# Modeling the Spread of COVID-19 in Enclosed Spaces

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Gammaitoni and Nucci Model

#### Wells–Riley Equation

#### 2.2. G–N Extension

#### 2.3. SEIR Model

#### 2.4. Incubation Period

#### 2.5. Combining Gammaitoni–Nucci and SEIR

#### 2.6. Multi-Age SIR Model

#### 2.7. General Contact Matrix

#### 2.8. Combining G–N and Age-Structured SEIR

#### 2.9. Next Generation Matrix

#### 2.10. Transmission and Transition Matrices

## 3. Results

#### 3.1. Creating ${C}_{ij}$ for Proposed Model

#### 3.2. Parameter Sensitivity Analysis

#### 3.3. Stability Analysis

#### Elderly Care Facility

#### 3.4. Initial Infector and Contact Rate

## 4. Conclusions

#### Further Research

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

COVID-19 | Coronavirus disease of 2019 |

G–N Model | Gammaitoni–Nucci Model |

ACH | Air changes per hour |

SIR | Susceptible-Infected-Removed |

SEIR | Susceptible-Exposed-Infected-Removed model |

NGM | Next Generation Matrix |

## Appendix A. Mossong Data Tables

All Reported Contacts (Physical and Non-Physical Contacts) | |||||||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|

Age Group of Participant | |||||||||||||||

Age of Contact | 00-04 | 05–09 | 10–14 | 15–19 | 20–24 | 25–29 | 30–34 | 35–39 | 40–44 | 45–49 | 50–54 | 55–59 | 60–64 | 65–69 | 70+ |

00–04 | 2.375 | 0.89875 | 0.27 | 0.18125 | 0.27 | 0.50375 | 0.82375 | 0.65625 | 0.68375 | 0.3225 | 0.2425 | 0.2775 | 0.32875 | 0.1875 | 0.15875 |

05–09 | 1.1975 | 6.65625 | 1.1275 | 0.365 | 0.21875 | 0.45375 | 0.92625 | 0.97125 | 0.7 | 0.34625 | 0.46875 | 0.3525 | 0.25875 | 0.315 | 0.2175 |

10–14 | 0.44875 | 1.31625 | 9.3 | 1.3725 | 0.2875 | 0.2675 | 0.66 | 0.75125 | 0.91125 | 0.55625 | 0.64125 | 0.37125 | 0.31 | 0.22125 | 0.4 |

15–19 | 0.26375 | 0.33 | 1.62 | 9.05875 | 1.56625 | 0.62375 | 0.53875 | 0.53 | 0.99 | 1.225 | 0.77125 | 0.49875 | 0.31125 | 0.20625 | 0.42375 |

20–24 | 0.38125 | 0.27125 | 0.4 | 1.45625 | 3.71375 | 1.68875 | 0.79625 | 0.7075 | 1.0225 | 0.89625 | 1.01 | 0.65125 | 0.4475 | 0.305 | 0.2475 |

25–29 | 0.7725 | 0.6525 | 0.3875 | 0.67 | 1.89875 | 2.47625 | 1.59125 | 1.16625 | 1.00375 | 1.03875 | 1.29125 | 0.91875 | 0.7125 | 0.5825 | 0.40375 |

30–34 | 1.15375 | 0.96625 | 0.58625 | 0.52 | 1.31875 | 1.65875 | 2.36625 | 1.54875 | 1.37375 | 1.18 | 1.06 | 1.075 | 1.0075 | 0.6875 | 0.4325 |

35–39 | 1.03 | 1.19875 | 0.9925 | 0.8025 | 0.945 | 1.2 | 2.03875 | 2.4175 | 1.5475 | 1.33875 | 1.06875 | 0.93125 | 0.97375 | 0.86375 | 0.5025 |

40–44 | 0.6375 | 1.1225 | 1.31125 | 0.995 | 0.855 | 0.995 | 1.4875 | 2.0125 | 2.13125 | 1.5275 | 1.215 | 1.12 | 0.9275 | 0.86 | 0.67625 |

45–49 | 0.40625 | 0.5175 | 0.84875 | 1.2 | 1.0675 | 0.925 | 1.00625 | 1.25625 | 1.545 | 1.86375 | 1.34125 | 1.00125 | 0.73375 | 0.5625 | 0.7 |

50–54 | 0.43 | 0.40625 | 0.46875 | 0.6175 | 0.87125 | 1.01875 | 0.87375 | 0.98625 | 1.1425 | 1.31 | 1.46125 | 1.23 | 0.76125 | 0.59375 | 0.5325 |

55–59 | 0.39625 | 0.3175 | 0.26875 | 0.335 | 0.4725 | 0.66625 | 0.6325 | 0.56 | 0.4525 | 0.6975 | 1.0775 | 1.55125 | 1.06875 | 0.65375 | 0.4675 |

60–64 | 0.3325 | 0.29875 | 0.18 | 0.1575 | 0.2225 | 0.37875 | 0.4875 | 0.57125 | 0.425 | 0.41 | 0.57875 | 0.825 | 1.12125 | 0.83375 | 0.59375 |

65–69 | 0.2425 | 0.21375 | 0.17625 | 0.1275 | 0.13 | 0.18875 | 0.25875 | 0.4125 | 0.30125 | 0.21375 | 0.24125 | 0.47375 | 0.695 | 0.90125 | 0.66125 |

70+ | 0.31625 | 0.35875 | 0.3625 | 0.25 | 0.315 | 0.35875 | 0.37625 | 0.4375 | 0.56125 | 0.685 | 0.70875 | 0.72375 | 0.89 | 1.05 | 1.45 |

4 Categories | 0–19 | 20–39 | 40–59 | 60+ |
---|---|---|---|---|

0–19 | 36.78125 | 10.04875 | 9.35875 | 3.33875 |

20–39 | 12.24125 | 27.5325 | 17.4075 | 7.16625 |

40–59 | 10.27875 | 15.68625 | 20.6675 | 8.5375 |

60+ | 3.01625 | 4.1375 | 6.1475 | 8.19625 |

## Appendix B. NGM Submatrices

## Appendix C. COVID-19 Statistics

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**Figure 4.**Infection rate for asymptomatic vs. symptomatic contact percentage on overall sickness rate.

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Gaddis, M.D.; Manoranjan, V.S. Modeling the Spread of COVID-19 in Enclosed Spaces. *Math. Comput. Appl.* **2021**, *26*, 79.
https://doi.org/10.3390/mca26040079

**AMA Style**

Gaddis MD, Manoranjan VS. Modeling the Spread of COVID-19 in Enclosed Spaces. *Mathematical and Computational Applications*. 2021; 26(4):79.
https://doi.org/10.3390/mca26040079

**Chicago/Turabian Style**

Gaddis, Matthew David, and Valipuram S. Manoranjan. 2021. "Modeling the Spread of COVID-19 in Enclosed Spaces" *Mathematical and Computational Applications* 26, no. 4: 79.
https://doi.org/10.3390/mca26040079