Nearly one dimensional dynamics in an epidemic

William M. Schaffer; Mark Kot

doi:10.1016/S0022-5193(85)80294-0

Nearly one dimensional dynamics in an epidemic

William M. Schaffer
, Mark Kot

Ecology and Evolutionary Biology

Research output: Contribution to journal › Article › peer-review

184 Scopus citations

Abstract

The incidence of measles in New York City and Baltimore was studied using recently developed techniques in nonlinear dynamics. The data, monthly case reports for the years 1928-1963, suggest almost two dimensional, chaotic flows whose essential attributes are captured by one dimensional, unimodal maps. The effects of noise, inevitable in ecological and epidemiological systems are discussed.

Original language	English (US)
Pages (from-to)	403-427
Number of pages	25
Journal	Journal of Theoretical Biology
Volume	112
Issue number	2
DOIs	https://doi.org/10.1016/S0022-5193(85)80294-0
State	Published - Jan 21 1985

ASJC Scopus subject areas

Statistics and Probability
Modeling and Simulation
General Biochemistry, Genetics and Molecular Biology
General Immunology and Microbiology
General Agricultural and Biological Sciences
Applied Mathematics

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10.1016/S0022-5193(85)80294-0

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title = "Nearly one dimensional dynamics in an epidemic",

abstract = "The incidence of measles in New York City and Baltimore was studied using recently developed techniques in nonlinear dynamics. The data, monthly case reports for the years 1928-1963, suggest almost two dimensional, chaotic flows whose essential attributes are captured by one dimensional, unimodal maps. The effects of noise, inevitable in ecological and epidemiological systems are discussed.",

author = "Schaffer, \{William M.\} and Mark Kot",

note = "Funding Information: Steve Ellner, Bob May and Harry Swinney were sources of good ideas and helpful commentary. Itamar Proccacia pointed out an error in a previous version of the paper. This work was supported by the University of Arizona. Most of the computations, including graphics, were performed on a TRS-80 Model II microcomputer. We thank the Tandy Corporation for manufacturing so fine a machine. WMS thanks his wife for tolerating its presence in their home.",

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N1 - Funding Information: Steve Ellner, Bob May and Harry Swinney were sources of good ideas and helpful commentary. Itamar Proccacia pointed out an error in a previous version of the paper. This work was supported by the University of Arizona. Most of the computations, including graphics, were performed on a TRS-80 Model II microcomputer. We thank the Tandy Corporation for manufacturing so fine a machine. WMS thanks his wife for tolerating its presence in their home.

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N2 - The incidence of measles in New York City and Baltimore was studied using recently developed techniques in nonlinear dynamics. The data, monthly case reports for the years 1928-1963, suggest almost two dimensional, chaotic flows whose essential attributes are captured by one dimensional, unimodal maps. The effects of noise, inevitable in ecological and epidemiological systems are discussed.

AB - The incidence of measles in New York City and Baltimore was studied using recently developed techniques in nonlinear dynamics. The data, monthly case reports for the years 1928-1963, suggest almost two dimensional, chaotic flows whose essential attributes are captured by one dimensional, unimodal maps. The effects of noise, inevitable in ecological and epidemiological systems are discussed.

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Nearly one dimensional dynamics in an epidemic

Abstract

ASJC Scopus subject areas

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