Link operations for slowing the spread of disease in complex networks

A variety of social, biological and communication networks can be modelled using graph theoretical tools. Similar graphical tools can be used to model the topology by which disease, errors, and/or other undesired phenomenon etc. is spread and propagated through such networks. Certain network operations are proposed in this work that can be used to slow the spread of diseases in complex network topologies. The approach considered in this work differs from existing techniques in that it is based on optimally removing (or immunizing) individual links in the network as opposed to individual nodes. A systematic algorithm is outlined to achieve this edgewise immunization via a relaxed convex optimization protocol.

[1]  Narsingh Deo,et al.  Graph Theory with Applications to Engineering and Computer Science , 1975, Networks.

[2]  N.R. Malik,et al.  Graph theory with applications to engineering and computer science , 1975, Proceedings of the IEEE.

[3]  A. Klovdahl,et al.  Social networks and the spread of infectious diseases: the AIDS example. , 1985, Social science & medicine.

[4]  John Scott.  What is social network analysis , 2010 .

[5]  Fan Chung,et al.  Spectral Graph Theory , 1996 .

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

[7]  S H Strogatz,et al.  Random graph models of social networks , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[8]  Albert-László Barabási,et al.  Linked: The New Science of Networks , 2002 .

[9]  Reuven Cohen,et al.  Efficient immunization strategies for computer networks and populations. , 2002, Physical review letters.

[10]  Petter Holme,et al.  Efficient local strategies for vaccination and network attack , 2004, q-bio/0403021.

[11]  Aravind Srinivasan,et al.  Modelling disease outbreaks in realistic urban social networks , 2004, Nature.

[12]  N. Madar,et al.  Immunization and epidemic dynamics in complex networks , 2004 .

[13]  Martin H. Levinson.  Linked: The New Science of Networks , 2004 .

[14]  A. Gionis,et al.  Models and Algorithms for Network Immunization , 2005 .

[15]  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..

[16]  Alessandro Vespignani,et al.  Epidemics and immunization in scale‐free networks , 2002, cond-mat/0205260.

[17]  L. Meyers.  Contact network epidemiology: Bond percolation applied to infectious disease prediction and control , 2006 .

[18]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[19]  Stephen P. Boyd.  Convex optimization of graph Laplacian eigenvalues , 2006 .

[20]  Donald F. Towsley,et al.  Modeling and Simulation Study of the Propagation and Defense of Internet E-mail Worms , 2007, IEEE Transactions on Dependable and Secure Computing.

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

[22]  Christos Faloutsos,et al.  Epidemic thresholds in real networks , 2008, TSEC.

[23]  P. Van Mieghem,et al.  Virus Spread in Networks , 2009, IEEE/ACM Transactions on Networking.

[24]  Piet Van Mieghem,et al.  Protecting Against Network Infections: A Game Theoretic Perspective , 2009, IEEE INFOCOM 2009.

[25]  J. Borge-Holthoefer,et al.  Discrete-time Markov chain approach to contact-based disease spreading in complex networks , 2009, 0907.1313.

[26]  Piet Van Mieghem,et al.  In-homogeneous Virus Spread in Networks , 2013, ArXiv.