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The Effective Reproduction Number as a Prelude to Statistical Estimation of Time-Dependent Epidemic Trends

In: Mathematical and Statistical Estimation Approaches in Epidemiology

Author

Listed:
  • Hiroshi Nishiura

    (University of Utrecht, Theoretical Epidemiology)

  • Gerardo Chowell

    (Arizona State University, School of Human Evolution and Social Change
    Arizona State University, Mathematical, Computational, Modeling Sciences Center
    National Institutes of Health, Division of Epidemiology and Population Studies, Fogarty International Center)

Abstract

Although the basic reproduction number, R 0, is useful for understanding the transmissibility of a disease and designing various intervention strategies, the classic threshold quantity theoretically assumes that the epidemic first occurs in a fully susceptible population, and hence, R 0 is essentially a mathematically defined quantity. In many instances, it is of practical importance to evaluate time-dependent variations in the transmission potential of infectious diseases. Explanation of the time course of an epidemic can be partly achieved by estimating the effective reproduction number, R(t), defined as the actual average number of secondary cases per primary case at calendar time t (for t >0). R(t) shows time-dependent variation due to the decline in susceptible individuals (intrinsic factors) and the implementation of control measures (extrinsic factors). If R(t) 1). This chapter describes the primer of mathematics and statistics of R(t) and discusses other similar markers of transmissibility as a function of time.

Suggested Citation

  • Hiroshi Nishiura & Gerardo Chowell, 2009. "The Effective Reproduction Number as a Prelude to Statistical Estimation of Time-Dependent Epidemic Trends," Springer Books, in: Gerardo Chowell & James M. Hyman & Luís M. A. Bettencourt & Carlos Castillo-Chavez (ed.), Mathematical and Statistical Estimation Approaches in Epidemiology, pages 103-121, Springer.
    • Handle: RePEc:spr:sprchp:978-90-481-2313-1_5
    DOI: 10.1007/978-90-481-2313-1_5
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