A Mathematical Study of COVID-19 Spread by Vaccination Status in Virginia
Abstract
:1. Introduction
2. Materials and Methods
2.1. n-Stage Vaccination Model
2.2. Governing System of Differential Equations
2.3. Basic and Effective Reproduction Number
2.4. Data Fitting Techniques
2.5. Parameter Sensitivity Analysis
3. Results
3.1. Fitting Two-Stage Vaccination Model to Virginia Data
3.2. Efficacy of Vaccination
3.3. Transmissibility of Delta Variant
3.4. Effect of Waning Immunity and Delta Variant on Vaccine Efficacy
3.5. Parameter Sensitivity Analysis
3.6. Modeling with Different Vaccine Coverage Levels
3.7. Modeling with Booster Shots
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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Parameter | Units | Interpretation |
---|---|---|
N | people | Population size (total) |
people | Population size (ith class) | |
people | Vaccination uptake curve (ith class) | |
days | Vaccination uptake rate (ith class) | |
people | Maximum vaccination total (ith class) | |
none | Maximum vaccination proportion (ith class) | |
days | Vaccination time shift (ith class) | |
none | Vaccination shape parameter (ith class) | |
days | Baseline transmission rate for unvaccinated | |
none | Reduction from baseline transmission rate (ith class) | |
days | Removal rate (ith class) | |
days | Hospitalization rate (ith class) | |
days | Death rate (ith class) | |
none | Proportion infected to hospitalized (ith class) | |
none | Proportion hospitalized to deceased (ith class) |
Initial Conditions | Parameters | ||||
---|---|---|---|---|---|
Parameter | Value | Source | Parameter | Value | Source |
N | 8,535,519 | [25] | fitted | ||
8,136,306 | assumed (9) | fitted | |||
289,839 | assumed (9) | fitted | |||
109,375 | assumed (9) | fitted | |||
7,695,938 | assumed (10) | fitted | |||
19,557 | fitted | fitted | |||
411,709 | fitted | fitted | |||
823 | fitted | fitted | |||
8279 | assumed | fitted | |||
281,970 | assumed (10) | fitted | |||
7642 | fitted | fitted | |||
227 | fitted | fitted | |||
0 | assumed | fitted | |||
0 | assumed | fitted | |||
108,839 | assumed (10) | fitted | |||
536 | fitted | fitted | |||
0 | fitted | fitted | |||
0 | assumed | fitted | |||
0 | assumed | fitted |
Interval | Dates | % Part Vax | % Full Vax | ||
---|---|---|---|---|---|
1 | 1/23–2/21 | 4.4% | 0.5% | 0.153 | 0.786 |
2 | 2/22–3/23 | 14.0% | 6.1% | 0.200 | 0.978 |
3 | 3/24–4/22 | 26.7% | 14.7% | 0.251 | 1.106 |
4 | 4/23–5/21 | 44.3% | 29.1% | 0.241 | 0.906 |
5 | 5/22–6/20 | 53.2% | 42.7% | 0.238 | 0.762 |
6 | 6/21–7/20 | 58.2% | 50.3% | 0.464 | 1.312 |
7 | 7/21–8/19 | 60.7% | 53.7% | 0.539 | 1.404 |
8 | 8/20–9/18 | 64.2% | 56.1% | 0.453 | 1.119 |
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Johnston, M.D.; Pell, B.; Nelson, P. A Mathematical Study of COVID-19 Spread by Vaccination Status in Virginia. Appl. Sci. 2022, 12, 1723. https://doi.org/10.3390/app12031723
Johnston MD, Pell B, Nelson P. A Mathematical Study of COVID-19 Spread by Vaccination Status in Virginia. Applied Sciences. 2022; 12(3):1723. https://doi.org/10.3390/app12031723
Chicago/Turabian StyleJohnston, Matthew D., Bruce Pell, and Patrick Nelson. 2022. "A Mathematical Study of COVID-19 Spread by Vaccination Status in Virginia" Applied Sciences 12, no. 3: 1723. https://doi.org/10.3390/app12031723
APA StyleJohnston, M. D., Pell, B., & Nelson, P. (2022). A Mathematical Study of COVID-19 Spread by Vaccination Status in Virginia. Applied Sciences, 12(3), 1723. https://doi.org/10.3390/app12031723