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Estimation for discrete time branching processes with application to epidemics

N Becker

    Biometrics
    |September 1, 1977
    PubMed
    Summary
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    This study examines branching process estimators under different models, finding some remain robust for predicting subcritical behavior. This robustness aids in estimating community immunity needs, as shown with smallpox data.

    Area of Science:

    • Branching process theory
    • Stochastic modeling
    • Epidemic modeling

    Background:

    • Galton-Watson processes are fundamental stochastic models.
    • Estimating offspring distribution means is crucial for process analysis.
    • Real-world processes often deviate from simple Galton-Watson assumptions.

    Purpose of the Study:

    • To evaluate the robustness of estimators for the mean offspring distribution of Galton-Watson processes.
    • To determine estimator consistency under alternative models like multitype or random environment branching processes.
    • To inform the selection of estimators for practical applications, such as epidemic control.

    Main Methods:

    • Asymptotic analysis of estimator behavior.
    • Comparison of estimator performance under standard vs. alternative branching process models.

    Related Experiment Videos

  • Application of findings to estimate herd immunity thresholds.

    • Main Results:

    • Identified specific estimators that maintain consistency in indicating subcriticality even with altered underlying models.
    • Demonstrated the 'robustness' of certain estimators against model misspecification.
    • Quantified the impact of estimator choice on epidemic threshold estimation.

    Conclusions:

    • Certain estimators for Galton-Watson processes exhibit desirable robustness.
    • Robust estimators are valuable for accurately assessing epidemic potential and required immunity levels.
    • The study provides a framework for selecting reliable estimators in complex population dynamics scenarios.