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Targeted Immunization Strategies
Targeted immunization strategies are approaches designed to increase the immunization level of populations and decrease the chances of epidemic outbreaks. Though often in regards to use in healthcare practices and the administration of vaccines to prevent biological epidemic outbreaks, these strategies refer in general to immunization schemes in complex networks, biological, social or artificial in nature. Identification of at-risk groups and individuals with higher odds of spreading the disease often plays an important role in these strategies.

Background
The success of vaccines and anti-virus software in preventing major outbreaks relies on the mechanism of herd immunity, also known as community immunity, where the immunization of individuals provides protection for not only the individuals, but also the community at large. In cases of biological contagions such as influenza, measles, and chicken pox, immunizing a critical community size can provide protection against the disease for members who cannot be vaccinated themselves (infants, pregnant women, and immunocompromised individuals). Often however these vaccine programmes require the immunization of a large majority of the population to provide herd immunity. A few successful vaccine programmes have led to the eradication of infectious diseases like small pox and rinderpest, and the near eradication of polio, which plagued the world before the second half of the 20th century.

Network-based Strategies
More recently researchers have looked at exploiting network connectivity properties to better understand and design immunization strategies to prevent major epidemic outbreaks. Many real networks like the Internet, world wide web, and even sexual contact networks have been shown to be scale-free networks and as such exhibit a power-law distribution for the degree distribution. In large networks this results in the vast majority of nodes (individuals in social networks) having few connections or low degree k, while a few "hubs" have many more connections than the average . This wide variability (heterogeneity) in degree offers immunization strategies based on targeting members of the network according to their connectivity rather than random immunization of the network. In epidemic modeling on scale-free networks, targeted immunization schemes can considerably lower the vulnerability of a network to epidemic outbreaks over random immunization schemes. Typically these strategies result in the need for far fewer nodes to be immunized in order to provide the same level of protection to the entire network as in random immunization. In circumstances then where vaccines are scarce, efficient immunization strategies become necessary to preventing infectious outbreaks.

Examples

A common approach for targeted immunization studies in scale-free networks focuses on targeting the highest degree nodes for immunization. These nodes are the most highly connected in the network, making them more likely to spread the contagion if infected. Immunizing this segment of the network can drastically reduce the impact of the disease on the network and requires the immunization of far fewer nodes compared to randomly selecting nodes. However, this strategy relies on knowing the global structure of the network, which may not always be practical.

Another strategy, acquaintance immunization, tries to target all of the most highly connected nodes for immunization by going through their neighbors without knowing the full network topology. In this approach a random group of nodes are chosen and then a random set of their neighbors are selected for immunization. The most highly connected nodes are far more likely to be in this group of neighbors so immunizing this group results in targeting the most highly connected but requiring far less information about the network. Another variant of this strategy again calls for the random selection of nodes but instead asks for one of their neighbors with a higher degree, or at least more than a given threshold degree and immunizes them. These degree based strategies consistently require fewer nodes to be immunized and as such improve a network's chances against epidemic attacks.

A plot comparing the fraction of immunized nodes needed to prevent epidemic outbreaks in scale-free networks for two degree based strategies compared to random immunization can be found here.

Figure 1. shows the fraction of immunized nodes $$f_c$$ needed to prevent epidemic outbreaks in scale-free networks as a function of the power-law exponent $$\lambda$$ for two degree based strategies compared to random immunization. These targeted immunization strategies consistently require fewer nodes to be immunized and as such improve a network's resilience against epidemic attacks.

In epidemic modeling on networks, a critical value to characterizing a contagion's chances of becoming an epidemic is the epidemic threshold. This threshold is the rate of infection of "healthy" or susceptible individuals connected to infected ones at which an infectious outbreak dies before spreading to the entire network. Above this rate a contagion is able to propagate itself before the infectious period is over and becomes an epidemic. Network science researchers have shown that many real world networks are scale-free networks and as such exhibit a power-law distribution for the degree distribution. This results in the vast majority of nodes (individuals in social networks) having few connections or low degree k, while a few "hubs" have many more connections than the average .