Optimal Covid-19 Control on Effectiveness of Detection Campaign and Treatment
The COVID-19 pandemic has seen the development of several mathematical models. In recent years, the very topical issue of re-susceptibility has led to the proposal of more complex models to address this issue. The paper deals with an optimal control problem applied to COVID-19. The Pontryagin maximu...
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Ram Arti Publishers
2025-04-01
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| Series: | International Journal of Mathematical, Engineering and Management Sciences |
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| Online Access: | https://www.ijmems.in/cms/storage/app/public/uploads/volumes/21-IJMEMS-24-0447-10-2-420-440-2025.pdf |
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| author | Mouhamadou A. M. T. Baldé Sidy Ly Léna Tendeng |
| author_facet | Mouhamadou A. M. T. Baldé Sidy Ly Léna Tendeng |
| author_sort | Mouhamadou A. M. T. Baldé |
| collection | DOAJ |
| description | The COVID-19 pandemic has seen the development of several mathematical models. In recent years, the very topical issue of re-susceptibility has led to the proposal of more complex models to address this issue. The paper deals with an optimal control problem applied to COVID-19. The Pontryagin maximum principle and the dynamic programming principle are used to solve the problem. A compartmental Ordinary Differential Equation (ODE) model is proposed to study the evolution of the pandemic by controlling the effectiveness of the detection campaign and the treatment. We prove the global stability of the Disease-Free Equilibrium (DFE) and the existence of optimal control and trajectories of the model. In the optimal control problem, we bring the system back to the DFE. Numerical simulations based on COVID-19 data in Senegal show possibilities to reduce the disease evolution, sometimes by emphasizing the detection campaign and/or the treatment proposed to patients. |
| format | Article |
| id | doaj-art-ea8e64ab4dfa41b184a1a2a300d13cf6 |
| institution | Kabale University |
| issn | 2455-7749 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | Ram Arti Publishers |
| record_format | Article |
| series | International Journal of Mathematical, Engineering and Management Sciences |
| spelling | doaj-art-ea8e64ab4dfa41b184a1a2a300d13cf62025-02-07T15:59:53ZengRam Arti PublishersInternational Journal of Mathematical, Engineering and Management Sciences2455-77492025-04-01102420440https://doi.org/10.33889/IJMEMS.2025.10.2.021Optimal Covid-19 Control on Effectiveness of Detection Campaign and TreatmentMouhamadou A. M. T. Baldé0Sidy Ly1Léna Tendeng2Laboratory of Mathematics of Decision and Numerical Analysis, University of Cheikh Anta Diop, BP, 5005, Dakar, Senegal.Laboratory of Mathematics of Decision and Numerical Analysis, University of Cheikh Anta Diop, BP, 5005, Dakar, Senegal.Laboratory of Mathematics of Decision and Numerical Analysis, University of Cheikh Anta Diop, BP, 5005, Dakar, Senegal.The COVID-19 pandemic has seen the development of several mathematical models. In recent years, the very topical issue of re-susceptibility has led to the proposal of more complex models to address this issue. The paper deals with an optimal control problem applied to COVID-19. The Pontryagin maximum principle and the dynamic programming principle are used to solve the problem. A compartmental Ordinary Differential Equation (ODE) model is proposed to study the evolution of the pandemic by controlling the effectiveness of the detection campaign and the treatment. We prove the global stability of the Disease-Free Equilibrium (DFE) and the existence of optimal control and trajectories of the model. In the optimal control problem, we bring the system back to the DFE. Numerical simulations based on COVID-19 data in Senegal show possibilities to reduce the disease evolution, sometimes by emphasizing the detection campaign and/or the treatment proposed to patients.https://www.ijmems.in/cms/storage/app/public/uploads/volumes/21-IJMEMS-24-0447-10-2-420-440-2025.pdfdifferential equationsdynamic programming principlehamilton-jacobi-bellman equationspontryagin maximum principlecovid-19 |
| spellingShingle | Mouhamadou A. M. T. Baldé Sidy Ly Léna Tendeng Optimal Covid-19 Control on Effectiveness of Detection Campaign and Treatment International Journal of Mathematical, Engineering and Management Sciences differential equations dynamic programming principle hamilton-jacobi-bellman equations pontryagin maximum principle covid-19 |
| title | Optimal Covid-19 Control on Effectiveness of Detection Campaign and Treatment |
| title_full | Optimal Covid-19 Control on Effectiveness of Detection Campaign and Treatment |
| title_fullStr | Optimal Covid-19 Control on Effectiveness of Detection Campaign and Treatment |
| title_full_unstemmed | Optimal Covid-19 Control on Effectiveness of Detection Campaign and Treatment |
| title_short | Optimal Covid-19 Control on Effectiveness of Detection Campaign and Treatment |
| title_sort | optimal covid 19 control on effectiveness of detection campaign and treatment |
| topic | differential equations dynamic programming principle hamilton-jacobi-bellman equations pontryagin maximum principle covid-19 |
| url | https://www.ijmems.in/cms/storage/app/public/uploads/volumes/21-IJMEMS-24-0447-10-2-420-440-2025.pdf |
| work_keys_str_mv | AT mouhamadouamtbalde optimalcovid19controloneffectivenessofdetectioncampaignandtreatment AT sidyly optimalcovid19controloneffectivenessofdetectioncampaignandtreatment AT lenatendeng optimalcovid19controloneffectivenessofdetectioncampaignandtreatment |