The role of vaccination coverage, individual behaviors, and the public health response in the control of measles epidemics: an agent-based simulation for California

Abstract

Background: Measles cases continue to occur among susceptible individuals despite the elimination of endemic measles transmission in the United States. Clustering of disease susceptibility can threaten herd immunity and impact the likelihood of disease outbreaks in a highly vaccinated population. Previous studies have examined the role of contact tracing to control infectious diseases among clustered populations, but have not explicitly modeled the public health response using an agent-based model.

Methods: We developed an agent-based simulation model of measles transmission using the Framework for Reconstructing Epidemiological Dynamics (FRED) and the Synthetic Population Database maintained by RTI International. The simulation of measles transmission was based on interactions among individuals in different places: households, schools, daycares, workplaces, and neighborhoods. The model simulated different levels of immunity clustering, vaccination coverage, and contact investigations with delays caused by individuals' behaviors and/or the delay in a health department's response. We examined the effects of these characteristics on the probability of uncontrolled measles outbreaks and the outbreak size in 365 days after the introduction of one index case into a synthetic population.

Results: We found that large measles outbreaks can be prevented with contact investigations and moderate contact rates by having (1) a very high vaccination coverage (≥ 95%) with a moderate to low level of immunity clustering (≤ 0.5) for individuals aged less than or equal to 18 years, or (2) a moderate vaccination coverage (85% or 90%) with no immunity clustering for individuals (≤ 18 years of age), a short intervention delay, and a high probability that a contact can be traced. Without contact investigations, measles outbreaks may be prevented by the highest vaccination coverage with no immunity clustering for individuals (≤ 18 years of age) with moderate contact rates; but for the highest contact rates, even the highest coverage with no immunity clustering for individuals (≤ 18 years of age) cannot completely prevent measles outbreaks.

Conclusions: The simulation results demonstrated the importance of vaccination coverage, clustering of immunity, and contact investigations in preventing uncontrolled measles outbreaks.

Figure 1

Effects of vaccination coverage and clustering of immunity on the control of measles epidemics. For each combination of vaccination coverage V and the level of immunity clustering Ω (all other parameters’ values are shown in Table 1), we ran 256 iterations to obtain the outbreak size and the uncontrolled outbreak probability in 365 simulated days. The combinations with which the simulated uncontrolled outbreak probabilities >0 are represented by red cells and scaled from light red (lower uncontrolled outbreak probability) to dark red (higher uncontrolled outbreak probability); the values of simulated uncontrolled outbreak probabilities are shown in red cells. The combinations without uncontrolled outbreaks (the simulated uncontrolled outbreak probabilities =0) are shown by blue cells and scaled from light blue (higher outbreak size) to dark blue (lower outbreak size); the values of simulated outbreak sizes are shown in blue cells. The frontiers between adjacent combinations with and without uncontrolled outbreaks are shown by the black lines. These simulations suggest that the vaccination coverage is important in the control of measles epidemics (the higher vaccination coverage, the lower the probability of uncontrolled measles outbreaks and the smaller outbreak size); for a given vaccination coverage, a lower level of immunity clustering (i.e., the lower the chance of unvaccinated individuals clustered together in a household) may have better control of measles epidemics.

