Abstract
TEMPORAL changes in the incidence of measles virus infection within large urban communities in the developed world have been the focus of much discussion in the context of the identification and analysis of nonlinear and chaotic patterns in biological time series1–11. In contrast, the measles records for small isolated island populations are highly irregular, because of frequent fade-outs of infection12–14, and traditional analysis15 does not yield useful insight. Here we use measurements of the distribution of epidemic sizes and duration to show that regularities in the dynamics of such systems do become apparent. Specifically, these biological systems are characterized by well-defined power laws in a manner reminiscent of other nonlinear, spatially extended dynamical systems in the physical sciences16–19. We further show that the observed power-law exponents are well described by a simple lattice-based model which reflects the social interaction between individual hosts.
This is a preview of subscription content, access via your institution
Access options
Subscribe to this journal
Receive 51 print issues and online access
$199.00 per year
only $3.90 per issue
Buy this article
- Purchase on Springer Link
- Instant access to full article PDF
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
References
May, R. M. Nature 261, 459–467 (1967).
May, R. M. Proc. R. Soc. Lond. A 413, 27–44 (1987).
Grenfell, B. T. J. R. statist Soc. B 54, 383–398 (1992).
Grenfell, B. T., Kleczkowski, A., Ellner, S. & Bolker, B. M. Phil. Trans. R. Soc. Lond. A 348, 515–530 (1994).
Bolker, B. M. & Grenfell, B. T. Proc. R. Soc. Lond. B 251, 75–81 (1993).
Grenfell, B. T., Bolker, B. M. & Kleczkowski, A. Proc. R. Soc. Lond. B 259, 97–103 (1995).
Olsen, L. F., Truty, G. L. & Schaffer, W. M. Theor. Pop. Biol. 33, 344–370 (1988).
Olsen, L. F. & Schaffer, W. M. Science 249, 499–504 (1990).
Sugihara, G. & May, R. M. Nature 344, 734–741 (1990).
Sugihara, G., Grenfell, B. & May, R. M. Phil. Trans. R. Soc. Lond. B 330, 235–251 (1990).
Tidd, C. W., Olsen, L. F. & Schaffer, W. M. Proc. R. Soc. Lond. B 254, 257–273 (1993).
Bartlett, M. S. J. R. statist. Soc. A 120, 48–70 (1957).
Bartlett, M. S. J. R. statist. Soc. A 123, 37–44 (1960).
Black, F. L. J. theor. Biol. 11, 207–211 (1966).
Anderson, R. M. & May, R. M. Infectious Diseases of Humans, Dynamics and Control (Oxford Univ. Press, 1991).
Bak, P., Tang, C. & Weisenfeld, K. S. Phys. Rev. A 38, 364–374 (1988).
Chen, K., Bak, P. & Obukhov, S. P. Phys. Rev. A 43, 620–635 (1991).
Clar, S., Drossel, B. & Schwabl, F. Phys. Rev. E 50, 1009–1018 (1994).
Sornette, A. & Sornette, D. Europhys. Lett. 9, 197–202 (1989).
Cliff, A. D., Haggett, P. & Smallman-Raynor, M. Measles. An Historical Geography of a Major Human Viral Disease from Global Expansion to Local Retreat 1840–1990 (Blackwell, Oxford, 1993).
Gutenberg, B. & Richter, C. F. Ann. Geofis. 9, 1–10 (1956).
Bak, P., Chen, K. & Tang, C. Phys. Lett. A 147, 297–300 (1990).
Drossel, B. & Schwabl, F. Phys. Rev. Lett. 69, 1629–1632 (1992).
Ferguson, N., May, R. M. & Anderson, R. M. in Spatial Ecology: The Role of Space in Population Dynamics and Interspecific Interactions (eds Tilman, D. & Kareiva, P.) (Princeton Monographs in Population Biology, in the press).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Rhodes, C., Anderson, R. Power laws governing epidemics in isolated populations. Nature 381, 600–602 (1996). https://doi.org/10.1038/381600a0
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1038/381600a0
This article is cited by
-
A spatio-temporal analysis of dengue spread in a Brazilian dry climate region
Scientific Reports (2021)
-
A novel geo-hierarchical population mobility model for spatial spreading of resurgent epidemics
Scientific Reports (2021)
-
Signatures of self-organized criticality in an ultracold atomic gas
Nature (2020)
-
Navigable networks as Nash equilibria of navigation games
Nature Communications (2015)
-
A measure of individual role in collective dynamics
Scientific Reports (2012)
Comments
By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.