 5.869 × 10^{–4} in the R_{0}≈31 scenario. | This article (Vaccination) |

*NegBin, negative binomial probability distribution; R_{0}≈16, scenario in which basic reproduction number R_{0}≈16 is considered; R_{0}≈31, scenario in which basic reproduction number R_{0}≈31 is considered.

We used a compartmental approach to describe the part of the population not yet infected. We considered 2 subgroups—susceptible and vaccinated—to represent the nonvaccinated and vaccinated school populations, respectively, at the beginning of the outbreak. Susceptible persons were assumed to have been completely unexposed (naive) to measles virus and to have a high probability of becoming infected (P_{inf}) if they contacted an infectious person. Vaccinated persons were assumed to have acquired protection from measles virus by vaccination and to have a reduced probability of becoming infected (P_{inf,vac}>0) to account for an imperfect vaccine.

For susceptible (or eventually a vaccinated) persons who became infected, the model took an individual-based approach and followed each person from the time of infection until the end of the simulation. Persons who had had measles before the outbreak were included as affected but were already immune to infection from the beginning of the simulation. Each affected person had individual transmission and clinical time lines, depending on time since infection, which varied from one person to another.

From the moment a person became infected, and therefore affected, 2 parallel time lines were updated in 1-day steps. The time lines describe the disease history: transmission and clinical (

The transmission time line describes when the affected person became infectious, after a latent period of duration (D_{lat}), and when that person ceased to be infectious because the person recovered after the infectious period of duration (D_{inf}) had passed. Durations of these periods were generated randomly from their respective probability distributions (

In contrast, the clinical time line describes events that can actually be observed. This time line indicates the moment of the rash onset, after the incubation period (D_{inc}), and the moment when the affected person recovered from the disease, after the symptomatic period (D_{symp}) had passed. The values of these periods for each affected person are drawn from the probability distributions indicated in the Table. For simplicity, we assumed that the symptomatic period ended at the same time that the infectious period ended.

Persons who had been infected before the outbreak were considered recovered at the start of our simulations. That is, they were at the end of their disease time lines and did not contribute to the final size of the outbreak.

We assumed that every person in the school mixed with everybody, i.e., homogeneous mixing, and considered daily contact distribution as shown in the Table. Therefore, each day the number of contacts that an infectious affected person had (n_{cont}) was drawn from this distribution. From these contacts, the number of newly infected susceptible and vaccinated persons was computed according to the infection probabilities, P_{inf} and P_{inf,vac}, respectively.

The percentage of vaccinated persons at the beginning of the outbreak was determined by the BVR, and we assumed that vaccination-acquired protection does not wane with time. The high effectiveness of the measles vaccine (_{inf,vac} = (1-VE_{S})P_{inf}, where VE_{S} is the vaccine effectiveness value (_{imm}]; probability distribution is indicated in the Table) after the vaccination day and then become part of the vaccinated group.

Usually, persons with measles stay home while recovering from the disease. Therefore, we assumed that after disease symptoms developed (after the incubation period D_{inc}), infected persons stopped attending school. This absenteeism prevents further contact at school and further spread of the disease, even if the affected person remains infectious at home. For this study, we ignored the possibility of siblings attending the same school.

We calibrated our models by using data from a retrospective cohort study conducted at a public day school in Duisburg, Germany, where a large measles outbreak had occurred in 2006 (_{inf}) in our models to describe this situation. Assuming a BVR of 91.3%, calculated by Wichmann et al. (_{inf}) in our models so that the size distribution of large outbreaks from our simulations peaked at 55 cases. The calibrated P_{inf} value in combination with our assumed contact distribution (_{0}≈16, which is consistent with reported basic reproduction number estimations for measles (_{inf} value in combination with a BVR of 91.3% yielded roughly an effective reproduction number (R_{eff}) as follows: R_{eff}≈R_{0}[1−(BVR/100%)] = 1.4. In theory, if BVR is high enough that R_{eff} is <1, then 1 case generates on average <1 secondary case, leading to herd immunity effects and no large outbreaks (

In a later study, van Boven et al. (_{inf}) is needed in our models to reproduce the observed outbreak size, which translates to a higher basic reproduction number, R_{0}≈31, needed to produce an outbreak in a population with such a high BVR. The conditions in this scenario yield an R_{eff} of ≈1.8, indicating that our simulated outbreaks spread more quickly and had higher attack rates than in the less contagious case of R_{0}≈16 and R_{ef}≈1.4. To obtain equivalent outbreak sizes, the attack rate (percentage of affected susceptible persons) has to be higher in a population in which BVR is larger because the number of susceptible children is smaller.

