### Abstract

We consider a single outbreak susceptible-infected-recovered (SIR) model and corresponding estimation procedures for the effective reproductive number Ti.{t). We discuss the estimation of the underlying SIR parameters with a generalized least squares (GLS) estimation technique. We do this in the context of appropriate statistical models for the measurement process. We use asymptotic statistical theories to derive the mean and variance of the limiting (Gaussian) sampling distribution and to perform post statistical analysis of the inverse problems. We illustrate the ideas and pitfalls (e.g., large condition numbers on the corresponding Fisher information matrix) with both synthetic and influenza incidence data sets.

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

Pages (from-to) | 261-282 |

Number of pages | 22 |

Journal | Mathematical Biosciences and Engineering |

Volume | 6 |

Issue number | 2 |

DOIs | |

State | Published - Apr 2009 |

### Fingerprint

### Keywords

- Basic reproduction ratio
- Effective reproductive number
- Generalized least squares
- H, h(t), ho
- Parameter estimation
- Reproduction number
- Residual plots

### ASJC Scopus subject areas

- Applied Mathematics
- Modeling and Simulation
- Computational Mathematics
- Agricultural and Biological Sciences(all)
- Medicine(all)

### Cite this

*Mathematical Biosciences and Engineering*,

*6*(2), 261-282. https://doi.org/10.3934/mbe.2009.6.261

**The estimation of the effective reproductive number from disease outbreak data.** / Cintrôn-Arias, Ariel; Castillo-Chavez, Carlos; Bettencourt, Luis M A; Lloyd, Alun L.; Banks, H. T.

Research output: Contribution to journal › Article

*Mathematical Biosciences and Engineering*, vol. 6, no. 2, pp. 261-282. https://doi.org/10.3934/mbe.2009.6.261

}

TY - JOUR

T1 - The estimation of the effective reproductive number from disease outbreak data

AU - Cintrôn-Arias, Ariel

AU - Castillo-Chavez, Carlos

AU - Bettencourt, Luis M A

AU - Lloyd, Alun L.

AU - Banks, H. T.

PY - 2009/4

Y1 - 2009/4

N2 - We consider a single outbreak susceptible-infected-recovered (SIR) model and corresponding estimation procedures for the effective reproductive number Ti.{t). We discuss the estimation of the underlying SIR parameters with a generalized least squares (GLS) estimation technique. We do this in the context of appropriate statistical models for the measurement process. We use asymptotic statistical theories to derive the mean and variance of the limiting (Gaussian) sampling distribution and to perform post statistical analysis of the inverse problems. We illustrate the ideas and pitfalls (e.g., large condition numbers on the corresponding Fisher information matrix) with both synthetic and influenza incidence data sets.

AB - We consider a single outbreak susceptible-infected-recovered (SIR) model and corresponding estimation procedures for the effective reproductive number Ti.{t). We discuss the estimation of the underlying SIR parameters with a generalized least squares (GLS) estimation technique. We do this in the context of appropriate statistical models for the measurement process. We use asymptotic statistical theories to derive the mean and variance of the limiting (Gaussian) sampling distribution and to perform post statistical analysis of the inverse problems. We illustrate the ideas and pitfalls (e.g., large condition numbers on the corresponding Fisher information matrix) with both synthetic and influenza incidence data sets.

KW - Basic reproduction ratio

KW - Effective reproductive number

KW - Generalized least squares

KW - H, h(t), ho

KW - Parameter estimation

KW - Reproduction number

KW - Residual plots

UR - http://www.scopus.com/inward/record.url?scp=67650458331&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67650458331&partnerID=8YFLogxK

U2 - 10.3934/mbe.2009.6.261

DO - 10.3934/mbe.2009.6.261

M3 - Article

C2 - 19364152

AN - SCOPUS:67650458331

VL - 6

SP - 261

EP - 282

JO - Mathematical Biosciences and Engineering

JF - Mathematical Biosciences and Engineering

SN - 1547-1063

IS - 2

ER -