Mathematical and Statistical Estimation Approaches in Epidemiology
pp 103121
The Effective Reproduction Number as a Prelude to Statistical Estimation of TimeDependent 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
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 timedependent 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 timedependent 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.
 Title
 The Effective Reproduction Number as a Prelude to Statistical Estimation of TimeDependent Epidemic Trends
 Book Title
 Mathematical and Statistical Estimation Approaches in Epidemiology
 Pages
 pp 103121
 Copyright
 2009
 DOI
 10.1007/9789048123131_5
 Print ISBN
 9789048123124
 Online ISBN
 9789048123131
 Publisher
 Springer Netherlands
 Copyright Holder
 Springer Science+Business Media B.V.
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 Editors

 Dr. Gerardo Chowell ^{(1)}
 Dr. James M. Hyman ^{(2)}
 Dr. Luís M. A. Bettencourt ^{(2)}
 Carlos CastilloChavez ^{(3)}
 Editor Affiliations

 1. Arizona State University School of Human Evolution & Social Change
 2. Los Alamos National Laboratory
 3. Dept. Mathematics & Statistics, Arizona State University
 Authors

 Hiroshi Nishiura ^{(4)}
 Gerardo Chowell ^{(5)} ^{(6)} ^{(7)}
 Author Affiliations

 4. Theoretical Epidemiology, University of Utrecht, Yalelaan 7, Utrecht, 3584 CL, The Netherlands
 5. School of Human Evolution and Social Change, Arizona State University, Box 872402, Tempe, AZ 85287, USA
 6. Mathematical, Computational, Modeling Sciences Center, Arizona State University, Tempe, AZ 85287, USA
 7. Division of Epidemiology and Population Studies, Fogarty International Center, National Institutes of Health, Bethesda, MD, USA
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