Distributing Antidote Using PageRank Vectors

We give an analysis of a variant of the contact process on finite graphs, allowing for nonuniform cure rates, modeling antidote distribution. We examine an inoculation scheme using PageRank vectors that quantify the correlations among vertices in the contact graph. We show that for a contact graph on n nodes we can select a set H of nodes to inoculate such that with probability at least 1 − 2ε, any infection from any starting infected set of s nodes will die out in c log s+cˈ time, where c and cˈ depend only on the probabilistic error bound ε and the infection rate, and the size of H depends only on s, ε, and the topology around the initially infected nodes, independent of the size of the whole graph.

[1]  W. O. Kermack,et al.  A contribution to the mathematical theory of epidemics , 1927 .

[2]  Sergey Brin,et al.  The Anatomy of a Large-Scale Hypertextual Web Search Engine , 1998, Comput. Networks.

[3]  R. May,et al.  Infection dynamics on scale-free networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Alessandro Vespignani,et al.  Epidemic spreading in scale-free networks. , 2000, Physical review letters.

[5]  M. Newman.  Spread of epidemic disease on networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Alessandro Vespignani,et al.  Epidemic dynamics in finite size scale-free networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  A. Barabasi,et al.  Halting viruses in scale-free networks. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Lev S. Tsimring,et al.  Modeling of contact tracing in social networks , 2003 .

[9]  Kathleen M. Carley,et al.  The Impact of Network Topology on the Spread of Anti-Virus Countermeasures , 2003 .

[10]  Amin Saberi,et al.  On the spread of viruses on the internet , 2005, SODA '05.

[11]  Donald F. Towsley,et al.  The effect of network topology on the spread of epidemics , 2005, Proceedings IEEE 24th Annual Joint Conference of the IEEE Computer and Communications Societies..

[12]  I. Kiss,et al.  Infectious disease control using contact tracing in random and scale-free networks , 2006, Journal of The Royal Society Interface.

[13]  Fan Chung Graham,et al.  Local Graph Partitioning using PageRank Vectors , 2006, 2006 47th Annual IEEE Symposium on Foundations of Computer Science (FOCS'06).

[14]  Joel C. Miller,et al.  Effective vaccination strategies for realistic social networks , 2007 .

[15]  Christopher A Gilligan,et al.  Optimizing the control of disease infestations at the landscape scale , 2007, Proceedings of the National Academy of Sciences.

[16]  Fan Chung Graham,et al.  Detecting Sharp Drops in PageRank and a Simplified Local Partitioning Algorithm , 2007, TAMC.

[17]  Amin Saberi,et al.  How to distribute antidote to control epidemics , 2010, Random Struct. Algorithms.

[18]  Amin Saberi,et al.  How to distribute antidote to control epidemics , 2010 .