Efficient network immunization under limited knowledge

Targeted immunization of centralized nodes in large-scale networks has attracted significant attention. However, in real-world scenarios, knowledge and observations of the network may be limited, thereby precluding a full assessment of the optimal nodes to immunize (or quarantine) in order to avoid epidemic spreading such as that of the current coronavirus disease (COVID-19) epidemic. Here, we study a novel immunization strategy where only n nodes are observed at a time and the most central among these n nodes is immunized. This process can globally immunize a network. We find that even for small n (approximate to 10) there is significant improvement in the immunization (quarantine), which is very close to the levels of immunization with full knowledge. We develop an analytical framework for our method and determine the critical percolation threshold p(c) and the size of the giant component P-infinity for networks with arbitrary degree distributions P(k). In the limit of n -> infinity we recover prior work on targeted immunization, whereas for n = 1 we recover the known case of random immunization. Between these two extremes, we observe that, as n increases, p(c) increases quickly towards its optimal value under targeted immunization with complete information. In particular, we find a new general scaling relationship between vertical bar p(c)(infinity) - p(c) (n)vertical bar and n as vertical bar p(c)(infinity) - p(c) (n)vertical bar similar to n(-1) exp (-alpha n). For scale-free (SF) networks, where P(k) similar to k(-gamma), 2 < gamma < 3, we find that p(c) has a transition from zero to nonzero when n increases from n = 1 to O (log N) (where N is the size of the network). Thus, for SF networks, having knowledge of approximate to log N nodes and immunizing the most optimal among them can dramatically reduce epidemic spreading. We also demonstrate our limited knowledge immunization strategy on several real-world networks and confirm that in these real networks, p(c) increases significantly even for small n.

Automated summary

The study introduces a novel immunization strategy where only the most central node among a group of n observed nodes is immunized, leading to significant improvement in immunization even for small n. The analytical framework developed in the study determines critical percolation threshold and the size of giant component for networks with arbitrary degree distributions. The results show a scaling relationship between p(c)(infinity) - p(c) (n) and n, indicating a rapid increase in p(c) towards its optimal value as n increases.