Exact solution of a stochastic susceptible-infectious-recovered model

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

Volumn 78, Issue 6, 2008, Pages

  Schütz, Gunter M ^a,b   Brandaut, Marian ^c   Trimper, Steffen ^c  

^a FORSCHUNGSZENTRUM JÜLICH   (Germany)

^b UNIVERSITY OF BONN   (Germany)

^c MARTIN LUTHER UNIVERSITY HALLE WITTENBERG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

DIFFERENTIAL EQUATIONS; MATHEMATICAL OPERATORS; MEAN FIELD THEORY; POPULATION STATISTICS; REACTION RATES;

AND RECOVERIES; CONNECTED GRAPHS; EVOLUTION EQUATIONS; EXACT RESULTS; EXACT SOLUTIONS; FIELD THEORIES; INDIVIDUAL-BASED; INFECTION RATES; INITIAL CONDITIONS; ISOLATED REGIONS; LINEAR CHAINS; MASTER EQUATIONS; OUT OF EQUILIBRIUMS; POPULATION SIZES; RANDOM INITIAL CONDITIONS; SIR MODELS; SPIN OPERATORS; STATIONARY DISTRIBUTIONS; TIME EVOLUTIONS; UNCORRELATED;

STOCHASTIC MODELS;

EID: 58249109573     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.78.061132     Document Type: Article

References (28)

1. W. O. Kermack and A. G. McKendrick, Proc. R. Soc. Edinburgh 115, 700 (1927).
2. O. Dieckmann and J. A. P. Heersterbeeck, Mathematical Epidemiology of Infectious Diseases (Wiley, New York, 2000).
3. J. D. Murray, Mathematical Biology I: An Introduction (Springer-Verlag, Berlin, 2002).
4. J. Satsuma, R. Willox, A. Ramani, B. Grammaticos, and A. S. Carstea, Physica A 336, 369 (2004). 10.1016/j.physa.2003.12.035
5. J. Wu, Z. Gao, and H. Sun, Mod. Phys. Lett. B 18, 1537 (2004). 10.1142/S0217984904008031
6. J. Joo and J. L. Lebowitz, Phys. Rev. E 70, 036114 (2004). 10.1103/PhysRevE.70.036114
7. N. Madar, T. Kalisky, R. Cohen, D. ben-Avraham, and S. Havlin, Eur. Phys. J. B 38, 269 (2004). 10.1140/epjb/e2004-00119-8
8. M. G. M. Gomes, A. Margheri, G. F. Medley, and C. Rebelo, J. Math. Biol. 51, 414 (2005). 10.1007/s00285-005-0331-9
9. N. Stollenwerk, J. Martins, and A. Pinto, Phys. Lett. A 371, 379 (2007). 10.1016/j.physleta.2007.06.040
10. Da-Fang Zheng, P. M. Hui, S. Trimper, and B. Zheng, Physica A 352, 659 (2005). 10.1016/j.physa.2004.12.049
11. A. Grabowski and R. A. Kosiński, Phys. Rev. E 70, 031908 (2004). 10.1103/PhysRevE.70.031908
12. H. N. Agiza, A. S. Elgazzar, and S. A. Youssef, Int. J. Mod. Phys. C 14, 825 (2003). 10.1142/S0129183103004978
13. A. Vazquez, Phys. Rev. E 74, 056101 (2006). 10.1103/PhysRevE.74.056101
14. R. Yang, B.-H. Wang, J. Ren, W.-J. Bai, Z.-W. Shi, W.-X. Wang, and T. Zao, Phys. Lett. A 364, 189 (2007). 10.1016/j.physleta.2006.12.021
15. R. Albert and A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002). 10.1103/RevModPhys.74.47
16. N. G. van Kampen, Stochastic Processes in Physics and Chemistry (North-Holland, Amsterdam, 1992).
17. M. Doi, J. Phys. A 9, 1465 (1976); 10.1088/0305-4470/9/9/008
18. M. Doi, J. Phys. A 9, 1479 (1976). 10.1088/0305-4470/9/9/009
19. P. Grassberger and M. Scheunert, Fortschr. Phys. 28, 547 (1980). 10.1002/prop.19800281004
20. S. Sandow and S. Trimper, Europhys. Lett. 21, 799 (1993). 10.1209/0295-5075/21/8/001
21. D. C. Mattis and M. L. Glasser, Rev. Mod. Phys. 70, 979 (1998). 10.1103/RevModPhys.70.979
22. G. M. Schütz, in Phase Transitions and Critical Phenomena, edited by, C. Domb, and, L. Lebowitz, (Academic Press, London, 2001), Vol. 19.
23. T. Michael, S. Trimper, and M. Schulz, Phys. Rev. E 73, 062101 (2006). 10.1103/PhysRevE.73.062101
24. E. Ben-Naim and P. L. Krapivsky, Phys. Rev. E 69, 050901 (R) (2004). 10.1103/PhysRevE.69.050901
25. T. Reichenbach, M. Mobilia, and E. Frey, Phys. Rev. Lett. 99, 238105 (2007). 10.1103/PhysRevLett.99.238105
26. R. Glauber, J. Math. Phys. 4, 294 (1963). 10.1063/1.1703954
27. I. Peschel, V. Rittenberg, and U. Schulze, Nucl. Phys. B 430, 633 (1994). 10.1016/0550-3213(94)90163-5
28. J. W. Evans and D. ben-Avraham, in Nonequilibrium Statistical Mechanics in One Dimension, edited by, V. Privman, (Cambridge University Press, Cambridge, England, 1997).