Behind the Model: Interactive Measles Outbreak Simulator

At a glance

We developed an interactive simulator for public health decision-makers to explore the potential impact of three key public health interventions—isolation, quarantine, and vaccination—on measles outbreaks. This simulator demonstrates that combining interventions early is the best way to reduce measles infections, particularly when baseline immunity is low.

Why are we modeling measles in communities?

Measles is one of the most contagious diseases. The risk for widespread measles in the United States remains low due to historically robust U.S. immunization, as well as monitoring programs and outbreak response capacity supported by federal, state, tribal, local, and territorial health partners. However, every year, measles cases occur in the United States due to unvaccinated travelers who get measles while they are in other countries. Outbreaks also occur when measles spreads in under-vaccinated communities. Anyone who is exposed to measles and not protected is at risk.

CDC developed a compartmental mathematical model of measles transmission to illustrate the potential impact of public health interventions on the magnitude and timing of measles outbreaks following the introduction of measles into a single community. The model incorporates the following public health measures:

  • Isolation, separating people who have symptoms of measles;
  • Quarantine, separating people who have known exposure to measles and no evidence of protection (e.g. vaccination or confirmed prior infection) but do not have symptoms; and
  • Vaccination for those who are eligible but not yet vaccinated against measles.

A summary of the model results showing how public health interventions may prevent or slow the spread of measles in communities is available for download and is explained in detail below.

Click below to view the simulator

How does the simulator work?

We developed an interactive model that public health decision-makers can use to explore the impact of these public health measures in their own communities following the introduction of measles. This model simulates an outbreak in an individual community. Users can input the number of people and the overall immunity in the population to reflect the characteristics of a specific community. This simulator is meant to be illustrative when used at the beginning of an outbreak. However, the output of this simulator is not a forecast of measles infections for any community.

The interactive simulator compares two scenarios for the same population: one with public health interventions and one without. In the interventions scenario, the three interventions—isolation, quarantine, and vaccination—can be turned on and off, and layered on top of one another. The start and end times for each intervention can be specified. For isolation and quarantine, population-level adherence can also be modified. For vaccination, the percentage of susceptible (i.e., non-immune) individuals vaccinated can be specified. Because the model is stochastic, simulations using the same parameters can yield different epidemic outcomes. We therefore run 100 individual simulations to produce a range of possible outcomes and use these simulations to estimate outcome uncertainty for each parameter set.

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A screenshot of the output plot generated by the Measles Outbreak Simulator.
Figure 1. Example output from the interactive Measles Outbreak Simulator. Each thin line represents an individual simulation of the model. All simulations within a given scenario (i.e., shown with the same color) are run under the same set of parameters, specified in the left-side panel, with default values and ranges based on the literature. Differences between each individual simulation (i.e., in the individual lines) are due to random variation (stochasticity) in the probability of transmission given contact. Bolded lines show the simulation closest to the median time of the outbreak peak across all epidemic trajectories for each scenario.

The interactive simulator produces a visualization of the epidemic curve (Figure 1) and a table summarizing the results, including median total infections and hospitalizations and the 95% credible intervals, and the relative difference (as a percent) between the no-interventions and interventions scenarios.

Key Simulator Results

What does the model show about controlling measles outbreaks?

The model demonstrates that combining interventions is the most effective way to reduce measles infections and hospitalizations, particularly when baseline immunity is low (Figure 2, Appendix Table 1). In addition, timely implementation of these interventions is key for effectively reducing infections and hospitalizations (Appendix Figure 1).

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Plot showing the impact of different public health interventions on the cumulative number of measles infections in a community.
Figure 2. Cumulative measles infections over one year following introduction of five measles infections into a community of 15,000 people, for different levels of baseline immunity. For each immunity level and scenario, isolation and quarantine adherence are set to 50%; vaccination uptake is set to 50% among those who are eligible and takes place over 21 days. Here, a randomly selected subset of 20 simulations of the model is displayed for each intervention scenario, with the simulation corresponding to the median time of the outbreak peak in bold. Parameter settings for these results can be found in Appendix Table 2 and in the Methods, below, under Model Inputs.

The reduction in measles infections by each intervention or combination of interventions depends on the baseline immunity in the community (including immunity both through past vaccination and previous infection) (Figure 2, Appendix Table 1). When baseline immunity is lower (80% or 85%), each additional intervention substantially reduces the magnitude of the outbreak. When baseline immunity is 90%, isolation alone reduces the outbreak size by 57%, and implementing both isolation and quarantine reduces the outbreak size by 97%. When baseline immunity is high (95%), very few additional infections occur after measles introduction even in the absence of interventions. This highlights that the best way to protect communities against measles is ensuring they have high levels of baseline immunity through the use of measles, mumps, and rubella (MMR) vaccine before measles is introduced.

