Finding and removing highly connected individuals using suboptimal vaccines

Abstract

Background: Social networks are often highly skewed, meaning that the vast majority of the population has only few contacts whereas a small minority has a large number of contacts. These highly connected individuals may play an important role in case of an infectious disease outbreak.

Methods: We propose a novel strategy of finding and immunizing highly connected individuals and evaluate this strategy by computer simulations, using a stochastic, individual-and network-based simulation approach. A small random sample of the population is asked to list their acquaintances, and those who are mentioned most frequently are offered vaccination. This intervention is combined with case isolation and contact tracing.

Results: Asking only 10% of the population for 10 acquaintances each and vaccinating the most frequently named people strongly diminishes the magnitude of an outbreak which would otherwise have exhausted the available isolation units and gone out of control. It is extremely important to immunize all identified highly connected individuals. Omitting a few of them because of unsuccessful vaccination jeopardizes the overall success, unless non-immunized individuals are taken under surveillance.

Conclusions: The strategy proposed in this paper is particularly successful because it attacks the very point from which the transmission network draws its strength: the highly connected individuals. Current preparedness and containment plans for smallpox and other infectious diseases may benefit from such knowledge.

Figure 1

Influence of the Removal of Highly Connected Individuals on the Maximum Eigenvalue of the Next Generation Matrix of the Remaining Casual Contact Network. The curve shows median values of 100 simulations, given in arbitrary units. Red and yellow curves: Individuals are first sorted by their number of contacts; the removal starts with the person who has most contacts and progresses towards less highly connected ones. (a) Red curve: the horizontal axis shows what percentage of the population has been removed. (b) Yellow curve: as before, but a random sample of 90% of the selected individuals is removed. (c) Blue curve: people are not pre-sorted by their number of contacts, but are removed at random.

Figure 2

Influence of Perfect Vaccination of Highly Connected Individuals on a Smallpox Outbreak. Efficacy = 100%. Simulated outbreak sizes, caused by 100 index cases in a population of 100,000: the boxes show 25%, 50%, 75% quantiles, the whiskers show 10% and 90% quantiles and the triangles show minimum and maximum results (for 2% vaccination, the upper limit is not given, as one of the 100 simulations afflicted more than half of the population, as did all simulations for 0% and 1% vaccination). Targeted vaccination: (a) everybody is asked to name all casual contacts; (b) these contacts are sorted by frequency; (c) vaccination starts with the most frequently named person and progresses towards less frequently named ones. The horizontal axis shows what percentage of the population is vaccinated.

Figure 3

Influence of Perfect Vaccination of Highly Connected Individuals on the Median Smallpox Outbreak Size. Each point was obtained from 1,000 simulations. Initial value: 100 index cases in a population of 100,000. Vaccine efficacy = 100%. Targeted vaccination: (a) a random sample of the population (percentage is shown next to the curves) is asked to name all casual contacts; (b) these contacts are sorted by frequency; (c) vaccination starts with the most frequently named person and progresses towards less frequently named ones. The horizontal axis shows what percentage of the population is vaccinated.

Figure 4

Influence of Perfect Vaccination of Highly Connected Individuals on the Median Smallpox Outbreak Size. Each point was obtained from 1,000 simulations. Initial value: 100 index cases in a population of 100,000. Vaccine efficacy = 100%. Targeted vaccination: (a) a random sample of 10% of the population is asked to name casual contacts each (number of contacts asked is given next to the curves); (b) these contacts are sorted by frequency; (c) vaccination starts with the most frequently named person and progresses towards less frequently named ones. The horizontal axis shows what percentage of the population is vaccinated.

Figure 5

Influence of Imperfect Vaccination of Highly Connected Individuals on the Median Smallpox Outbreak Size. Each point was obtained from 1,000 simulations. Initial value: 100 index cases in a population of 100,000. Targeted vaccination: (a) a random sample of 10% of the population is asked to name 20 casual contacts each; (b) these contacts are sorted by frequency; (c) the most frequently named person is first scheduled for vaccination, less frequently named ones follow. The horizontal axis shows what percentage of the population is scheduled for vaccination. Because of vaccination eligibility and/or vaccination efficacy, only a fraction of those scheduled for vaccination can successfully be immunized (percentage immunized is given next to the curves).

Figure 6

Combined Influence of Imperfect Vaccination and Surveillance of Highly Connected Individuals on the Median Smallpox Outbreak Size. Each point was obtained from 1,000 simulations. Initial value: 100 index cases in a population of 100,000. Targeted vaccination: (a) a random sample of 10% of the population is asked to name 20 casual contacts each; (b) these contacts are sorted by frequency; (c) the most frequently named person is first scheduled for vaccination, less frequently named ones follow. The horizontal axis shows what percentage of the population is scheduled for vaccination. Because of vaccination eligibility and/or vaccination efficacy, a fraction of 90% (red curve) or 100% (blue curve) are successfully immunized. Scheduled individuals who are not immunized are permanently taken under surveillance.