Modeling the Spread of COVID-19 in Enclosed Spaces
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 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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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
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 StyleGaddis, 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