International Journal of Information Engineering and Electronic Business (IJIEEB)
IJIEEB Vol. 3, No. 1, 8 Feb. 2011
Cover page and Table of Contents: PDF (size: 88KB)
Epidemic Dynamics for the Two-stage Model on Scale-free Networks
Full Text (PDF, 88KB), PP.23-29
Views: 0 Downloads: 0
Author(s)
Maoxing Liu
1,*
Yunli Zhang
1
Wei Han
1
Index Terms
Complex network, Epidemic, Two-stage model, Threshold
Abstract
In this paper, we will study a two-stage model on complex networks. The dynamic behaviors of the model on a heterogeneous 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. Four immunization strategies, proportional immunization, targeted immunization, acquaintance immunization and active immunization are applied in this model. We show that both targeted and acquaintance immunization strategies compare favorably to a proportional scheme in terms of effectiveness. For active immunization, the threshold is easier to apply practically.
Cite This Paper
Maoxing Liu, Yunli Zhang, Wei Han, "Epidemic Dynamics for the Two-stage Model on Scale-free Networks", International Journal of Information Engineering and Electronic Business(IJIEEB), vol.3, no.1, pp.23-29, 2011. DOI:10.5815/ijieeb.2011.01.04
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.
[22]N. Madar, T. Kalisky, R. Cohen, D. ben-Avraham, and S. Havlin, Eur. Phys. J. B 38, (2004) 269 .
[23]Xinchu Fu, Michael Small, David M. Walker, and Haifeng Zhang, Epidemic dynamics on scale-free networks with piecewise linear infectivity and immunization, PHYSICAL REVIEW E 77, (2008) 036113.
[24]D. S. Callaway, M. E. J. Newman, S. H. Strogatz, and D. J.Watts, Phys. Rev. Lett. 85, (2000) 5468.
[25]R. Cohen, K. Erez, D. ben-Avraham, and S. Havlin, Phys. Rev.Lett. 85, (2000) 4626.