What does the model show about the timing of public health measures?

The model also highlights the impact of early intervention on measles outbreaks: starting interventions immediately after measles leads to the highest impact, although interventions help reduce spread even when implemented later (Appendix Figure 1). In this scenario, delaying the implementation of isolation, quarantine, and vaccination by four weeks results in a median outbreak size, over one year, that is approximately 80% larger compared to implementing the same interventions immediately.

Modeling Methods

This model examines measles transmission in a population after the introduction of one or more measles infections. It is a stochastic discrete-time compartmental model, with compartments for Susceptible, Exposed, Infectious, Recovered, and Vaccinated (SEIRV structure) and assumes all-or-nothing vaccination (i.e., a proportion of vaccinated people corresponding to the vaccine's effectiveness are assumed to be completely protected from infection) (Figure 3). People who are immune at the beginning of the simulation through either MMR vaccination or past infection begin in the vaccinated (V) compartment, regardless of how they became immune. People who have been vaccinated but do not have protection from infection because the vaccine is not 100% effective begin in the Susceptible-vaccinated (SV) compartment and can still be infected.

In a classic SEIR model, the probability of a given person remaining in a specific compartment, like the exposed or infected compartment, follows an exponential distribution. This means some people spend very short or very long amounts of time in each compartment. This is not typically seen for measles, which has an incubation period of approximately 11 days and an infectious period of approximately 9 days (Appendix Table 2). To more closely reflect waiting times for measles infections, both the "Exposed" and "Infectious" disease states are split into two chained compartments (E1 and E2, and I1 and I2). By chaining the compartments, the waiting times in this model follow a 2-parameter Gamma distribution with the same mean, which has lower variance than the exponential distribution1. For the infectious period, this also corresponds to a pre-rash onset period (I1) and a post-rash onset period (I2), reflecting the progression of symptoms for a typical measles infection (Appendix Table 2). Introduced infections are assumed to arrive in their pre-rash infectious stage (I1) and are modeled to become symptomatic, on average, halfway through their infectious period. The interactive simulator displays weekly or daily incident infections at the time of rash onset, calculated as the number of people in the I2 category—this corresponds to all infections, whether diagnosed and reported to public health authorities or not.

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Annotated diagram of the compartmental model underlying the outbreak simulator.
Figure 3. Model schematic. The model is an adapted SEIRV compartmental model, with all-or-nothing vaccination and Exposed (E) and Infectious (I) compartments each split into two chained compartments to reduce the variance in latent and infectious periods.

Three public health interventions are built into the model and can be turned on and off: isolation, quarantine, and vaccination. The proportion of the population that adheres to isolation and quarantine can be modified by the user, and for vaccination, the percent of susceptible people to be vaccinated can be modified. When enabled, the start time and duration of each intervention can be modified independently. The interactive simulator defaults to enabled interventions starting four days after the first introduction, which corresponds to the average day of rash onset occurrence among the introduced infections (Appendix Table 2).

Isolation

In this model, isolation is defined as a person showing measles-specific symptoms (e.g., after rash onset) restricting contact with other people. The typical onset of rash from measles is on day 5 of a 9-day infectious period (Appendix Table 2). While it is possible in the real world that a rash—and therefore isolation—could begin sooner, isolation in this model reduces contagiousness in the second half of the infectious period only (I2 compartment).

Quarantine

The second intervention, quarantine, is defined as those who have exposure to measles and no evidence of protection (e.g., vaccination or confirmed prior infection), but who do not have symptoms, restricting contact with other people. This measure reduces contagiousness for the first half of the infectious period (I1 compartment), before rash onset. Since quarantine might not be perfectly followed, the effectiveness of quarantine among those designated as quarantining in the model is assumed to be 60% (Appendix Table 2). This means that people who are quarantining are 60% less likely to transmit to other people before their rash onset (i.e., their contagiousness during the I1 compartment is reduced by 60%). Because quarantine is a more restrictive measure than isolation, we assume every person who is infected and quarantining also isolates once they show symptoms. In the interactive simulator, this means that quarantine adherence cannot be higher than isolation adherence, while isolation adherence can be higher than quarantine adherence.

Vaccination campaign

The third intervention in the model is a vaccination campaign for those who are not yet vaccinated against measles and have not had prior infection. Vaccination is modeled as "all-or-nothing," meaning that for some people, the vaccine provides complete protection (V), while in others, it gives no protection after vaccination (SV). The proportion of people receiving protection from the vaccine is equal to the vaccine effectiveness (VE) parameter. For the MMR vaccine, one-dose VE is assumed to be 93% against measles and two-dose VE is 97% against measles (Appendix Table 2). In the proportion of the population who have immunity at baseline, either due to past infection or through vaccination, 97% have protective immunity (Appendix Table 2). People who are vaccinated during the vaccination campaign, however, are assumed to be receiving their first dose of MMR vaccine, and therefore 93% of this group get protective immunity when they are vaccinated.

