Stability of spreading processes over time-varying large-scale networks

IEEE Transactions on Network Science and Engineering

Volumn 3, Issue 1, 2016, Pages 44-57

  Ogura, Masaki ^a   Preciado, Victor M ^a  

^a UNIVERSITY OF PENNSYLVANIA   (United States)

Author keywords

Complex networks; Dynamic random graphs; Epidemics; Random matrix theory; Stochastic processes

Indexed keywords

COMPLEX NETWORKS; EIGENVALUES AND EIGENFUNCTIONS; GRAPH THEORY; MARKOV PROCESSES; MATRIX ALGEBRA; RANDOM PROCESSES; RANDOM VARIABLES; STABILITY; STOCHASTIC SYSTEMS;

ARBITRARY ACCURACY; EPIDEMIC THRESHOLD; EPIDEMICS; LARGE-SCALE NETWORK; RANDOM GRAPH PROCESS; RANDOM GRAPHS; RANDOM MATRIX THEORY; STABILITY CONDITION;

TIME VARYING NETWORKS;

EID: 84963838148     PISSN: None     EISSN: 23274697     Source Type: Journal    
DOI: 10.1109/TNSE.2016.2516346     Document Type: Article

References (51)

1. K. Lerman and R. Ghosh, "Information contagion: An empirical study of the spread of news on Digg and Twitter social networks," in Proc. 4th Int. AAAI Conf. Weblogs Social Media, 2010, pp. 90-97.
2. M. Garetto, W. Gong, and D. Towsley, "Modeling malware spreading dynamics," in Proc. 22nd Annu. Joint Conf. IEEE Comput. Commun. Soc., 2003, vol. 3, pp. 1869-1879.
3. M. Tizzoni, P. Bajardi, C. Poletto, J. J. Ramasco, D. Balcan, B. Gonçalves, N. Perra, V. Colizza, and A. Vespignani, "Real-time numerical forecast of global epidemic spreading: Case study of 2009 A/H1N1pdm," BMC Medicine, vol. 10, p. 165, 2012.
4. R. Pastor-Satorras, C. Castellano, P. Van Mieghem, and A. Vespignani, "Epidemic processes in complex networks," Rev. Modern Phys., vol. 87, pp. 925-979, 2015.
5. C. Nowzari, V. M. Preciado, and G. J. Pappas, "Analysis and control of epidemics: A survey of spreading processes on complex networks," IEEE Control Systems Magazine, vol. 36, pp. 26-46, 2016, Doi 10.1109/MCS.2015.2495000
6. H. J. Ahn and B. Hassibi, "On the mixing time of the SIS Markov chain model for epidemic spread," in Proc. 53rd IEEE Conf. Decision Control, 2014, pp. 6221-6227.
7. A. Ganesh, L. Massoulie, and D. Towsley, "The effect of network topology on the spread of epidemics," in Proc. IEEE 24th Annu. Joint Conf. IEEE Comput. Commun. Soc., vol. 2, 2005, pp. 1455-1466.
8. D. Chakrabarti, Y. Wang, C. Wang, J. Leskovec, and C. Faloutsos, "Epidemic thresholds in real networks," ACM Trans. Inform. Syst. Security, vol. 10, no. 4, article no. 13, 2008.
9. P. Van Mieghem, J. Omic, and R. Kooij, "Virus spread in networks," IEEE/ACM Trans. Netw., vol. 17, pp. 1-14, 2009.
10. F. Darabi Sahneh, C. Scoglio, and P. Van Mieghem, "Generalized epidemic mean-field model for spreading processes over multilayer complex networks," IEEE/ACM Trans. Netw., vol. 21, pp. 1609-1620, 2013.
11. Y. Wan, S. Roy, and A. Saberi, "Designing spatially heterogeneous strategies for control of virus spread," IET Syst. Biol., vol. 2, pp. 184-201, 2008.
12. V. M. Preciado, M. Zargham, C. Enyioha, A. Jadbabaie, and G. Pappas, "Optimal vaccine allocation to control epidemic outbreaks in arbitrary networks," in Proc. 52nd IEEE Conf. Decision Control, 2013, pp. 7486-7491.
