# A Statistical Model to Assess Risk for Supporting COVID-19 Quarantine Decisions

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## Abstract

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## 1. Introduction

#### 1.1. COVID-19 Pandemic and Situation in Germany

#### 1.2. Quarantine Decisions in Germany

- had face-to-face contact for at least 15 min or
- had direct contact to bodily fluids or
- were exposed to a relevant aerosol concentration.

#### 1.3. Structure of the Paper

## 2. Materials and Methods

#### 2.1. Use Case

“Under which conditions can a group quarantine be released (earlier) such that the probability of overlooking a (secondary) infection is low?”

“How likely is it that there is no secondary infection, given all N out of M people are tested negative?”

#### 2.2. Statistical Model

#### 2.3. Prior Distribution

#### 2.4. Likelihood

## 3. Result

#### 3.1. Prior Distribution for School Classes

#### 3.2. Posterior Probabilities and Decision Support for School Classes

#### 3.3. Decision about Quarantine Cancellation for School Classes

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**

**Left**: Timeline of the events starting from the group event until the quarantine decision.

**Right**: Overview of the group with M, the possible number of infected K, and the negative tested persons N. For N and K, the contact persons are divided into subgroups ${N}_{d}$ and ${K}_{d}$, which are tested on day ${D}_{d},d\in \{1,\dots ,n\}$, are also illustrated.

**Figure 2.**Plots of the Beta-binomial distribution as school class prior for $M=15,25,\begin{array}{c}\hfill 35\end{array}$.

**Figure 3.**

**Left**: Posterior probability that no transmission occurred given that N out of M persons are tested negative using the specific school prior for different group sizes and number of tests made 4 days after the group event.

**Right**: Decision of a quarantine cancellation based the condition that ${p}_{0}>0.9$. The black line shows the situation that $30\%$ are tested.

Category | Infection Risk |
---|---|

1. | high, close contact to infectious person |

2. | low, sparse contact to infectious person |

3. | medical staff with adequate protection |

**Table 2.**A dataset of a school class from the health department in Berlin-Reinickendorf, which contains the last contact date, the PCR test date, and the PCR results.

Case Number | Date of Last Contact | PCR Test Date | PCR Test Result |
---|---|---|---|

1 | 10 August 2020 | — | — |

2 | 10 August 2020 | — | — |

3 | 10 August 2020 | — | — |

4 | 10 August 2020 | 18 August 2020 | negative |

5 | 10 August 2020 | 19 August 2020 | negative |

6 | 10 August 2020 | 19 August 2020 | negative |

7 | 10 August 2020 | 19 August 2020 | negative |

8 | 10 August 2020 | 20 August 2020 | negative |

9 | 10 August 2020 | 19 August 2020 | negative |

10 | 10 August 2020 | 19 August 2020 | negative |

11 | 10 August 2020 | 19 August 2020 | negative |

12 | 10 August 2020 | 19 August 2020 | negative |

13 | 10 August 2020 | 19 August 2020 | negative |

14 | 10 August 2020 | 19 August 2020 | negative |

15 | 10 August 2020 | 19 August 2020 | negative |

16 | 16 August 2020 | 19 August 2020 | negative |

17 | 18 August 2020 | 24 August 2020 | negative |

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**MDPI and ACS Style**

Jäckle, S.; Röger, E.; Dicken, V.; Geisler, B.; Schumacher, J.; Westphal, M.
A Statistical Model to Assess Risk for Supporting COVID-19 Quarantine Decisions. *Int. J. Environ. Res. Public Health* **2021**, *18*, 9166.
https://doi.org/10.3390/ijerph18179166

**AMA Style**

Jäckle S, Röger E, Dicken V, Geisler B, Schumacher J, Westphal M.
A Statistical Model to Assess Risk for Supporting COVID-19 Quarantine Decisions. *International Journal of Environmental Research and Public Health*. 2021; 18(17):9166.
https://doi.org/10.3390/ijerph18179166

**Chicago/Turabian Style**

Jäckle, Sonja, Elias Röger, Volker Dicken, Benjamin Geisler, Jakob Schumacher, and Max Westphal.
2021. "A Statistical Model to Assess Risk for Supporting COVID-19 Quarantine Decisions" *International Journal of Environmental Research and Public Health* 18, no. 17: 9166.
https://doi.org/10.3390/ijerph18179166