We assume that people who are exposed and infected with measles are not yet aware of their exposure status and so they are equally likely as susceptible people to seek vaccination. However, any vaccines given to people in the exposed compartment do not confer any protection in the model, and those who were already infected before vaccination continue with disease progression. They are assumed to be equally contagious as those who were never vaccinated.

Those who have been vaccinated but do not develop protective immunity are moved into a vaccinated but susceptible compartment (SV). If they become infected, they then move into separated exposed compartments (EV1 and EV2) to ensure that they are not re-vaccinated during the vaccination campaign.

MMR vaccine doses are distributed evenly and constantly over the full duration of the campaign. The number of doses administered may be lower than the number of doses scheduled if by the time of the campaign, the daily dose rate scheduled exceeds the number of people eligible for vaccination, or if the campaign is scheduled to go beyond the last day of the simulation (day 365).

The model is stochastic, meaning there is built-in random variation in the model output. This stochasticity is implemented as a random probability of infection for each potentially infectious contact. For each setting in the interactive simulator, the model is run 100 separate times to produce a range of possible outcomes and estimates of associated uncertainty. The median and 95% prediction intervals are reported in the model output. We conduct a two-sample K-S test2 to determine if the total measles infections from the Interventions scenario are statistically distinguishable (e.g., if p < 0.05) from the total measles infections of the no-Interventions scenario, which is shown if the outcomes are not statistically distinguishable.

The model has a modifiable population size, which is allowed to range from 1,000 to 100,000 people. In the results presented above (Figure 2, Appendix Table 1), five initial measles infections are introduced into a community of 15,000 people. All five are assumed to be introduced and infectious at the same time. Baseline immunity against measles is varied from 80%-95%. In the results shown, for each intervention, we assume 50% of the eligible population follow each of the implemented public health interventions. Each intervention, when implemented, starts on day five in the model, which is the average time of rash onset occurrence for the introduced infections, and which we assume to be the first day that measles infections would be identified in the population. The vaccination campaign is conducted over a three-week period, while isolation and quarantine remain in place for the duration of the simulation. Measles-specific disease parameters are described in Appendix Table 2, and users can modify many of these assumptions in the interactive simulator under the disease parameters tab.

This model has several simplifications to make it both easy to use and generalizable to as many communities as possible. While these simplifications reduce the ability of the model to replicate exactly what happens in specific measles outbreaks, they allow users to see overall trends clearly under a variety of settings.

First, this is a model of a well-mixed population, which means all people in the community have the same probability of contact with each other. If certain groups of people (e.g., those who are not vaccinated) are more likely to come in contact with each other, this simplification could lead to overestimating the size of outbreaks in the community. Additionally, the modeled population has no age structure, so baseline immunity accounts for vaccination coverage and immunity averaged over the entire population. This means that the model may not be a good representation of small, closed populations (e.g., schools—though are available that are more applicable to these settings), or communities with very distinct sub-populations.

There have also been simplifying assumptions made to all three interventions. For vaccination, the MMR vaccine is modeled as an "all-or-nothing" vaccine, meaning that it provides complete immune protection corresponding to the VE parameter (i.e., for 93% of people after one dose) and no immune protection for others (i.e., 7% of people who have received one dose). This is a relatively close model for the mechanism underlying MMR vaccine efficacy.3 This model assumes protection from immunity immediately following vaccination but does not incorporate any potential effect of vaccination for people who have already been infected (e.g., as a post-exposure prophylaxis). Because this is a simplified vaccination campaign, we assume that all doses distributed during the modeled intervention are first doses, and that people who received the vaccine don't get a second dose over the course of the simulation (one year). We also make the simplifying assumption that everyone who was vaccinated at baseline has VE corresponding to two doses of the MMR vaccine. This likely overestimates immunity in the population, since children ages 1-4 years only have a single dose of MMR vaccine, which has a slightly lower VE (93% compared to 97%). However, as these estimates are both very high, this simplification is not likely to have a significant impact on the results of the model.

