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Nearly one dimensional dynamics in an epidemic.

W M Schaffer, M Kot

    Journal of Theoretical Biology
    |January 21, 1985
    PubMed
    Summary
    This summary is machine-generated.

    Measles outbreaks in NYC and Baltimore (1928-1963) exhibited chaotic dynamics, predictable by simple mathematical models. Noise impacts these epidemiological patterns, offering insights into disease spread.

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    Area of Science:

    • Epidemiology
    • Nonlinear Dynamics
    • Mathematical Biology

    Background:

    • Measles incidence data from New York City and Baltimore spanning 1928-1963.
    • Application of advanced nonlinear dynamics techniques to epidemiological time series.

    Purpose of the Study:

    • To analyze historical measles incidence data using nonlinear dynamics.
    • To identify underlying chaotic patterns in disease outbreaks.
    • To explore the influence of noise on epidemiological dynamics.

    Main Methods:

    • Utilized monthly case reports from 1928 to 1963.
    • Applied nonlinear dynamics techniques to analyze time-series data.
    • Modeled chaotic flows using one-dimensional, unimodal maps.

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    Main Results:

    • Identified nearly two-dimensional chaotic flows in measles incidence.
    • Demonstrated that one-dimensional, unimodal maps effectively capture essential attributes of these flows.
    • Discussed the significant effects of inherent noise in epidemiological systems.

    Conclusions:

    • Historical measles incidence displays complex, chaotic behavior.
    • Simple mathematical models can represent complex disease dynamics.
    • Noise is a critical factor influencing measles transmission patterns.