Stochastic amplification in epidemics

Journal of the Royal Society Interface

Volumn 4, Issue 14, 2007, Pages 575-582

  Alonso, David ^a   McKane, Alan J ^b   Pascual, Mercedes ^a  

^a UNIVERSITY OF MICHIGAN   (United States)

^b UNIVERSITY OF MANCHESTER   (United Kingdom)

Author keywords

Childhood diseases; Endogenous stochastic resonance; Epidemics; Oscillations; Stochastic modelling

Indexed keywords

ARTICLE; CHILDHOOD DISEASE; DISEASE COURSE; DISEASE TRANSMISSION; EPIDEMIOLOGICAL DATA; POPULATION DYNAMICS; SEASONAL VARIATION; STOCHASTIC MODEL;

EID: 34249804787     PISSN: 17425689     EISSN: 17425662     Source Type: Journal    
DOI: 10.1098/rsif.2006.0192     Document Type: Article

References (32)

1. Bartlett, M. S. 1957 Measles periodicity and community size. J. R. Stat. Soc. A 120, 37-44.
2. Bauch, C. T. & Earn, D. J. D. 2003a Interepidemic intervals in forced and unforced SEIR models. Fields Inst. Commun. 36, 33-44.
3. Bauch, C. T. & Earn, D. J. D. 20036 Transients and attractors in epidemics. Proc. R. Soc. B 270, 1573-1578. (doi:10.1098/rspb.2003. 2410)
4. Bjørnstad, O. N., Finkenstädt, B. F. & Grenfell, B. T. 2002 Dynamics of measles epidemics: estimating scaling transmission rates using a time series SIR model. Ecol. Monogr. 72, 169-184.
5. Bolker, B. M. & Grenfell, B. T. 1995 Impact of vaccination on the spatial correlation and persistence of measles dynamics. Proc. Natl Acad. Sci. USA 93, 12 648-12 653. (doi:10.1073/pnas.93.22.12648)
6. Dekker, H. 1980a Critical dynamics and the expansion of the master equation including a critical point. Diffusion approximation. Physica A 103, 55-79. (doi:10.1016/0378-4371(80)90207-1)
7. Dekker, H. 1980b Critical dynamics and the expansion of the master equation including a critical point. General Markov processes. Physica A 103, 80-98. (doi: 10.1016/0378-4371(80)90208-3)
8. de Valpine, D. P. & Hastings, A. 2002 Fitting population models with process noise and observation error. Ecol. Monogr. 72, 57-76.
9. Durrett, R. & Levin, S. 1994 The importance of being discrete (and spatial). Theor. Popul. Biol. 46, 363-394. (doi:10.1006/tpbi.l994. 1032)
10. Dushoff, J., Plotkin, J. B., Levin, S. A. & Earn, D. J. D. 2004 Dynamical resonance can account for seasonality of influenza epidemics. Proc. Natl Acad. Sci. USA 101, 16 915-16 916. (doi:10.1073/pnas. 0407293101)
11. Earn, D. J. D., Rohani, P., Bolker, B. M. & Grenfell, B. T. 2000 A simple model for complex dynamical transitions in epidemics. Science 287, 667-670. (doi:10.1126/science.287.5453.667)
12. Gillespie, D. T. 1976 A general method for numerically simulating the stochastic time evolution of coupled chemical reactions. J. Comput. Phys. 22, 403-434. (doi:10.1016/0021-9991(76)90041-3)
13. Grassly, N. C., Frasser, C. & Garnett, G. P. 2005 Host immunity and synchronized epidemics of syphilis across the United States. Nature 433, 417-421. (doi:10.1038/nature03072)
14. Grenfell, B. T., Bjørnstad, O. N. & Finkenstadt, B. F. 2002 Dynamics of measles epidemics: scaling noise, determinism, and predictability with the TSIR model. Ecol. Monogr. 72, 185-202.
15. Hastings, A. 2001 Transient dynamics and persistence of ecological systems. Ecol. Lett. 4, 215-220. (doi:10.1046/j.1461-0248.2001. 00220.x)
16. Hastings, A. 2004 Transients: the key to long-term ecological understanding? Trends Ecol. Evol. 19, 39-45. (doi: 10.1016/j.tree.2003.09.007)
17. Hethcote, H. W. 1998 Oscillations in an endemic model for pertussis. Can. Appl. Math. Q. 6, 61-88.
18. Hethcote, H. W. & Levin, S. A. 1989 Periodicity in epidemiological models. In Applied mathematical ecology (eds L. Gross, T. G. Hallam & S. A. Levin), pp. 193-211. Berlin, Germany: Springer.
19. Jansen, V. A. A., Stollenwerk, N., Jensen, H. J., Ramsay, M. E., Edmunds, W. J. & Rhodes, C. J. 2003 Measles outbreaks in a population with declining vaccine uptake. Science 301, 804. (doi:10.1126/science.1086726)
20. Keeling, M. J., Rohani, P. & Grenfell, B. T. 2001 Seasonally forced disease dynamics explored as switching between attractors. Physica D 148, 317-335. (doi:10.1016/S0167-2789(00)00187-1)
21. Lloyd, A. L. & Jansen, V. V. A. 2002 Spatiotemporal dynamics of epidemics: synchrony in metapopulation models. Math. Biosci. 5, 20-29.
22. May, R. M. 2000 Simple rules with complex dynamics. Science 287, 601-602. (doi:10.1126/science.287.5453.601)
23. McKane, A. J. & Newman, T. J. 2005 Predator-prey cycles from resonant amplification of demographic stochasticity. Phys. Rev. Lett. 94, 218 102. (doi:10.1103/PhysRevLett.94.218102)
24. Neubert, R. & Caswell, H. 1997 Alternatives to resilience for measuring the responses of ecological systems to perturbations. Ecology 78, 653-665. (doi:10.2307/2266047)
25. Nisbet, R. M. & Gurney, W. S. C. 1982 Modelling fluctuating populations. New York, NY: Wiley.
26. Olsen, L. F. & Schaffer, W. M. 1990 Chaos versus noisy periodicity: an alternative hypothesis for childhood epidemics. Science 249, 499-504. (doi:10.1126/science.2382131)
27. Rand, D. A. & Wilson, H. B. 1991 Chaotic stochasticity: a ubiquitous source of unpredictability in epidemics. Proc. R. Soc. B 246, 179-184.
28. Rohani, P., Earn, D. J. D. & Grenfell, B. T. 1999 Opposite patterns of synchrony in sympatric disease metapopulations. Science 286, 968-971. (doi:10.1126/science.286.5441.968)
29. Rohani, P., Keeling, M. J. & Grenfell, B. T. 2002 The interplay between determinism and stochasticity in childhood diseases. Am. Nat. 159, 469-481. (doi:10.1086/339467)
30. Sidorowich, J. J. 1992 Repellors attract attention. Nature 355, 584-585. (doi:10.1038/355584a0)
31. van Kampen, N. G. 1992 Stochastic processes in physics and chemistry. Amsterdam, The Netherlands: Elsevier.
32. Xia, Y., Bjørnstad, O. N. & Grenfell, B. T. 2004 Measles metapopulation dynamics: a gravity model for epidemiological coupling and dynamics. Am. Nat. 164, 267-268. (doi:10.1086/422341)