Accurate noise projection for reduced stochastic epidemic models

Chaos

Volumn 19, Issue 4, 2009, Pages

  Forgoston, Eric ^a   Billings, Lora ^b   Schwartz, Ira B ^a  

^a NAVAL RESEARCH LABORATORY   (United States)

^b MONTCLAIR STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

ANIMAL; ARTICLE; BIOLOGICAL MODEL; COMPUTER SIMULATION; EPIDEMIC; HUMAN; METHODOLOGY; NONLINEAR SYSTEM; POPULATION DYNAMICS; PREVALENCE; RISK ASSESSMENT; RISK FACTOR; STATISTICAL MODEL; STATISTICS;

ANIMALS; COMPUTER SIMULATION; DISEASE OUTBREAKS; HUMANS; MODELS, BIOLOGICAL; MODELS, STATISTICAL; NONLINEAR DYNAMICS; POPULATION DYNAMICS; PREVALENCE; RISK ASSESSMENT; RISK FACTORS; STOCHASTIC PROCESSES;

EID: 74349095208     PISSN: 10541500     EISSN: None     Source Type: Journal    
DOI: 10.1063/1.3247350     Document Type: Article

References (35)

1. R. M. Anderson and R. M. May, Infectious Diseases of Humans (Oxford University Press, New York, 1991).
2. N. T. J. Bailey, The Mathematical Theory of Infectious Diseases (Griffin, London, 1975).
3. G. Marion, E. Renshaw, and G. Gibson, Theor Popul. Biol. 0040-5809 57, 197 (2000). 10.1006/tpbi.2000.1450 (Pubitemid 30369055)
4. H. T. H. Nguyen and P. Rohani, J. R. Soc., Interface 1742-5689 5, 403 (2008). 10.1098/rsif.2007.1168 (Pubitemid 351253065)
5. P. Rohani, M. J. Keeling, and B. T. Grenfell, Am. Nat. 0003-0147 159, 469 (2002). 10.1086/339467 (Pubitemid 34443778)
6. D. A. Rand and H. B. Wilson, Proc. R. Soc. London, Ser. B 0962-8452 246, 179 (1991). 10.1098/rspb.1991.0142
7. L. Billings, E. M. Bollt, and I. B. Schwartz, Phys. Rev. Lett. 0031-9007 88, 234101 (2002). 10.1103/PhysRevLett.88.234101
8. L. Stone, R. Olinky, and A. Huppert, Nature (London) 0028-0836 446, 533 (2007). 10.1038/nature05638 (Pubitemid 46514727)
9. I. B. Schwartz, L. Billings, and E. M. Bollt, Phys. Rev. E 1063-651X 70, 046220 (2004). 10.1103/PhysRevE.70.046220 (Pubitemid 40010354)
10. R. Pastor-Satorras and A. Vespignani, Phys. Rev. E 1063-651X 63, 066117 (2001). 10.1103/PhysRevE.63.066117
11. Y. Moreno, R. Pastor-Satorras, and A. Vespignani, Eur. Phys. J. B 1434-6028 26, 521 (2002).
12. A. Vazquez, Phys. Rev. E 1063-651X 74, 056101 (2006). 10.1103/PhysRevE.74.056101 (Pubitemid 44684177)
13. D. J. Watts, R. Muhamad, D. C. Medina, and P. S. Dodds, Proc. Natl. Acad. Sci. U.S.A. 0027-8424 102, 11157 (2005). 10.1073/pnas.0501226102 (Pubitemid 41153791)
14. V. Colizza, A. Barrat, M. Barthelemy, and A. Vespignani, Bull. Math. Biol. 0092-8240 68, 1893 (2006). 10.1007/s11538-006-9077-9 (Pubitemid 44705853)
15. L. B. Shaw and I. B. Schwartz, Phys. Rev. E 1063-651X 77, 066101 (2008). 10.1103/PhysRevE.77.066101
16. W. T. Mocek, R. Rudnicki, and E. O. Voit, Math. Biosci. 0025-5564 198, 190 (2005). 10.1016/j.mbs.2005.08.001 (Pubitemid 41715120)
17. E. Forgoston and I. B. Schwartz, SIAM J. Appl. Dyn. Syst. 1536-0040 8, 1190 (2009). 10.1137/090755710
18. P. Boxler, Probab. Theory Relat. Fields 0178-8051 83, 509 (1989). 10.1007/BF01845701
19. P. H. Coullet, C. Elphick, and E. Tirapegui, Phys. Lett. A 0375-9601 111, 277 (1985). 10.1016/0375-9601(85)90626-7
20. E. Knobloch and K. A. Wiesenfeld, J. Stat. Phys. 0022-4715 33, 611 (1983). 10.1007/BF01018837
21. N. S. Namachchivaya, Appl. Math. Comput. 0096-3003 38, 101 (1990). 10.1016/0096-3003(90)90051-4
22. N. S. Namachchivaya and Y. K. Lin, Int. J. Non-Linear Mech. 0020-7462 26, 931 (1991). 10.1016/0020-7462(91)90042-R
23. L. Arnold, Random Dynamical Systems (Springer-Verlag, Berlin, 1998).
24. L. Arnold and P. Imkeller, Probab. Theory Relat. Fields 0178-8051 110, 559 (1998). 10.1007/s004400050159 (Pubitemid 128086343)
25. A. J. Roberts, Physica A 0378-4371 387, 12 (2008). 10.1016/j.physa.2007. 08.023 (Pubitemid 350051255)
26. I. Schwartz and H. Smith, J. Math. Biol. 0303-6812 18, 233 (1983). 10.1007/BF00276090
27. L. Billings and I. B. Schwartz, J. Math. Biol. 0303-6812 44, 31 (2002). 10.1007/s002850100110 (Pubitemid 44200140)
28. Mathematical Epidemiology, edited by, F. Brauer, P. van den Driessche, and, J. Wu, (Springer-Verlag, Berlin, 2008).
29. O. N. Bjørnstad, B. F. Finkenstädt, and B. T. Grenfell, Ecol. Monogr. 0012-9615 72, 169 (2002).
30. M. W. Hirsch and S. Smale, Differential Equations, Dynamical Systems, and Linear Algebra (Academic, New York, 1974).
31. S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos (Springer-Verlag, Berlin, 1990).
32. J. Carr, Applications of Centre Manifold Theory (Springer-Verlag, Berlin, 1981).
33. A. Doostan, R. G. Ghanem, and J. Red-Horse, Comput. Methods Appl. Mech. Eng. 0045-7825 196, 3951 (2007). 10.1016/j.cma.2006.10.047 (Pubitemid 47029549)
34. D. Venturi, X. Wan, and G. E. Karniadakis, J. Fluid Mech. 0022-1120 606, 339 (2008). 10.1017/S0022112008001821 (Pubitemid 351850786)
35. M. I. Dykman, I. B. Schwartz, and A. S. Landsman, Phys. Rev. Lett. 0031-9007 101, 078101 (2008). 10.1103/PhysRevLett.101.078101