Virus and Warning Spread in Dynamical Networks

Abstract

Recent work on information survival in sensor and human P2P networks try to study the datum preservation or the virus spreading in a network under the dynamical system approach. Some interesting solutions propose to use non-linear dynamical systems and fixed point stability theorems, providing closed form formulas that depend on the largest eigenvalue of the dynamic system matrix. Given that in the Web there can be messages from one place to another, and that these messages can be, with some probability, new unclassified virus warning messages as well as worms or other kind of viruses, the sites can be infected very fast. The question to answer is how and when a network infection can become global and how it can be controlled or at least how to stabilize the spreading in such a way that it becomes confined below a fixed portion of the network. In this paper, we try to be a step ahead in this direction and apply classic results of the dynamical systems theory to model the behavior of a network where warning messages and viruses spread. 341Advs. Complex Syst. 2011.14:341-358. Downloaded from www.worldscientific.com by UNIVERSITY OF MICHIGAN on 02/09/15. For personal use only.342 C. R. Lucatero and R. B. Jaquez sensor networks, social nets or wireless networks, where information is to be stored, generated and retrieved. So under these new environments, it is very important to study and model how the information is spread or how to keep the spreading of a virus under control in such a way that the information is still useful under these vulnerable circumstances. In [8] the problem of information survival threshold in sensor and P2P networks, modeling the problem as a nonlinear dynamical system and using fixed point stability theorems, and obtaining a closed form solution that depends on an additional parameter, the largest eigenvalue of the dynamical system matrix is being studied. In the sensor networks for instance, the nodes can loss their communication links and the nodes can stop working because of a system failure produced by a virus infection and quarantine process or a system maintenance procedure. Under such conditions they try to answer the following question: Under what conditions can a datum survive in a sensor network? Given that the nodes as well as the links can fail with some probability the obvious model can be a Markov Chain, but such a model can grow in complexity very quickly because the number of possible states becomes 3 N where N is the number of states. To avoid this mathematical problem, one alternative is to model the system as a nonlinear dynamical system. Recently, there have appeared in the conferences and journal articles some very interesting and relevant research articles about the virus spread behavior in a P2P network or in scale free nets such as the Web. In [10] the authors study the communication mechanisms for gossip based protocols. Another very recent and interesting work on how to distribute antidotes for controlling the epidemics spread is presented in [3]. In this research t...

Analysis of Epidemic Models in Complex Networks and Node Isolation Strategie Proposal for Reducing Virus Propagation

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Analysis of some Epidemic Models in complex networks and some ideas about isolation strategies

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