Journal ArticleDOI
A simple model for complex dynamical transitions in epidemics.
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This work has shown that measles is a natural ecological system that exhibits different dynamical transitions at different times and places, yet all of these transitions can be predicted as bifurcations of a single nonlinear model.Abstract:
Dramatic changes in patterns of epidemics have been observed throughout this century. For childhood infectious diseases such as measles, the major transitions are between regular cycles and irregular, possibly chaotic epidemics, and from regionally synchronized oscillations to complex, spatially incoherent epidemics. A simple model can explain both kinds of transitions as the consequences of changes in birth and vaccination rates. Measles is a natural ecological system that exhibits different dynamical transitions at different times and places, yet all of these transitions can be predicted as bifurcations of a single nonlinear model.read more
Citations
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Journal ArticleDOI
The Mathematics of Infectious Diseases
TL;DR: Threshold theorems involving the basic reproduction number, the contact number, and the replacement number $R$ are reviewed for classic SIR epidemic and endemic models and results with new expressions for $R_{0}$ are obtained for MSEIR and SEIR endemic models with either continuous age or age groups.
Journal ArticleDOI
Networks and epidemic models.
TL;DR: A variety of methods are described that allow the mixing network, or an approximation to the network, to be ascertained and how the two fields of network theory and epidemiological modelling can deliver an improved understanding of disease dynamics and better public health through effective disease control are suggested.
Journal ArticleDOI
Seasonality and the dynamics of infectious diseases.
Sonia Altizer,Andrew P. Dobson,Parviez R. Hosseini,Peter J. Hudson,Mercedes Pascual,Pejman Rohani +5 more
TL;DR: Examples from human and wildlife disease systems are reviewed to illustrate the challenges inherent in understanding the mechanisms and impacts of seasonal environmental drivers, and to highlight general insights that are relevant to other ecological interactions.
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
Ecological forecasts: an emerging imperative.
James S. Clark,Steven R. Carpenter,Mary Barber,Scott L. Collins,Andrew P. Dobson,Jonathan A. Foley,David M. Lodge,Mercedes Pascual,Roger A. Pielke,William A. Pizer,Catherine M. Pringle,W. V. Reid,Kenneth A. Rose,Osvaldo E. Sala,William H. Schlesinger,Diana H. Wall,David N. Wear +16 more
TL;DR: Access to reliable forecasts of ecosystem state, ecosystem services, and natural capital will increase the ability to forecast ecosystem change and create a capacity to produce, evaluate, and communicate forecasts of critical ecosystem services.
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.
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Prevention of Population Cycles by Parasite Removal
TL;DR: Treatment of the grouse population prevented population crashes, demonstrating that parasites were the cause of the cyclic fluctuations.
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Meta) population dynamics of infectious diseases
Bryan T. Grenfell,John Harwood +1 more
TL;DR: The metapopulation concept provides a very powerful tool for analysing the persistence of spatially-disaggregated populations, in terms of a balance between local extinction and colonization.