_{0}≈16 and R_{0}≈31. The typical bimodal distribution predicted by stochastic models appears in both scenarios (_{0}≈31. The bimodal distribution arises because it is always possible that chance events will cause a new outbreak to die out before becoming large. We interpreted the local minimum in both distributions of _{0}≈16 model, 39% of the simulated outbreaks instances become large outbreaks, and in the R_{0}≈31 model, 64% of the instances become large.

Measles outbreak size histograms calculated with calibrated models. The y-axis indicates the number of model instances counted in their corresponding outbreak size histogram bin, indicated in the x-axis. The dotted line indicates the limit from which large and small outbreaks are defined. BVR, baseline vaccination ratio; R_{0}, reproduction number, R_{eff}, effective reproduction number.

_{0}≈16 model. Because of the stochastic nature of the model, as a result of chance events, some outbreaks died out before the intervention was implemented, as could happen in real life. To study the effect of the intervention, we considered only those outbreaks that were still developing at the moment of vaccination. The longer it took to implement the vaccination campaign, the more the outbreak size distributions shifted toward larger outbreaks. Outbreaks were expected to remain small (<20 infected children) if the vaccination delay was 12–24 days. Although the reaction must be quick to avoid an outbreak involving >20 children, a reaction as late as 50 days reduced the final size of large outbreaks in 95% of the simulations. With vaccination delays of

Distribution of measles outbreak sizes as function of vaccination delay for models with basic reproduction number (R_{0}) of ≈16 and baseline vaccination ratio (BVR) of 91.3% (effective reproduction number ≈1.4). We considered the outbreaks that were still ongoing at the day of implementation of the outbreak-response vaccination campaign and not those that had spontaneously died out earlier by chance. For every given vaccination delay, the squares indicate the most likely large outbreak size, and the thick solid line indicates the median outbreak size value. The thin solid lines indicate 25th and 75th percentiles, and the tiny dotted lines indicate 5th and 95th percentiles of the outbreak size distribution as a function of vaccination delay. The dashed line shows the outbreak size from the observed data, and the dotted line indicates the chosen limit to separate large and small outbreaks.

We also considered the scenario described by van Boven et al. (_{0}≈31 estimate on the same school outbreak with a high BVR (94.3%). The high R_{0} value of 31 implies that the infection is more contagious than that in our R_{0}≈16 model, leading to a higher effective reproduction number. _{0}≈16 model. However, because of the higher infectiousness of the disease, outbreaks spread more quickly than in the models with R_{0}≈16. This provided only a small time frame of 6–14 days to implement the vaccination campaign if the outbreak size was to be kept small (<20 persons). In 95% of the simulations, a vaccination campaign implemented as late as 40 days after start of the outbreak reduced the final size of the outbreak. There was almost no difference between implementing an outbreak-response campaign after ≈60 days and not implementing one at all.

Distribution of measles outbreak sizes as function of vaccination delay for models with basic reproduction number (R_{0}) of ≈31 and baseline vaccination ratio (BVR) of 94.3% (effective reproduction number ≈1.8). We considered the outbreaks that were still ongoing at the day of implementation of the outbreak-response vaccination campaign and not those that had spontaneously died out earlier by chance. For every given vaccination delay, the squares indicate the most likely large outbreak size, and the thick solid line indicates the median outbreak size value. The thin solid lines indicate 25th and 75th percentiles, and the tiny dotted lines indicate 5th and 95th percentiles of the outbreak size distribution as a function of vaccination delay. The dashed line shows the outbreak size from the observed data, and the dotted line indicates the chosen limit to separate large and small outbreaks.

