Journal ArticleDOI
Power laws governing epidemics in isolated populations
C. J. Rhodes,Roy M. Anderson +1 more
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Measurements of the distribution of epidemic sizes and duration are used to show that regularities in the dynamics of such systems do become apparent and that the observed power-law exponents are well described by a simple lattice-based model which reflects the social interaction between individual hosts.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.read more
Citations
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Journal ArticleDOI
Self-organized criticality
TL;DR: In this paper, the authors introduced the concept of self-organized criticality to explain the behavior of the sandpile model, where particles are randomly dropped onto a square grid of boxes and when a box accumulates four particles they are redistributed to the four adjacent boxes or lost off the edge of the grid.
Journal ArticleDOI
Travelling waves and spatial hierarchies in measles epidemics
TL;DR: This work demonstrates recurrent epidemic travelling waves in an exhaustive spatio-temporal data set for measles in England and Wales and uses wavelet phase analysis, which allows for dynamical non-stationarity—a complication in interpreting spatio–temporal patterns in these and many other ecological time series.
Journal ArticleDOI
Population Biology of Multihost Pathogens
TL;DR: The majority of pathogens, including many of medical and veterinary importance, can infect more than one species of host, and factors that predispose pathogens to generalism include high levels of genetic diversity and abundant opportunities for cross-species transmission.
Journal ArticleDOI
Forest fires: An example of self-organized critical behavior
TL;DR: A simple forest fire model, which is an example of self-organized criticality, exhibits power-law frequency-area statistics over many orders of magnitude, which can be used to quantify the risk of large fires.
Journal ArticleDOI
Dynamics of measles epidemics: Estimating scaling of transmission rates using a time series sir model
TL;DR: In this paper, the authors developed a model, the TSIR (Time-series Suscep- tible-Infected-Recovered) model, that can capture both endemic cycles and episodic out-breaks in measles.
References
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Book
Infectious Diseases of Humans: Dynamics and Control
Roy M. Anderson,Robert M. May +1 more
TL;DR: This book discusses the biology of host-microparasite associations, dynamics of acquired immunity heterogeneity within the human community indirectly transmitted helminths, and the ecology and genetics of hosts and parasites.
Journal ArticleDOI
Simple mathematical models with very complicated dynamics
Robert M. May,Robert M. May +1 more
TL;DR: This is an interpretive review of first-order difference equations, which can exhibit a surprising array of dynamical behaviour, from stable points, to a bifurcating hierarchy of stable cycles, to apparently random fluctuations.
Journal ArticleDOI
Self-organized criticality
TL;DR: In this article, the authors show that certain extended dissipative dynamical systems naturally evolve into a critical state, with no characteristic time or length scales, and the temporal fingerprint of the self-organized critical state is the presence of flicker noise or 1/f noise; its spatial signature is the emergence of scale-invariant (fractal) structure.
Journal ArticleDOI
Nonlinear forecasting as a way of distinguishing chaos from measurement error in time series
George Sugihara,Robert M. May +1 more
TL;DR: An approach is presented for making short-term predictions about the trajectories of chaotic dynamical systems, applied to data on measles, chickenpox, and marine phytoplankton populations, to show how apparent noise associated with deterministic chaos can be distinguished from sampling error and other sources of externally induced environmental noise.