Weak mean-field approximation for discrete epidemic models in scale-free networks

Journal of Biological Systems

Volumn 19, Issue 3, 2011, Pages 403-416

  Wu, Qingchu ^a   Fu, Xinchu ^b  

^a JIANGXI NORMAL UNIVERSITY   (China)

^b SHANGHAI UNIVERSITY   (China)

Author keywords

Complex Networks; Discrete Models; Epidemic Dynamics; Mean Field Approximation

Indexed keywords

EID: 80052430234     PISSN: 02183390     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218339011003981     Document Type: Article

References (26)

1. Barabasi AL, Albert R, Emergence of scaling in random networks, Science 286509-286512, 1999.
2. Pastor-Satorras R, Vespignani A, Epidemic spreading in scale-free networks, Phys Rev Lett 86:3200-3203, 2001. (Pubitemid 32317894)
3. Pastor-Satorras R, Vespignani A, Infection dynamics in finite size scale-free networks, Phys Rev E 65:035108(R), 2002.
4. Santos FC, Rodrigues JF, Pacheco JM, Epidemic spreading and cooperation dynamics on homogeneous small-world networks, Phys Rev E 72:056128, 2005.
5. Newman MEJ, Spread of epidemic disease on networks, Phys Rev E 66:016128, 2002.
6. A. d'Onofrio, A note on the global behaviour of the network-based SIS epidemic model, Nonlinear Analysis RWA 9:1567-1572, 2008.
7. Wu QC, Fu XC, Small M, Zhang HF, Oscillations and phase transition in the mean infection rate of a finite population, Int J Mod Phys C 21:1207-1215, 2010.
8. Fu XC, Small M, Walker DM, Zhang HF, Epidemic dynamics on scale-free networks with piecewise linear infectivity and immunization, Phys Rev E 77:036113, 2008.
9. Nagy V, Mean-field theory of a recurrent epidemiological model, Phys Rev E 79:066105, 2009.
10. Yan G, Fu ZQ, Ren J, Wang WX, Collective synchronization induced by epidemic dynamics on complex networks with communities, Phys Rev E 75:016108, 2007.
11. Zhang HF, Zhang J, Zhou CS, Small M, Wang BH, Hub nodes inhibit the outbreak of epidemic under voluntary vaccination, New J Phys 12:023015, 2010.
12. Kiss IZ, Green DM, Kao RR, The effect of contact heterogeneity and multiple routes of transmission on final epidemic size, Math Biosci 203:124-136, 2006. (Pubitemid 44311149)
13. Wang Y, Chakrabarti D, Wangand C, Faloutsos C, Epidemic Spreading in Real Networks: An Eigenvalue Viewpoint, Proc IEEE SRDS, 2003.
14. Ball F, Neal P, Network epidemic models with two levels of mixing, Math Biosci 212:69-87, 2008.
15. Small M, Tse CK, Small world and scale free model of transmission of SARS, Int J Bifur and Chaos 15:1745-1755, 2005. (Pubitemid 40983165)
16. Small M, Walker DM, Tse CK, Scale-free distribution of avian influenza outbreaks, Phys Rev Lett 99:188702, 2007.
17. Castillo-Chavez C, Yakubu AA, Discrete-time S-I-S model with complex dynamics, Nonlinear Analysis 47:4753-4762, 2001. (Pubitemid 32724508)
18. Trapman P, On analytical approaches to epidemics on networks, Theor Popul Biol 71:160-173, 2007. (Pubitemid 46186472)
19. Volz E, Meyers LA, Epidemic thresholds in dynamic contact networks, J R Soc Interface 6:233-241, 2009.
20. Saramaki J, Kaski K, Sale-free networks generated by random walkers, Physica A 341:80-86, 2004.
21. Allen Linda JS, Driessche P. van den, The basic reproduction number in some discretetime epidemic models, J Difference Equations and Applications 14:1127-1147, 2008.
22. Reed WJ, A stochastic model for the spread of a sexually transmitted disease which results in a scale-free network, Math Biosci 201:3-14, 2006. (Pubitemid 43776244)
23. Gross T, DLima C, Dommar J, Blasius B, Epidemic dynamics on an adaptive network, Phys Rev Lett 96:208701, 2006.
24. Shaw LB, Schwartz IB, Fluctuating epidemics on adaptive networks, Phys Rev E 77:066101, 2008.
25. Funk S, Gilad E, Watkins C, Jansen VAA, The spread of awareness and its impact on epidemic outbreaks, Proc Natl Acad Sci USA 106:6872, 2009.
26. Lindquist J, Ma JL, Driessche P van den, Willeboordse FH, Effective degree network disease models, J Math Biol 62(2):143-164, 2011.