Chapter

Mathematical and Statistical Estimation Approaches in Epidemiology

pp 103-121

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

  • Hiroshi NishiuraAffiliated withTheoretical Epidemiology, University of Utrecht
  • , Gerardo ChowellAffiliated withSchool of Human Evolution and Social Change, Arizona State UniversityMathematical, Computational, Modeling Sciences Center, Arizona State UniversityDivision of Epidemiology and Population Studies, Fogarty International Center, National Institutes of Health

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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, 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.