Figure 2

Effects of intervention delays and the contact finding probability on the control of measles epidemics. We simulated the main outcomes for each combination of the intervention delay for contacts of the index case and the contact finding probability under 9 combinations (A, B, C, D, E, F, G, H and I) of vaccination coverage (V= 0.85, 0.9 and 0.95) and the level of immunity clustering (Ω=0, 0.5 and 1). Cells in red indicate the combinations with which the simulations had uncontrolled outbreaks with the uncontrolled outbreak probabilities ranging from low to high. Cells in light blue show the combinations without uncontrolled outbreaks but with higher outbreak sizes than the combinations without uncontrolled outbreaks represented by dark blue cells. The frontiers between adjacent combinations with and without uncontrolled outbreaks are shown by the black lines. The results in (A), (B) and (C) suggest that increasing vaccination coverage levels and the contact finding probability while reducing intervention delays may reduce the uncontrolled outbreak probability. However, measles outbreaks may not be prevented with the highest level of immunity clustering. The results in (D), (E) and (F) suggest that scenarios with a lower level of immunity clustering, increasing vaccination coverage and contact finding probability, and reducing intervention delays have smaller uncontrolled outbreak probabilities than the highest level of immunity clustering (shown in Figures 2 (A), (B) and (C)), and 95% of vaccination may be enough to prevent measles outbreak which is consistent with the result shown in Figure 1 (the cell with V=95% and Ω=0.5); when V=90%, measles outbreaks may be prevented by the combinations of low intervention delays and a high contact finding probability. The results in (G), (H) and (I) suggest that with the lowest level of immunity clustering, increasing vaccination coverage may dramatically reduce measles outbreaks.

Figure 3

Effects of vaccination coverage and the contact rate in neighborhoods on the control of measles epidemics. We used the parameters’ values in Table 1 and combinations of vaccination coverage and contact rates in the neighborhood, and ran 256 iterations for each combination to simulate the uncontrolled outbreak probability and the outbreak size in 365 days under three scenarios: (A) without contact investigations, (B) with contact investigations and less intervention delay for contacts of the index case, and (C) with contact investigations and more intervention delay for contacts of the index case. For each of the scenarios A, B, and C, red cells show the combinations with uncontrolled outbreaks (the simulated uncontrolled outbreak probabilities >0; light red cells indicate combinations with lower uncontrolled outbreak probabilities; dark red cells indicate combinations with higher uncontrolled outbreak probabilities); and blue cells represent the simulated outbreak sizes of the combinations without uncontrolled outbreaks (the simulated uncontrolled outbreak probabilities =0), and scale the outbreak sizes from low (dark blue) to high (light blue). The frontiers between adjacent combinations with and without uncontrolled outbreaks are shown by the black lines. These simulations suggest: contact investigation plays an important role in preventing measles uncontrolled outbreaks and reducing the total outbreak size; with contact investigations, reducing the contact rates in the neighborhood may lower the vaccination coverage required to prevent uncontrolled measles outbreaks; with contact investigations and the highest vaccination coverage, measles outbreaks may be prevented even with very high contact rates in the neighborhood; less intervention delays for contacts of the index case may help contact investigations reduce the probability of uncontrolled measles outbreaks and the total outbreak size.

Figure 4

Effects of vaccination coverage and contact rates in all places on the control of measles epidemics. We used a scale parameter ranging from 0 to 1 to scale contact rates in school, daycare, workplace, household and neighborhood. For each combination of vaccination coverage V and the scale of all contact rates, the main outcomes were obtained by running the simulation for each of three scenarios: (A) without contact investigations, (B) with contact investigations and less intervention delays for contacts of the index case, and (C) with contact investigations and more intervention delays for contacts of the index case. For scenarios A, B, and C, red cells show the combinations with uncontrolled outbreaks and blue cells represent the simulated outbreak sizes of the combinations without uncontrolled outbreaks. The values of simulated uncontrolled outbreak probabilities are shown with blue numbers in red cells; the values of simulated outbreak sizes are shown with red numbers in blue cells. The frontiers between adjacent combinations with and without uncontrolled outbreaks are shown by the black lines. These simulations suggest: (1) contact investigations play an important role in preventing uncontrolled measles outbreaks and reducing the total outbreak size; (2) without contact investigations but with the lowest scale of contact rates in all places, even an 80% vaccination coverage may prevent uncontrolled measles outbreaks; (3) with contact investigations, reducing the contact rates in all settings may lower the vaccination coverage required to prevent uncontrolled measles outbreaks; (4) with contact investigations and the highest vaccination coverage level, uncontrolled measles outbreaks may be prevented even with very high contact rates in all settings; (5) less intervention delay for contacts of the index case may help contact investigations reduce the number of measles cases.