INFORMATION CHANGE THE WORLD

International Journal of Engineering and Manufacturing(IJEM)

ISSN: 2305-3631 (Print), ISSN: 2306-5982 (Online)

Published By: MECS Press

IJEM Vol.1, No.6, Dec. 2011

The Analysis for the Two-stage Model on Scale-free Networks

Full Text (PDF, 225KB), PP.57-63


Views:92   Downloads:1

Author(s)

Maoxing Liu,Yunli Zhang

Index Terms

Complex network; Two-stage model; Epidemic; Threshold

Abstract

In this paper, we will study a two-stage model by complex networks. The dynamic behaviors of the model on a heterogenous scale-free (SF) network are considered, where the absence of the threshold on the SF network is demonstrated, and the stability of the disease-free equilibrium is obtained.

Cite This Paper

Maoxing Liu,Yunli Zhang,"The Analysis for the Two-stage Model on Scale-free Networks", IJEM, vol.1, no.6, pp.57-63, 2011.

Reference

[1] R. M. Anderson, R. M. May, Infectious Diseases of Humans, Oxford University Press, Oxford, UK (1991).

[2] Kermack, W. O. and A. G. McKendrick. 1927. A Contribution to the Mathematical. Theory of Epidemics. Proc. Roy. Soc. A. 115, 700-721.

[3] T. Harris, Contact interactions on a lattice, Ann. Probab., 2 (1974) 969-988.

[4] H. W. Hethcote, J. A. Yorke, Gonorrhoea: transmission dynamics and control in: Lecture Notes in Biomathematics, vol. 56. Springer, New York, 1984.

[5] M. Kretzschmar, Y.T.H.P. Van Duynhoven, A. J. Severijnen, Modeling prevention strategies for gonorrhoea and chlamydia using stochastic network simulations. Am. J. Epidemiol., 144 (1997) 306-317.

[6] S. M. Krone, The two-stage contact process, The Annals of Applied Probability, 9 (2) 1999 331-351.

[7] R. Pastor-Satorras, A. Vespignani, Epidemic spreading in scale-free networks, Phys. Rev. Lett., 86 (2001a) 3200-3203.

[8] R. Pastor-Satorras, A. Vespignani, Epidemic dynamics and endemic states in complex networks, Phys. Rev. E, 63 (2001b) 066117.

[9] R. Pastor-Satorras, A. Vespignani, Immunization of complex networks, Phys. Rev. E, 65 (2002) 036104.

[10] D. S. Callaway, M. E. J. Newman, S. H. Strogatz, D. J. Watts, Network robustness and fragility: percolation on random graphs, Phys. Rev. Lett.,85 (2000) 5468-5471.

[11] R. Cohen, K. Erez, D. Ben-Avraham, S. Havlin, Resilience of the Internet to random breakdowns, Phys. Rev. Lett., 85 (2000) 4626-4628.

[12] R. Cohen, S. Havlin, D. Ben-Avraham, , Phys. Rev. Lett., 91 (2003) 247901.

[13] M. E. J. Newman, Spread of epidemic disease on networks, Phys. Rev. E, 66 (2002) 016128.

[14] H. Shi, Z. Duan, G. Chen, An SIS model with infective medium on complex networks, Physica A 387 (2008) 2133-2144.

[15] Y. Y. Ahn, H. Jeong, N. Masuda, J. D. Noh, Epidemic dynamics of two species of interacting particles on scale-free networks, Phys. Rev. E, 74 (2006) 066113.

[16] M. E. J. Newman, Threshold Effects for Two Pathogens Spreading on a Network, Phys. Rev. Lett., 95 (2005) 108701.

[17] N.K. Masuda, N. Konno, Multi-state epidemic processes on complex networks, Journal of Theoretical Biology, 243 (2006) 64-75.

[18] A. -L. Barabasi, R. Albert, Emergence of scaling in random networks, Science 286 (1999) 509-512.

[19] W. P. Guo, X. Li, X. F. Wang, Epidemics and immunization on Euclidean distance preferred small-world networks, Physica A 380 (2007) 684-690.

[20] X. L, X. F. Wang, Controlling the spreading in small-world evolving networks: stability, oscillation, and topology, IEEE Trans. Automat.Control 51 (3) (2006) 534-540.

[21] X. L, X. F. Wang, On the stability of epidemic spreading in small-world networks: how prompt the recovery should be?, Int. J. Syst. Sci. 38 (5) (2007) 400-407.