Accuracy criterion for the mean-field approximation in susceptible-infected-susceptible epidemics on networks

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 91, Issue 3, 2015, Pages

  Van Mieghem, P ^a   Van De Bovenkamp, R ^b  

^a Department of Microelectronics   (Netherlands)

^b NONE

Author keywords

[No Author keywords available]

Indexed keywords

COVARIANCE MATRIX; EPIDEMIOLOGY; GRAPHIC METHODS; MATRIX ALGEBRA;

ADJACENCY MATRICES; AVERAGE DEGREE; COMPLETE GRAPHS; MEAN FIELD APPROXIMATION; PRECISE SIMULATION; SPECTRAL RADII; SQUARE LATTICES; SUSCEPTIBLE-INFECTED-SUSCEPTIBLE;

GRAPH THEORY;

EID: 84961343643     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.91.032812     Document Type: Article

References (37)

1. R. Pastor-Satorras, C. Castellano, P. Van Mieghem, and A. Vespignani, Epidemic processes in complex networks, arXiv:1408.2701 [Rev. Mod. Phys. (to be published)].
2. L. Onsager, Crystal statistics: A two-dimensional model with an order-disorder transition, Phys. Rev. 65, 117 (1944). PHRVAO 0031-899X 10.1103/PhysRev.65.117
3. S. H. Strogatz, From Kuramoto to Crawford: Exploring the onset of synchronization in populations of coupled oscillators, Physica D 143, 1 (2000). PDNPDT 0167-2789 10.1016/S0167-2789(00)00094-4
4. P. Bak, C. Tang, and K. Wiesenfeld, Self-organized criticality: An explanation of 1/f noise, Phys. Rev. Lett. 59, 381 (1987). PRLTAO 0031-9007 10.1103/PhysRevLett.59.381
5. K.-I. Goh, D.-S. Lee, B. Kahng, and D. Kim, Sand pile on scale-free networks, Phys. Rev. Lett. 91, 148701 (2003). PRLTAO 0031-9007 10.1103/PhysRevLett.91.148701
6. T. Kleiberg and P. Van Mieghem, Self-Organization of Internet Paths, in IFIP Fourth International Workshop on Self-Organizing Systems 2009, Lecture Notes in Computer Science Vol. 5918 (Springer, Berlin, 2009), pp. 77-88.
7. C. Castellano, S. Fortunato, and V. Loreto, Statistical physics of social dynamics, Rev. Mod. Phys. 81, 591 (2009). RMPHAT 0034-6861 10.1103/RevModPhys.81.591
8. Q. Li, L. A. Braunstein, H. Wang, J. Shao, H. E. Stanley, and S. Havlin, Nonconsensus opinion models on complex networks, J. Stat. Phys. 151, 92 (2013). JSTPBS 0022-4715 10.1007/s10955-012-0625-4
9. H. E. Stanley, Introduction to Phase Transitions and Critical Phenomena (Oxford University Press, Oxford, 1987).
10. N. T. J. Bailey, The Mathematical Theory of Infectious Diseases and its Applications, 2nd ed. (Charlin Griffin, London, 1975).
11. R. M. Anderson and R. M. May, Infectious Diseases of Humans: Dynamics and Control (Oxford University Press, Oxford, 1991).
12. D. J. Daley and J. Gani, Epidemic Modeling: An Introduction (Cambridge University Press, Cambridge, 1999).
13. O. Diekmann, H. Heesterbeek, and T. Britton, Mathematical Tools for Understanding Infectious Disease Dynamics (Princeton University Press, Princeton, NJ, 2012).
14. P. Van Mieghem, Performance Analysis of Complex Networks and Systems (Cambridge University Press, Cambridge, 2014).
15. P. Van Mieghem, J. Omic, and R. E. Kooij, Virus spread in networks, IEEE/ACM Trans. Networking 17, 1 (2009). IEANEP 1063-6692 10.1109/TNET.2008.925623
16. P. Van Mieghem, The N -Intertwined SIS epidemic network model, Computing 93, 147 (2011). 0010-485X 10.1007/s00607-011-0155-y
