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

  • Hiroshi Nishiura
  • Gerardo Chowell


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, it suggests that the epidemic is in decline and may be regarded as being under control at time t (vice versa, 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.


Generation Time Reproduction Number Epidemic Model Basic Reproduction Number Calendar Time 
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Copyright information

© Springer Science+Business Media B.V. 2009

Authors and Affiliations

  • Hiroshi Nishiura
    • 1
  • Gerardo Chowell
    • 2
    • 3
    • 4
  1. 1.Theoretical EpidemiologyUniversity of UtrechtUtrechtThe Netherlands
  2. 2.School of Human Evolution and Social ChangeArizona State UniversityTempeUSA
  3. 3.Mathematical, Computational, Modeling Sciences CenterArizona State UniversityTempeUSA
  4. 4.Division of Epidemiology and Population Studies, Fogarty International CenterNational Institutes of HealthBethesdaUSA

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