Fractional-Order Epidemic Model for Measles Infection
In this study, a nonlinear dynamic SEVIQR measles epidemic model is constructed and analyzed using the novel Caputo fractional-order derivative operator. The model’s existence and uniqueness are established. In addition, the model equilibria are determined, and the novel Jacobian determinant method...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2024-01-01
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| Series: | Scientifica |
| Online Access: | http://dx.doi.org/10.1155/2024/8997302 |
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| _version_ | 1832543805456252928 |
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| author | Philip N. A. Akuka Baba Seidu Eric Okyere Stephen Abagna |
| author_facet | Philip N. A. Akuka Baba Seidu Eric Okyere Stephen Abagna |
| author_sort | Philip N. A. Akuka |
| collection | DOAJ |
| description | In this study, a nonlinear dynamic SEVIQR measles epidemic model is constructed and analyzed using the novel Caputo fractional-order derivative operator. The model’s existence and uniqueness are established. In addition, the model equilibria are determined, and the novel Jacobian determinant method recently constructed in the literature of epidemiological modeling of infectious diseases is applied to determine the threshold quantity, R0. Furthermore, we construct appropriate Lyapunov functions to establish the global asymptotic stability of the disease-free and endemic equilibrium points. Finally, the numerical solution of the model is executed employing the efficient and widely known Adams-type predictor-corrector iterative scheme, and simulation is conducted to investigate the impact of memory index and diverse preventive measures on the occurrence of the disease. Numerical simulation of the model indicates that quarantine, vaccination, and treatment can reduce the numbers of infectious and exposed populations, thereby controlling the disease. Therefore, it is recommended that the government provide financial assistance for vaccine distribution. |
| format | Article |
| id | doaj-art-d0f69d76502f4a19a73123d3340b9c01 |
| institution | Kabale University |
| issn | 2090-908X |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Scientifica |
| spelling | doaj-art-d0f69d76502f4a19a73123d3340b9c012025-02-03T11:27:29ZengWileyScientifica2090-908X2024-01-01202410.1155/2024/8997302Fractional-Order Epidemic Model for Measles InfectionPhilip N. A. Akuka0Baba Seidu1Eric Okyere2Stephen Abagna3Department of MathematicsDepartment of MathematicsDepartment of Mathematics and StatisticsDepartment of MathematicsIn this study, a nonlinear dynamic SEVIQR measles epidemic model is constructed and analyzed using the novel Caputo fractional-order derivative operator. The model’s existence and uniqueness are established. In addition, the model equilibria are determined, and the novel Jacobian determinant method recently constructed in the literature of epidemiological modeling of infectious diseases is applied to determine the threshold quantity, R0. Furthermore, we construct appropriate Lyapunov functions to establish the global asymptotic stability of the disease-free and endemic equilibrium points. Finally, the numerical solution of the model is executed employing the efficient and widely known Adams-type predictor-corrector iterative scheme, and simulation is conducted to investigate the impact of memory index and diverse preventive measures on the occurrence of the disease. Numerical simulation of the model indicates that quarantine, vaccination, and treatment can reduce the numbers of infectious and exposed populations, thereby controlling the disease. Therefore, it is recommended that the government provide financial assistance for vaccine distribution.http://dx.doi.org/10.1155/2024/8997302 |
| spellingShingle | Philip N. A. Akuka Baba Seidu Eric Okyere Stephen Abagna Fractional-Order Epidemic Model for Measles Infection Scientifica |
| title | Fractional-Order Epidemic Model for Measles Infection |
| title_full | Fractional-Order Epidemic Model for Measles Infection |
| title_fullStr | Fractional-Order Epidemic Model for Measles Infection |
| title_full_unstemmed | Fractional-Order Epidemic Model for Measles Infection |
| title_short | Fractional-Order Epidemic Model for Measles Infection |
| title_sort | fractional order epidemic model for measles infection |
| url | http://dx.doi.org/10.1155/2024/8997302 |
| work_keys_str_mv | AT philipnaakuka fractionalorderepidemicmodelformeaslesinfection AT babaseidu fractionalorderepidemicmodelformeaslesinfection AT ericokyere fractionalorderepidemicmodelformeaslesinfection AT stephenabagna fractionalorderepidemicmodelformeaslesinfection |