### Abstract

The basic reproduction number (R_{0}) is a central quantity in epidemiology as it measures the transmission potential of infectious diseases. In this chapter we review the basic theory of the spread of infectious diseases using simple compartmental models based on ordinary differential equations including the simple Kermack-McKendrick epidemic model, SIR (susceptible- infectious-removed) models with demographics, the SIS (susceptible-infectious- susceptible) model, backward bifurcations, endemic equilibria, and the analytical derivation of R_{0} using the next-generation approach. This theory is followed by simple methodology for the estimation of R_{0} with its corresponding uncertainty from epidemic time series data. The 1918-1919 influenza pandemic in Winnipeg, Canada, and the 1968 influenza pandemic in US cities are used for illustration.

Original language | English (US) |
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Title of host publication | Mathematical and Statistical Estimation Approaches in Epidemiology |

Publisher | Springer Netherlands |

Pages | 1-30 |

Number of pages | 30 |

ISBN (Print) | 9789048123124 |

DOIs | |

State | Published - 2009 |

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### Keywords

- Basic reproduction number
- Epidemiology
- Influenza
- Model
- Pandemic

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Mathematical and Statistical Estimation Approaches in Epidemiology*(pp. 1-30). Springer Netherlands. https://doi.org/10.1007/978-90-481-2313-1_1

**The basic reproduction number of infectious diseases : Computation and estimation using compartmental epidemic models.** / Chowell, Gerardo; Brauer, Fred.

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

*Mathematical and Statistical Estimation Approaches in Epidemiology.*Springer Netherlands, pp. 1-30. https://doi.org/10.1007/978-90-481-2313-1_1

}

TY - CHAP

T1 - The basic reproduction number of infectious diseases

T2 - Computation and estimation using compartmental epidemic models

AU - Chowell, Gerardo

AU - Brauer, Fred

PY - 2009

Y1 - 2009

N2 - The basic reproduction number (R0) is a central quantity in epidemiology as it measures the transmission potential of infectious diseases. In this chapter we review the basic theory of the spread of infectious diseases using simple compartmental models based on ordinary differential equations including the simple Kermack-McKendrick epidemic model, SIR (susceptible- infectious-removed) models with demographics, the SIS (susceptible-infectious- susceptible) model, backward bifurcations, endemic equilibria, and the analytical derivation of R0 using the next-generation approach. This theory is followed by simple methodology for the estimation of R0 with its corresponding uncertainty from epidemic time series data. The 1918-1919 influenza pandemic in Winnipeg, Canada, and the 1968 influenza pandemic in US cities are used for illustration.

AB - The basic reproduction number (R0) is a central quantity in epidemiology as it measures the transmission potential of infectious diseases. In this chapter we review the basic theory of the spread of infectious diseases using simple compartmental models based on ordinary differential equations including the simple Kermack-McKendrick epidemic model, SIR (susceptible- infectious-removed) models with demographics, the SIS (susceptible-infectious- susceptible) model, backward bifurcations, endemic equilibria, and the analytical derivation of R0 using the next-generation approach. This theory is followed by simple methodology for the estimation of R0 with its corresponding uncertainty from epidemic time series data. The 1918-1919 influenza pandemic in Winnipeg, Canada, and the 1968 influenza pandemic in US cities are used for illustration.

KW - Basic reproduction number

KW - Epidemiology

KW - Influenza

KW - Model

KW - Pandemic

UR - http://www.scopus.com/inward/record.url?scp=77954692449&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=77954692449&partnerID=8YFLogxK

U2 - 10.1007/978-90-481-2313-1_1

DO - 10.1007/978-90-481-2313-1_1

M3 - Chapter

AN - SCOPUS:77954692449

SN - 9789048123124

SP - 1

EP - 30

BT - Mathematical and Statistical Estimation Approaches in Epidemiology

PB - Springer Netherlands

ER -