Mathematical Model and Analysis on the Impacts of Vaccination and Treatment in the Control of the COVID-19 Pandemic with Optimal Control
In this study, a nonlinear deterministic mathematical model that evaluates two important therapeutic measures of the COVID-19 pandemic: vaccination of susceptible and treatment for infected people who are in quarantine, is formulated and rigorously analyzed. Some of the fundamental properties of the...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2023-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2023/8570311 |
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| _version_ | 1849306385724997632 |
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| author | Alemzewde Ayalew Yezbalem Molla Tenaw Tilahun Tadele Tesfa |
| author_facet | Alemzewde Ayalew Yezbalem Molla Tenaw Tilahun Tadele Tesfa |
| author_sort | Alemzewde Ayalew |
| collection | DOAJ |
| description | In this study, a nonlinear deterministic mathematical model that evaluates two important therapeutic measures of the COVID-19 pandemic: vaccination of susceptible and treatment for infected people who are in quarantine, is formulated and rigorously analyzed. Some of the fundamental properties of the model system including existence and uniqueness, positivity, and invariant region of solutions are proved under a certain meaningful set. The model exhibits two equilibrium points: disease-free and endemic equilibrium points under certain conditions. The basic reproduction number, R0, is derived via the next-generation matrix approach, and the dynamical behavior of the model is explored in detail. The analytical analysis reveals that the disease-free equilibrium solution is locally as well as globally asymptotically stable when the associated basic reproduction number is less than unity which indicates that COVID-19 dies out in the population. Also, the endemic equilibrium point is globally asymptotically stable whenever the associated basic reproduction number exceeds a unity which implies that COVID-19 establishes itself in the population. The sensitivity analysis of the basic reproduction number is computed to identify the most dominant parameters for the spreading out as well as control of infection and should be targeted by intervention strategies. Furthermore, we extended the considered model to optimal control problem system by introducing two time-dependent variables that represent the educational campaign to susceptibles and continuous treatment for quarantined individuals. Finally, some numerical results are illustrated to supplement the analytical results of the model using MATLAB ode45. |
| format | Article |
| id | doaj-art-346347be06584cd28bd3a2565275cbb1 |
| institution | Kabale University |
| issn | 1687-0042 |
| language | English |
| publishDate | 2023-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-346347be06584cd28bd3a2565275cbb12025-08-20T03:55:06ZengWileyJournal of Applied Mathematics1687-00422023-01-01202310.1155/2023/8570311Mathematical Model and Analysis on the Impacts of Vaccination and Treatment in the Control of the COVID-19 Pandemic with Optimal ControlAlemzewde Ayalew0Yezbalem Molla1Tenaw Tilahun2Tadele Tesfa3Department of MathematicsDepartment of MathematicsDepartment of MathematicsDepartment of MathematicsIn this study, a nonlinear deterministic mathematical model that evaluates two important therapeutic measures of the COVID-19 pandemic: vaccination of susceptible and treatment for infected people who are in quarantine, is formulated and rigorously analyzed. Some of the fundamental properties of the model system including existence and uniqueness, positivity, and invariant region of solutions are proved under a certain meaningful set. The model exhibits two equilibrium points: disease-free and endemic equilibrium points under certain conditions. The basic reproduction number, R0, is derived via the next-generation matrix approach, and the dynamical behavior of the model is explored in detail. The analytical analysis reveals that the disease-free equilibrium solution is locally as well as globally asymptotically stable when the associated basic reproduction number is less than unity which indicates that COVID-19 dies out in the population. Also, the endemic equilibrium point is globally asymptotically stable whenever the associated basic reproduction number exceeds a unity which implies that COVID-19 establishes itself in the population. The sensitivity analysis of the basic reproduction number is computed to identify the most dominant parameters for the spreading out as well as control of infection and should be targeted by intervention strategies. Furthermore, we extended the considered model to optimal control problem system by introducing two time-dependent variables that represent the educational campaign to susceptibles and continuous treatment for quarantined individuals. Finally, some numerical results are illustrated to supplement the analytical results of the model using MATLAB ode45.http://dx.doi.org/10.1155/2023/8570311 |
| spellingShingle | Alemzewde Ayalew Yezbalem Molla Tenaw Tilahun Tadele Tesfa Mathematical Model and Analysis on the Impacts of Vaccination and Treatment in the Control of the COVID-19 Pandemic with Optimal Control Journal of Applied Mathematics |
| title | Mathematical Model and Analysis on the Impacts of Vaccination and Treatment in the Control of the COVID-19 Pandemic with Optimal Control |
| title_full | Mathematical Model and Analysis on the Impacts of Vaccination and Treatment in the Control of the COVID-19 Pandemic with Optimal Control |
| title_fullStr | Mathematical Model and Analysis on the Impacts of Vaccination and Treatment in the Control of the COVID-19 Pandemic with Optimal Control |
| title_full_unstemmed | Mathematical Model and Analysis on the Impacts of Vaccination and Treatment in the Control of the COVID-19 Pandemic with Optimal Control |
| title_short | Mathematical Model and Analysis on the Impacts of Vaccination and Treatment in the Control of the COVID-19 Pandemic with Optimal Control |
| title_sort | mathematical model and analysis on the impacts of vaccination and treatment in the control of the covid 19 pandemic with optimal control |
| url | http://dx.doi.org/10.1155/2023/8570311 |
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