13. V. M. Preciado, M. Zargham, C. Enyioha, A. Jadbabaie, and G. J. Pappas, "Optimal resource allocation for network protection against spreading processes," IEEE Trans. Control Netw. Syst., vol. 1, pp. 99-108, 2014.
14. K. Drakopoulos, A. Ozdaglar, and J. Tsitsiklis, "An efficient curing policy for epidemics on graphs," IEEE Trans. Netw. Sci. Eng., vol. 1, pp. 67-75, 2014.
15. P. Holme and J. Saramcaki, "Temporal networks," Phys. Rep., vol. 519, pp. 97-125, 2012.
16. N. Fefferman and K. Ng, "How disease models in static networks can fail to approximate disease in dynamic networks," Phys. Rev. E, vol. 76, p. 031919, 2007.
17. N. Masuda and P. Holme, "Predicting and controlling infectious disease epidemics using temporal networks," F1000prime Rep., vol. 5, p. 6, 2013.
18. A. Vazquez, B. Racz, A. Lukacs, and A.-L. Barabasi, "Impact of non-Poissonian activity patterns on spreading processes," Phys. Rev. Lett., vol. 98, p. 158702, 2007.
19. M. Karsai, M. Kivelca, R. K. Pan, K. Kaski, J. Kertesz, A.-L. Barabasi, and J. Saramcaki, "Small but slow world: How network topology and burstiness slow down spreading," Phys. Rev. E, vol. 83, p. 025102, 2011.
20. P. Holme and F. Liljeros, "Birth and death of links control disease spreading in empirical contact networks," Sci. Rep., vol. 4, p. 4999, 2014.
21. C. L. Vestergaard, M. Genois, and A. Barrat, "How memory generates heterogeneous dynamics in temporal networks," Phys. Rev. E, vol. 90, p. 042805, 2014.
22. E. Volz and L. A. Meyers, "Epidemic thresholds in dynamic contact networks," J. Royal Soc., Interface/the Royal Soc., vol. 6, pp. 233- 241, 2009.
23. Y. Schwarzkopf, A. Rakos, and D. Mukamel, "Epidemic spreading in evolving networks," Phys. Rev. E, vol. 82, p. 036112, 2010.
24. N. Perra, A. Baronchelli, D. Mocanu, B. Gonçalves, R. Pastor-Satorras, and A. Vespignani, "Random walks and search in timevarying networks," Phys. Rev. Lett., vol. 109, p. 238701, 2012.
25. N. Perra, B. Gonçalves, R. Pastor-Satorras, and A. Vespignani, "Activity driven modeling of time varying networks," Sci. Rep., vol. 2, p. 469, 2012.
26. M. Karsai, N. Perra, and A. Vespignani, "Time varying networks and the weakness of strong ties," Sci. Rep., vol. 4, p. 4001, 2014.
27. A. E. Clementi, C. Macci, A. Monti, F. Pasquale, and R. Silvestri, "Flooding time in edge-Markovian dynamic graphs," in Proc. 27th ACM Symp. Principles Distrib. Comput., 2008, pp. 213-222.
28. I. Z. Kiss, L. Berthouze, T. J. Taylor, and P. L. Simon, "Modelling approaches for simple dynamic networks and applications to disease transmission models," Proc. Royal Soc. A: Math., Phys. Eng. Sci., vol. 468, pp. 1332-1355, 2012.
29. J. Whitbeck, V. Conan, and M. D. de Amorim, "Performance of opportunistic epidemic routing on Edge-Markovian dynamic graphs," IEEE Trans. Commun., vol. 59, pp. 1259-1263, May 2011.
30. L. Maggi and F. De Pellegrini, "Not always sparse: Flooding time in partially connected mobile ad hoc networks," Proc. 12th Int. Symp. Model. Optimization Mobile, Ad Hoc, Wireless Netw., pp. 413- 420, 2014.
31. H. Baumann, P. Crescenzi, and P. Fraigniaud, "Parsimonious flooding in dynamic graphs," Proc. 28th ACM Symp. Principles Distrib. Comput., p. 260, 2009.
