Comparative Analysis of Influenza Modeling Using Novel Fractional Operators with Real Data
Abstract
:1. Introduction
2. Preliminaries
3. The Development of the Model in the Classical Meaning
4. The Development of the Model in the Fractional Meaning
4.1. Caputo Meaning
4.2. Caputo–Fabrizio Meaning
4.3. Atangana–Baleanu–Caputo Meaning
5. Analysis of the Model
5.1. Disease-Free Equilibrium Point
5.2. Positivity and Boundedness
5.3. Reproduction Numbers
5.4. Stability Analysis
5.5. Global Stability of the Disease-Free Equilibrium
6. Numerical Results and Discussion
7. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Compartment | Description |
---|---|
S | Susceptible class |
V | Vaccinated class |
E | Exposed class |
I | Infected class |
H | Hospitalized class |
R | Recovered class |
Parameter | Description | Value | Source |
---|---|---|---|
Population recruitment rate | [39] | ||
Natural death rate | 0.000254 weeks−1 | [39] | |
Average effective contact rate | 0.858 | Fitted | |
Vaccination rate | 0.114 | Fitted | |
Vaccine inefficacy | 1 | Fitted | |
Average hospitalization rate | 0.0015 | Fitted | |
Recovery rate for infected class | 0.385 day−1 | [40] | |
Recovery rate for exposed class | 0.34 | Fitted | |
Recovery rate for hospitalized individuals | 0.68 | Fitted | |
Average latent or incubation period | 0.625 day−1 | [41] | |
Rate at which individuals lose immunity | 0.0067 day−1 | [39] |
Fractional Order | MAE | RMSE |
---|---|---|
0.99 | ||
0.98 | ||
0.97 | ||
0.96 | ||
0.95 |
Fractional Order | MAE | RMSE |
---|---|---|
0.99 | ||
0.98 | ||
0.97 | ||
0.96 | ||
0.95 |
Fractional Order | MAE | RMSE |
---|---|---|
0.99 | ||
0.98 | ||
0.97 | ||
0.96 | ||
0.95 | ||
Classical |
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Abdoon, M.A.; Alzahrani, A.B.M. Comparative Analysis of Influenza Modeling Using Novel Fractional Operators with Real Data. Symmetry 2024, 16, 1126. https://doi.org/10.3390/sym16091126
Abdoon MA, Alzahrani ABM. Comparative Analysis of Influenza Modeling Using Novel Fractional Operators with Real Data. Symmetry. 2024; 16(9):1126. https://doi.org/10.3390/sym16091126
Chicago/Turabian StyleAbdoon, Mohamed A., and Abdulrahman B. M. Alzahrani. 2024. "Comparative Analysis of Influenza Modeling Using Novel Fractional Operators with Real Data" Symmetry 16, no. 9: 1126. https://doi.org/10.3390/sym16091126