17. P. Van Mieghem and E. Cator, Epidemics in networks with nodal self-infections and the epidemic threshold, Phys. Rev. E 86, 016116 (2012). PLEEE8 1539-3755 10.1103/PhysRevE.86.016116
18. E. Cator and P. Van Mieghem, Susceptible-infected-susceptible epidemics on the complete graph and the star graph: Exact analysis, Phys. Rev. E 87, 012811 (2013). PLEEE8 1539-3755 10.1103/PhysRevE.87.012811
19. A. Economou, A. Gómez-Corral, and M. López-García, A stochastic SIS epidemic model with heterogeneous contacts, Physica A 421, 78 (2015). 10.1016/j.physa.2014.10.054
20. R. J. Baxter, Exactly Solved Models in Statistical Mechanics (Academic, London, 1982).
21. A. L. Fetter and J. D. Walecka, Quantum Theory of Many-particle Systems (McGraw-Hill, San Francisco, 1971).
22. P. A. M. Dirac, The Principles of Quantum Mechanics, 4th ed. (Clarendon, Oxford, 1986).
23. C. Cohen-Tannoudji, B. Diu, and F. Laloë, Mécanique Quantique (Hermann, Paris, 1977), Vols. I and II.
24. W. Feller, An Introduction to Probability Theory and Its Applications, 2nd ed. (Wiley, New York, 1971), Vol. 2.
25. C. Li, R. van de Bovenkamp, and P. Van Mieghem, Susceptible-infected-susceptible model: A comparison of N -intertwined and heterogeneous mean-field approximations, Phys. Rev. E 86, 026116 (2012). PLEEE8 1539-3755 10.1103/PhysRevE.86.026116
26. E. Cator and P. Van Mieghem, Second order mean-field SIS epidemic threshold, Phys. Rev. E 85, 056111 (2012). PLEEE8 1539-3755 10.1103/PhysRevE.85.056111
27. E. Cator and P. Van Mieghem, Nodal infection in Markovian SIS and SIR epidemics on networks are non-negatively correlated, Phys. Rev. E 89, 052802 (2014). PLEEE8 1539-3755 10.1103/PhysRevE.89.052802
28. P. Van Mieghem, Graph Spectra for Complex Networks (Cambridge University Press, Cambridge, 2011).
29. J. Als-Nielsen and R. J. Birgenau, Mean field theory, the Ginzbug criterion, and marginal dimensionality of phase transitions, Am. J. Phys. 45, 554 (1977). AJPIAS 0002-9505 10.1119/1.11019
30. P. Van Mieghem and R. van de Bovenkamp, Non-Markovian infection spread dramatically alters the SIS epidemic threshold in networks, Phys. Rev. Lett. 110, 108701 (2013). PRLTAO 0031-9007 10.1103/PhysRevLett.110.108701
31. P. Van Mieghem, Epidemic phase transition of the SIS-type in networks, Europhys. Lett. 97, 48004 (2012). EULEEJ 0295-5075 10.1209/0295-5075/97/48004
32. P. Van Mieghem, The viral conductance of a network, Comput. Commun. 35, 1494 (2012). 10.1016/j.comcom.2012.04.015
33. R. van de Bovenkamp and P. Van Mieghem, Survival time of the SIS infection process on a graph [Phys. Rev. E (to be published)].
34. R. E. Kooij, P. Schumm, C. Scoglio, and M. Youssef, A new metric for robustness with respect to virus spread, in Networking 2009, Lecture Notes in Computer Science Vol. 5550 (Springer, Heidelberg, 2009), p. 562.
35. M. Youssef, R. E. Kooij, and C. Scoglio, Viral conductance: Quantifying the robustness of networks with respect to spread of epidemics, J. Comput. Sci. 2, 286 (2011). 1877-7503 10.1016/j.jocs.2011.03.001
36. J. Martin Hernandez, T. Kleiberg, H. Wang, and P. Van Mieghem, International Symposium on Performance Evaluation of Computer and Telecommunication Systems (SPECTS 2007) (IEEE, New York, 2007).
37. P. Van Mieghem, Exact Markovian SIR and SIS epidemics on networks and an upper bound for the epidemic threshold, arXiv:1402.1731.