Mean-field theory of a recurrent epidemiological model

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

Volumn 79, Issue 6, 2009, Pages

  Nagy, Viktor ^a  

^a The Institute for Research in Electronics and Applied Physics   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ARBITRARY DEGREE; DEGREE DISTRIBUTIONS; DISCRETE TIME; EPIDEMIOLOGICAL MODELS; FIXED POINTS; INFECTION RATES; MEAN-FIELD EQUATIONS; NETWORK STRUCTURES; NUMERICAL SIMULATION; THEORETICAL RESULT;

CONTINUOUS TIME SYSTEMS;

MEAN FIELD THEORY;

EID: 67649510468     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.79.066105     Document Type: Article

References (15)

1. R. M. Anderson and R. M. May, Infectious Diseases of Humans (Oxford University Press, New York, 1991).
2. R. Pastor-Satorras and A. Vespignani, Phys. Rev. Lett. 86, 3200 (2001). 10.1103/PhysRevLett.86.3200
3. M. E. J. Newman, Phys. Rev. E 66, 016128 (2002). 10.1103/PhysRevE.66. 016128
4. Y. Moreno, R. Pastor-Satorras, and A. Vespignani, Eur. Phys. J. B 26, 521 (2002).
5. M. Barthelemy, A. Barrat, R. Pastor-Satorras, and A. Vespignani, Phys. Rev. Lett. 92, 178701 (2004). 10.1103/PhysRevLett.92.178701
6. M. Kuperman and G. Abramson, Phys. Rev. Lett. 86, 2909 (2001). 10.1103/PhysRevLett.86.2909
7. D. J. Watts and S. H. Strogatz, Nature (London) 393, 440 (1998). 10.1038/30918
8. G. Yan, Zhong-Qian Fu, J. Ren, and Wen-Xu Wang, Phys. Rev. E 75, 016108 (2007). 10.1103/PhysRevE.75.016108
9. Y. Kuramoto, Chemical Oscillations, Waves, and Turbulence (Springer, Berlin, 1984).
10. T. Gross, Carlos J. Dommar D'Lima, and B. Blasius, Phys. Rev. Lett. 96, 208701 (2006). 10.1103/PhysRevLett.96.208701
11. L. B. Shaw and I. B. Schwartz, Phys. Rev. E 77, 066101 (2008). 10.1103/PhysRevE.77.066101
12. M. Girvan, D. S. Callaway, M. E. J. Newman, and S. H. Strogatz, Phys. Rev. E 65, 031915 (2002). 10.1103/PhysRevE.65.031915
13. K. L. Cooke, D. F. Calef, and E. V. Level, Nonlinear Systems and its Applications (Academic, New York, 1977), pp. 73-93.
14. D. He and L. Stone, Proc. R. Soc. London, Ser. B 270, 1519 (2003). 10.1098/rspb.2003.2366
15. We emphasize that the curves given by Eqs. 22 23 are only possible stability boundaries of Eq. 20. For example, if we cross such a curve, one of the eigenvalues typically goes from |λ| <1 to |λ| >1, but if one of the other eigenvalues already has |λ| >1, then there is instability on both sides of the curve.