32. M. Taylor, T. J. Taylor, and I. Z. Kiss, "Epidemic threshold and control in a dynamic network," Phys. Rev. E, vol. 85, p. 016103, 2012.
33. C. Cattuto, W. van den Broeck, A. Barrat, V. Colizza, J. F. Pinton, and A. Vespignani, "Dynamics of person-to-person interactions from distributed RFID sensor networks," PLoS ONE, vol. 5, pp. 1- 9, 2010.
34. J. Stehle, N. Voirin, A. Barrat, C. Cattuto, L. Isella, J. F. Pinton, M. Quaggiotto, W. van den Broeck, C. Regis, B. Lina, and P. Vanhems, "High-resolution measurements of face-to-face contact patterns in a primary school," PLoS ONE, vol. 6, 2011.
35. J. Stehle, N. Voirin, A. Barrat, C. Cattuto, V. Colizza, L. Isella, C. Regis, J.-F. Pinton, N. Khanafer, W. Van den Broeck, and P. Vanhems, "Simulation of an SEIR infectious disease model on the dynamic contact network of conference attendees," BMC Medicine, vol. 9, p. 87, 2011.
36. D. R. Fredkin and J. A. Rice, "On aggregated Markov processes," J. Appl. Probability, vol. 23, pp. 208-214, 1986.
37. M. A. Rami, V. S. Bokharaie, O. Mason, and F. R. Wirth, "Stability criteria for SIS epidemiological models under switching policies," Discr. Continuous Dynamical Syst.- Series B, vol. 19, pp. 2865-2887, 2014.
38. R. W. Brockett. (2009). Stochastic Control [Online]. Available: Http://www.eeci-institute.eu/pdf/M015/RogersStochastic.pdf
39. F. Chung, L. Lu, and V. Vu, "Spectra of random graphs with given expected degrees," Proc. Nat. Acad. Sci. USA, vol. 100, pp. 6313- 6318, 2003.
40. C. Desoer and H. Haneda, "The measure of a matrix as a tool to analyze computer algorithms for circuit analysis," IEEE Trans. Circuit Theory, vol. 19, no. 5, pp. 480-486, Sep. 1972.
41. E. Çinlar, "Exceptional paper-Markov renewal theory: A survey," Manage. Sci., vol. 21, pp. 727-752, 1975.
42. R. Schassberger, "On the waiting time in the queuing system GI/G/1," Ann. Math. Statist., vol. 41, pp. 182-187, 1970.
43. C. Lanczos, "An iteration method for the solution of the eigenvalue problem of linear differential and integral operators," J. Res. Nat. Bureau Standards, vol. 45, pp. 255-282, 1950.
44. J. Saramcaki and K. Kaski, "Modelling development of epidemics with dynamic small-world networks," J. Theoretical Biol., vol. 234, pp. 413-21, 2005.
45. L. Erdcos and A. Renyi, "On random graphs. I," Publicationes Mathematicae, vol. 6, pp. 290-297, 1959.
46. E. Cator and P. Van Mieghem, "Susceptible-infected-susceptible epidemics on the complete graph and the star graph: Exact analysis," Phys. Rev. E, vol. 87, p. 012811, 2013.
47. O. L. V. Costa, M. D. Fragoso, and M. G. Todorov, Continuous- Time Markov Jump Linear Systems. New York, NY, US: Springer, 2013.
48. Y. Fang and K. Loparo, "Stabilization of continuous-time jump linear systems," IEEE Trans. Automat. Control, vol. 47, pp. 1590- 1603, 2002.
49. F. Chung and M. Radcliffe, "On the spectra of general random graphs," Electron. J. Combinatorics, vol. 18, p. 215, 2011.
50. N. K. Son and D. Hinrichsen, "Robust stability of positive continuous time systems," Numerical Functional Anal. Optimization, vol. 17, pp. 649-659, 1996.
51. P. Bolzern, "On almost sure stability of discrete-time Markov jump linear systems," in Proc. 43rd IEEE Conf. Decision Control, 2004, pp. 3204-3208.