From those outbreaks that did not die out before the vaccination campaign was implemented, we computed the percentage of those that would become large. This percentage can be interpreted as the probability that an outbreak will become large. The dependency of this percentage on the vaccination delay is shown in _{0} cases is considered. The large outbreak percentage was reduced to 31%–59% if the outbreak-response vaccination campaign was implemented with a delay of 28 days, and it was reduced further if the campaign was implemented earlier: 17%–42% with a 21-day delay, 7%–23% with a 14-day delay, and 1%–7% with a 7-day delay. Although the percentage of large outbreaks became increasingly larger as delay to vaccination became larger, later implementation of outbreak-response vaccination campaigns might still substantially reduce the size of large outbreaks (

Percentage of measles outbreaks that become large for the indicated models. We considered those outbreaks that are ongoing at the moment of implementation of the vaccination campaign, indicated by the vaccination delay in the x-axis. BVR, baseline vaccination ratio; R_{0}≈16, scenario in which basic reproduction number R_{0}≈16 is considered; R_{0}≈31, scenario in which basic reproduction number R_{0}≈31 is considered; R_{eff}, effective reproduction number.

To extend our study to different settings, we ran simulations in the same school setting and assumed various BVRs, the lowest being 80%, comparable to the current situation in Europe (_{0} developed more quickly under the same initial conditions and did not become large if the BVR was high enough to achieve herd immunity (>93.8% and >96.8% for R_{0}≈16 and R_{0}≈31, respectively). For lower BVRs, the final size was larger and outbreaks spread more quickly because of a larger effective reproduction number. Therefore, the time frame to react is smaller; e.g., if BVR = 80% and R_{0}≈16, a 1-week delay is already long enough to expect large outbreaks, but a reaction within 3–4 weeks might substantially reduce the outbreak size. Some outbreak sizes were larger than the number of nonvaccinated children in the population, which is explained by imperfect vaccine producing an effect similar to a lower BVR.

Measles outbreak size ranges as function of vaccination delay, for models with basic reproduction number R_{0}≈16 (A) and R_{0}≈31 (B) in the same school setting with various baseline vaccination ratios (BVRs). The ranges shown are between the 95th and 50th percentiles of the outbreak size distribution as a function of vaccination delay and are calculated for each BVR indicated.

We considered a school of 1,250 children, but there are many smaller institutions. In a simulation for a school of 500 children, while conserving the proportions of children with a history of measles and BVR, the boundary separating large and small outbreaks changed to 13 persons. However, results regarding the timing of vaccination remained approximately the same.

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 (R_{0}≈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 (

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 (

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 (_{0}≈31 scenario; and weeks 6–14, mode 8 weeks, for the R_{0}≈16 scenario. These data are consistent with the real outbreak described by Wichmann et al. (

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 (

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 (

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 (

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.

We thank Peter Teunis, Michiel van Boven, Susan Hahné, and Jacco Wallinga for useful discussions and guidance, and we thank all local and state public health authority staff and Robert Koch Institute staff who were involved in the outbreak investigation and collected the relevant data.

Dr Bonačić Marinović works as a researcher at the Centre for Infectious Disease Control Netherlands, National Institute for Public Health and the Environment (RIVM), Bilthoven, and the Julius Centre for Health Sciences & Primary Care, University Medical Centre Utrecht. His main research interests involve modeling infectious diseases.

To obtain credit, you should first read the journal article. After reading the article, you should be able to answer the following, related, multiple-choice questions. To complete the questions (with a minimum 70% passing score) and earn continuing medical education (CME) credit, please go to

A. The estimated basic reproduction number R_{0} for measles is in the range of 12 to 40

B. The case-fatality rate in industrialized countries is approximately 10%

C. Vaccination rates in Europe generally exceed 95%

D. Vaccinating during the incubation period of measles has no salutary effect

_{0} for measles is actually 16. Based on the results of the current study, what is the maximum amount of time that can pass before an outbreak response vaccination (ORV) is initiated in order to limit measles infection to no more than 20 children?

A. 2–4 days

B. 6–10 days

C. 11–15 days

D. 12–24 days

A. 25 days

B. 35 days

C. 50 days

D. 65 days

A. 1 to 3 weeks

B. 4 to 7 weeks

C. 6 to 14 weeks

D. 20 to 25 weeks

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