### Abstract

Using daily counts of newly infected individuals, Wallinga and Teunis (WT) introduced a conceptually simple method to estimate the number of secondary cases per primary case (R_{t}) for a given day. The method requires an estimate of the generation interval probability density function (pdf), which specifies the probabilities for the times between symptom onset in a primary case and symptom onset in a corresponding secondary case. Other methods to estimate R_{t} are based on explicit models such as the SIR model; therefore, one might expect the WT method to be more robust to departures from SIR- type behavior. This paper uses simulated data to compare the quality of daily Rt estimates based on a SIR model to those using the WT method for both structured (classical SIR assumptions are violated) and nonstructured (classical SIR assumptions hold) populations. By using detailed simulations that record the infection day of each new infection and the donor-recipient identities, the true R_{t} and the generation interval pdf is known with negligible error. We find that the generation interval pdf is time dependent in all cases, which agrees with recent results reported elsewhere. We also find that the WT method performs essentially the same in the structured populations (except for a spatial network) as it does in the nonstructured population. And, the WT method does as well or better than a SIR-model based method in three of the four structured populations. Therefore, even if the contact patterns are heterogeneous as in the structured populations evaluated here, the WT method provides reasonable estimates of R_{t}, as does the SIR method.

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

Pages (from-to) | 239-259 |

Number of pages | 21 |

Journal | Mathematical Biosciences and Engineering |

Volume | 6 |

Issue number | 2 |

DOIs | |

State | Published - Apr 2009 |

### Fingerprint

### Keywords

- Generation interval
- Reproduction number
- Structured population

### ASJC Scopus subject areas

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

### Cite this

_{t}in structured and nonstructured populations.

*Mathematical Biosciences and Engineering*,

*6*(2), 239-259. https://doi.org/10.3934/mbe.2009.6.239

**The reproduction number R _{t} in structured and nonstructured populations.** / Burr, Tom; Chowell, Gerardo.

Research output: Contribution to journal › Article

_{t}in structured and nonstructured populations',

*Mathematical Biosciences and Engineering*, vol. 6, no. 2, pp. 239-259. https://doi.org/10.3934/mbe.2009.6.239

_{t}in structured and nonstructured populations. Mathematical Biosciences and Engineering. 2009 Apr;6(2):239-259. https://doi.org/10.3934/mbe.2009.6.239

}

TY - JOUR

T1 - The reproduction number Rt in structured and nonstructured populations

AU - Burr, Tom

AU - Chowell, Gerardo

PY - 2009/4

Y1 - 2009/4

N2 - Using daily counts of newly infected individuals, Wallinga and Teunis (WT) introduced a conceptually simple method to estimate the number of secondary cases per primary case (Rt) for a given day. The method requires an estimate of the generation interval probability density function (pdf), which specifies the probabilities for the times between symptom onset in a primary case and symptom onset in a corresponding secondary case. Other methods to estimate Rt are based on explicit models such as the SIR model; therefore, one might expect the WT method to be more robust to departures from SIR- type behavior. This paper uses simulated data to compare the quality of daily Rt estimates based on a SIR model to those using the WT method for both structured (classical SIR assumptions are violated) and nonstructured (classical SIR assumptions hold) populations. By using detailed simulations that record the infection day of each new infection and the donor-recipient identities, the true Rt and the generation interval pdf is known with negligible error. We find that the generation interval pdf is time dependent in all cases, which agrees with recent results reported elsewhere. We also find that the WT method performs essentially the same in the structured populations (except for a spatial network) as it does in the nonstructured population. And, the WT method does as well or better than a SIR-model based method in three of the four structured populations. Therefore, even if the contact patterns are heterogeneous as in the structured populations evaluated here, the WT method provides reasonable estimates of Rt, as does the SIR method.

AB - Using daily counts of newly infected individuals, Wallinga and Teunis (WT) introduced a conceptually simple method to estimate the number of secondary cases per primary case (Rt) for a given day. The method requires an estimate of the generation interval probability density function (pdf), which specifies the probabilities for the times between symptom onset in a primary case and symptom onset in a corresponding secondary case. Other methods to estimate Rt are based on explicit models such as the SIR model; therefore, one might expect the WT method to be more robust to departures from SIR- type behavior. This paper uses simulated data to compare the quality of daily Rt estimates based on a SIR model to those using the WT method for both structured (classical SIR assumptions are violated) and nonstructured (classical SIR assumptions hold) populations. By using detailed simulations that record the infection day of each new infection and the donor-recipient identities, the true Rt and the generation interval pdf is known with negligible error. We find that the generation interval pdf is time dependent in all cases, which agrees with recent results reported elsewhere. We also find that the WT method performs essentially the same in the structured populations (except for a spatial network) as it does in the nonstructured population. And, the WT method does as well or better than a SIR-model based method in three of the four structured populations. Therefore, even if the contact patterns are heterogeneous as in the structured populations evaluated here, the WT method provides reasonable estimates of Rt, as does the SIR method.

KW - Generation interval

KW - Reproduction number

KW - Structured population

UR - http://www.scopus.com/inward/record.url?scp=67650499116&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67650499116&partnerID=8YFLogxK

U2 - 10.3934/mbe.2009.6.239

DO - 10.3934/mbe.2009.6.239

M3 - Article

C2 - 19364151

AN - SCOPUS:67650499116

VL - 6

SP - 239

EP - 259

JO - Mathematical Biosciences and Engineering

JF - Mathematical Biosciences and Engineering

SN - 1547-1063

IS - 2

ER -