For the isolation intervention, we assume perfect efficacy for those who adhere following rash onset. While in reality, people may not be able to fully prevent contact within households, the parameterization of the interventions in this model is based on real-world efficacy in a measles outbreak in the United States, which likely captured more realistic isolation conditions (Appendix Table 2). For the quarantine intervention, people in the model who were vaccinated or infected in the past but did not acquire immunity are assumed to quarantine at the same rates as people who are unvaccinated. In reality, quarantine is only recommended for people who are unvaccinated and have known exposures. This will lead the model to overestimate the number of people quarantining. However, because the VE for MMR vaccines is so high, this simplification is not likely to have a significant impact on the results of the model.

In addition, we selected conservative values for both the isolation and quarantine parameters that may underestimate the impact of these interventions. Therefore, the model may simulate larger outbreaks in the intervention scenario than might be observed in reality.

Finally, this is a compartmental model, not an agent-based model, so the quarantine and isolation interventions are not applied to specific people—rather, they act by decreasing the fraction of pre-symptomatic or post-rash infectious people in contact with the susceptible population. This model is therefore meant for understanding population-level dynamics and is not well-suited to analyzing outcomes in specific people.

Appendix

Median number of measles infections after one year by intervention scenario following introduction of five measles infections into a community of 15,000 people, for different levels of baseline immunity
Median measles infections (95% Prediction Interval),
reduction compared to no interventions
Baseline Immunity Intervention scenario*
No Interventions Isolation only Isolation + Quarantine Isolation + Quarantine + Vaccination
80% 3,160 (3,129–3,188) 2,868 (2,805–2,923), 9% 2,455 (2,330–2,543), 22% 1,726 (1,459–1,859), 45%
85% 2,294 (2,244–2,339) 1,885 (1,773–1,969), 18% 1,227 (27–1,464), 47% 288 (15–646), 87%
90% 1,313 (1,183–1,385) 548 (10–854), 58% 52 (8–298), 96% 20 (7–67), 98%
95% 57 (7–264) 15 (6–63), 74% 11 (6–30), 81% 9 (5–17), 84%

*All three interventions are started on day five in the model, which is the average time of rash onset occurrence for the introduced infections, and which we assume to be the first day that measles infections would be identified in the population. Isolation and Quarantine adherence is set to 50%. Vaccination uptake is also 50% among those who are eligible (i.e., 50% of all people who are not immune at baseline) and takes place over a total of 21 days. Parameter settings for these results can be found in Appendix Table 2 and in the Methods under Model Inputs.

Default Model Parameters
Parameter Default Estimate
(range that users can specify)		 Reference
Disease parameters
R0 12 (10-18)

Note:
Communities with higher contact rates — for example populations with higher population density or larger households — may have higher R0 .
Latent period (days) 11 (6-18) Measles Clinical Diagnosis Fact Sheet | Measles (Rubeola) | CDC
Infectious period (days) 9 (5-11) Measles Clinical Diagnosis Fact Sheet | Measles (Rubeola) | CDC
Rash onset (day of infectious period) 5 Measles Clinical Diagnosis Fact Sheet | Measles (Rubeola) | CDC

Note:
In this model, the rash onset day is half of the infectious period and rash onset date will dynamically change if the infectious period is altered.
Infection Hospitalization ratio 15% (5-25%) Measles Symptoms and Complications | Measles (Rubeola) | CDC
Intervention effectiveness parameters
MMR vaccine effectiveness (VE) 1 dose: 93%
2 doses: 97%		 Measles Vaccination | Measles (Rubeola) | CDC
Per-person reduction in infectiousness due to isolation 50%

Note:
In this model, isolation starts only at rash onset, halfway through the infectious period. For the first half of the infectious period, there is therefore no isolation and no impact on transmission. After rash onset, for the second half of the infectious period, isolation reduces transmission by 100%. This leads to a reduction of 50% overall, lower than the published estimate in the above study (where R0 was reduced from around 4.0 for those not isolated to around 0.89 for those isolated, a reduction of 78%).
Per-person reduction in infectiousness due to quarantine 60%

Note:
This study estimates that measures akin to quarantine for people who are unvaccinated but have been exposed to measles is 44-76% effective at reducing transmission when compared to no quarantine. We assume a 60% reduction in transmission for those who quarantine, the midpoint of this range.

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Plot showing the impact of delaying public health interventions by one month on the cumulative number of measles infections in a community.
Appendix Figure 1. Cumulative measles infections over one year following introduction of five measles infections into a community of 15,000 people with a baseline immunity of 85%. All three interventions (isolation and quarantine adherence set to 50% and vaccination uptake set to 50% among those who are eligible, and spread over 21 days) are either implemented immediately following rash onset in the introduced infections or after a 4-week delay. A randomly selected subset of 20 simulations of the model is displayed for each intervention timing scenario, with the simulation corresponding to the median time of the outbreak peak in bold. Parameter settings for these results can be found in Appendix Table 2 and in the Methods under Model Inputs.
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