Mathematical Modeling of COVID-19 Cases and Deaths and the Impact of Vaccinations during Three Years of the Pandemic in Peru
Abstract
:1. Introduction
2. Materials and Methods
2.1. Data Collection
- Cases: Total confirmed cases of COVID-19. Counts can include probable cases, where reported (from 6 March 2020 to 20 March 2023).
- Deaths: Total deaths attributed to COVID-19. Counts can include probable deaths, where reported (from 6 March 2020 to 20 March 2023).
- People vaccinated: Total number of people who received at least one vaccine dose (from 9 February 2021 to 20 March 2023).
2.2. Mathematical Modeling
2.3. Statistical Analysis
2.3.1. Normality Tests for the Variables: Cases, Deaths, and People Vaccinated
2.3.2. Correlation Test between People Vaccinated and Cases
2.3.3. Correlation Test between People Vaccinated and Deaths
2.3.4. Causality Tests for the Variables: Cases, Deaths, and People Vaccinated
2.3.5. Stationarity Tests for the Variables: Cases, Deaths, and People Vaccinated
2.3.6. Information Criteria for Determining the Lag-Orders
2.3.7. Comparison of Modeled Variables against Real Data
3. Results
3.1. Epidemiological Panorama of COVID-19 in Peru
3.2. Mathematical Modeling
3.2.1. Mathematical Modeling for Cases
3.2.2. Mathematical Modeling for Deaths
3.2.3. Mathematical Modeling for People Vaccinated
3.3. Statistical Analysis
3.3.1. Normality Tests for the Variables: Cases, Deaths, and People Vaccinated
3.3.2. Correlation Test between People Vaccinated and Cases
3.3.3. Correlation Test between People Vaccinated and Deaths
3.3.4. Information Criteria for Determining the Lag Orders
3.3.5. Stationarity Tests for the Variables: Cases, Deaths, and People Vaccinated
3.3.6. Causality Tests between the Variables: Cases, Deaths, and People Vaccinated
3.3.7. Comparison of Modeled Variables against Real Data
4. Discussion
5. Conclusions
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Parameter | Cases | Deaths | People Vaccinated |
---|---|---|---|
t1 | 642 | 343 | 222 |
A | 2,245,146 | 110,184 | 15,348,800 |
t2 | 1109 | 1109 | 769 |
B | 4,489,377 | 219,648 | 30,374,977 |
t3 | 876 | 726 | 496 |
I | 3,889,029 | 210,672 | 29,526,095 |
M | 4,834,759 | 220,528 | 30,429,043 |
a | 4.1998 | 3.2259 | 3.5568 |
Q | 66.673 | 25.176 | 35.051 |
k | −0.0067 | −0.0083 | −0.0133 |
tc | 627 | 389 | 268 |
Maximum speed at tc | 8098 | 459 | 101,175 |
Maximum value at tc | 2,418,709 | 141,432 | 19,890,913 |
Time Series | Lag-Order AIC | AIC Value | Lag-Order BIC | BIC Value |
---|---|---|---|---|
People vaccinated | 9 | 24,998.81 | 9 | 25,053.94 |
Cases | 10 | 19,654.12 | 10 | 19,714.27 |
Deaths | 16 | 10,476.19 | 15 | 10,562.1 |
Pair of Time Series | Lag-Order AIC | AIC Value | Lag-Order BIC | BIC Value |
---|---|---|---|---|
Deaths–people vaccinated | 21 | 24,296.05 | 15 | 24,464.87 |
Cases–people vaccinated | 21 | 24,305.82 | 15 | 24,472.33 |
Pair of Time Series | Deaths → Vaccinated | Vaccinated → Deaths | Cases → Vaccinated | Vaccinated → Cases |
---|---|---|---|---|
p-Value | 0.1828 | 0.01608 | 0.6495 | 0.9276 |
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Marín-Machuca, O.; Chacón, R.D.; Alvarez-Lovera, N.; Pesantes-Grados, P.; Pérez-Timaná, L.; Marín-Sánchez, O. Mathematical Modeling of COVID-19 Cases and Deaths and the Impact of Vaccinations during Three Years of the Pandemic in Peru. Vaccines 2023, 11, 1648. https://doi.org/10.3390/vaccines11111648
Marín-Machuca O, Chacón RD, Alvarez-Lovera N, Pesantes-Grados P, Pérez-Timaná L, Marín-Sánchez O. Mathematical Modeling of COVID-19 Cases and Deaths and the Impact of Vaccinations during Three Years of the Pandemic in Peru. Vaccines. 2023; 11(11):1648. https://doi.org/10.3390/vaccines11111648
Chicago/Turabian StyleMarín-Machuca, Olegario, Ruy D. Chacón, Natalia Alvarez-Lovera, Pedro Pesantes-Grados, Luis Pérez-Timaná, and Obert Marín-Sánchez. 2023. "Mathematical Modeling of COVID-19 Cases and Deaths and the Impact of Vaccinations during Three Years of the Pandemic in Peru" Vaccines 11, no. 11: 1648. https://doi.org/10.3390/vaccines11111648