Multi-competitive viruses over static and time-varying networks

Epidemic processes are used commonly for modeling and analysis of biological networks, computer networks, and human contact networks. The idea of competing viruses has been explored recently, motivated by the spread of different ideas along different social networks. Previous studies of competitive viruses have focused only on two viruses and on static networks. In this paper, we consider multiple competing viruses over static and dynamic graph structures, and investigate the eradication and propagation of diseases in these systems. Stability analysis for the class of models we consider is performed and an antidote control technique is proposed.

[1]  W. O. Kermack,et al.  Contributions to the mathematical theory of epidemics—II. The problem of endemicity , 1991, Bulletin of mathematical biology.

[2]  Christos Faloutsos,et al.  Epidemic spreading in real networks: an eigenvalue viewpoint , 2003, 22nd International Symposium on Reliable Distributed Systems, 2003. Proceedings..

[3]  Stephen P. Boyd,et al.  Enhancing Sparsity by Reweighted ℓ1 Minimization , 2007, 0711.1612.

[4]  Yan Wan,et al.  Network design problems for controlling virus spread , 2007, 2007 46th IEEE Conference on Decision and Control.

[5]  G. Sallet,et al.  Epidemiological Models and Lyapunov Functions , 2007 .

[6]  A. Saberi,et al.  Designing spatially heterogeneous strategies for control of virus spread. , 2008, IET systems biology.

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

[8]  John Wright,et al.  Robust Principal Component Analysis: Exact Recovery of Corrupted Low-Rank Matrices via Convex Optimization , 2009, NIPS.

[9]  Michalis Faloutsos,et al.  Virus Propagation on Time-Varying Networks: Theory and Immunization Algorithms , 2010, ECML/PKDD.

[10]  Chengbin Peng,et al.  Epidemic threshold and immunization on generalized networks , 2010 .

[11]  Oliver Mason,et al.  Spread of epidemics in time-dependent networks , 2010 .

[12]  Shouhuai Xu,et al.  A Stochastic Model of Multivirus Dynamics , 2012, IEEE Transactions on Dependable and Secure Computing.

[13]  Sandip Roy,et al.  Cost of fairness in disease spread control , 2012, 2012 IEEE 51st IEEE Conference on Decision and Control (CDC).

[14]  Christos Faloutsos,et al.  Winner takes all: competing viruses or ideas on fair-play networks , 2012, WWW.

[15]  Michalis Faloutsos,et al.  Competing Memes Propagation on Networks: A Network Science Perspective , 2013, IEEE Journal on Selected Areas in Communications.

[16]  Babak Hassibi,et al.  Global dynamics of epidemic spread over complex networks , 2013, 52nd IEEE Conference on Decision and Control.

[17]  Douglas Cochran,et al.  Conjoining Speeds up Information Diffusion in Overlaying Social-Physical Networks , 2011, IEEE Journal on Selected Areas in Communications.

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

[19]  M. A. Rami,et al.  Stability Criteria for SIS Epidemiological Models under Switching Policies , 2013, 1306.0135.

[20]  Francesco Bullo,et al.  Controllability Metrics, Limitations and Algorithms for Complex Networks , 2014, IEEE Trans. Control. Netw. Syst..

[21]  Bahman Gharesifard,et al.  Stability properties of infected networks with low curing rates , 2014, 2014 American Control Conference.

[22]  C. Scoglio,et al.  Competitive epidemic spreading over arbitrary multilayer networks. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Chinwendu Enyioha,et al.  Optimal Resource Allocation for Network Protection Against Spreading Processes , 2013, IEEE Transactions on Control of Network Systems.

[24]  Angelia Nedic,et al.  Stability analysis and control of virus spread over time-varying networks , 2015, 2015 54th IEEE Conference on Decision and Control (CDC).

[25]  José M. F. Moura,et al.  Bi-Virus SIS Epidemics over Networks: Qualitative Analysis , 2015, IEEE Transactions on Network Science and Engineering.

[26]  Tamer Basar,et al.  On the analysis of a continuous-time bi-virus model , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[27]  Angelia Nedić,et al.  Epidemic Processes Over Time-Varying Networks , 2016, IEEE Transactions on Control of Network Systems.

[28]  George J. Pappas,et al.  Optimal Resource Allocation for Competitive Spreading Processes on Bilayer Networks , 2015, IEEE Transactions on Control of Network Systems.