### 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.

Original language | English (US) |
---|---|

Title of host publication | Mathematical and Statistical Estimation Approaches in Epidemiology |

Publisher | Springer Netherlands |

Pages | 103-121 |

Number of pages | 19 |

ISBN (Print) | 9789048123124 |

DOIs | |

State | Published - 2009 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Mathematical and Statistical Estimation Approaches in Epidemiology*(pp. 103-121). Springer Netherlands. https://doi.org/10.1007/978-90-481-2313-1_5

**The effective reproduction number as a prelude to statistical estimation of time-dependent epidemic trends.** / Nishiura, Hiroshi; Chowell, Gerardo.

Research output: Chapter in Book/Report/Conference proceeding › Chapter

*Mathematical and Statistical Estimation Approaches in Epidemiology.*Springer Netherlands, pp. 103-121. https://doi.org/10.1007/978-90-481-2313-1_5

}

TY - CHAP

T1 - The effective reproduction number as a prelude to statistical estimation of time-dependent epidemic trends

AU - Nishiura, Hiroshi

AU - Chowell, Gerardo

PY - 2009

Y1 - 2009

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=75449113428&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=75449113428&partnerID=8YFLogxK

U2 - 10.1007/978-90-481-2313-1_5

DO - 10.1007/978-90-481-2313-1_5

M3 - Chapter

SN - 9789048123124

SP - 103

EP - 121

BT - Mathematical and Statistical Estimation Approaches in Epidemiology

PB - Springer Netherlands

ER -