We present an effective immunization strategy for computer networks and populations with broad and, in particular, scale-free degree distributions. The proposed strategy, acquaintance immunization, calls for the immunization of random acquaintances of random nodes (individuals). The strategy requires no knowledge of the node degrees or any other global knowledge, as do targeted immunization strategies. We study analytically the critical threshold for complete immunization. We also study the strategy with respect to the SIR (susceptible-infected-removed) epidemiological model. We show that the immunization threshold is dramatically reduced with the suggested strategy, for all studied cases. PACS numbers: 02.50. Cw, 02.10.Ox, 89.20.Hh, 64.60.Ak It is well established that random immunization requires immunizing a very large fraction of a computer network, or population, in order to arrest epidemics that spread upon contact between infected nodes (or individuals) [1, 2, 3, 4, 5, 6, 7] . Many diseases require 80%-100% immunization (for example, Measles requires 95% of the population to be immunized [1] ). The same is correct for the Internet, where stopping computer viruses requires almost 100% immunization [5, 6, 7] . On the other hand, targeted immunization of the most highly connected individuals [1, 5, 8, 9, 10, 11] , while effective, requires global information about the network in question, rendering it impractical in many cases. Here, we develop a mathematical model and propose an effective strategy, based on the immunization of a small fraction of random acquaintances of randomly selected nodes. In this way, the most highly connected nodes are immunized, and the process prevents epidemics with a small finite immunization threshold and without requiring specific knowledge of the network. Social networks are known to possess a broad distribution of the number of links (contacts), k, emanating from a node (an individual) [12, 13, 14] . Examples are the web of sexual contacts [15] , movie-actor networks, science citations and cooperation networks [16, 17] etc. Computer networks, both physical (such as the Internet [18] ) and logical (such as the WWW [19] , and e-mail [20] and trust networks [21] ) are also known to posses wide, scale-free, distributions. Studies of percolation on broad-scale networks show that a large fraction f c of the nodes need to be removed (immunized) before the integrity of the network is compromised. This is particularly true for scalefree networks, P (k) = ck −λ (k ≥ m), where 2 < λ < 3 -the case of most known networks [12, 13, 14] -where the percolation threshold f c → 1, and the network remains connected (contagious) even after removal of most of its nodes [6] . In other words, with a random immunization strategy almost all of the nodes need to be immunized
Cohen et al. REF proposed a mathematical model and an immunization policy based on a small fraction of random acquaintances, and analytically studied the critical threshold for complete immunization.
Efficient Immunization Strategies for Computer Networks and Populations
Phys. Rev. Lett. 91, 247901 (2003)
Physics Biology Medicine