Mathematical modeling and optimal control strategies of Buruli ulcer in possum mammals
Buruli is a neglected tropical disease that can now be found in many countries including developed countries like Australia. It is a skin disorder that usually occurs in the arms and legs. The disease has been identified in a number of mammals, particularly possum. Adequate eradication and control p...
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AIMS Press
2021-06-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://aimspress.com/article/doi/10.3934/math.2021572?viewType=HTML |
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| author | Muhammad Altaf Khan E. Bonyah Yi-Xia Li Taseer Muhammad K. O. Okosun |
| author_facet | Muhammad Altaf Khan E. Bonyah Yi-Xia Li Taseer Muhammad K. O. Okosun |
| author_sort | Muhammad Altaf Khan |
| collection | DOAJ |
| description | Buruli is a neglected tropical disease that can now be found in many countries including developed countries like Australia. It is a skin disorder that usually occurs in the arms and legs. The disease has been identified in a number of mammals, particularly possum. Adequate eradication and control programs are needed to minimize infection and its spread to less developed countries before it becomes an epidemic. In this work, a SIR type possum epidemic model is proposed. The properties of the model are thoroughly studied and obtained its stability results. We determine the stability of the model at its fixed points and show that the model is locally and globally asymptomatically stable. The stability of the disease-free case is shown for $ \mathcal{R}_0 < 1 $ and the endemic case is examined for $ \mathcal{R}_0 > 1$. We further extend the model using the control variables and obtain an optimal control system and using the optimal control theory to characterize the necessary condition for controlling the spread of Buruli ulcer (BU). The model results are plotted to determine the best strategies for disease elimination. Numerical simulation has shown that the useful strategy consists in implementing all suggested controls. |
| first_indexed | 2024-12-16T09:22:02Z |
| format | Article |
| id | doaj.art-7145f0e9cf364979ac531f7099d07484 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-12-16T09:22:02Z |
| publishDate | 2021-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-7145f0e9cf364979ac531f7099d074842022-12-21T22:36:44ZengAIMS PressAIMS Mathematics2473-69882021-06-01699859988110.3934/math.2021572Mathematical modeling and optimal control strategies of Buruli ulcer in possum mammalsMuhammad Altaf Khan0E. Bonyah 1Yi-Xia Li2Taseer Muhammad3K. O. Okosun41. Institute for Groundwater studies, Faculty of Natural and Agricultural Sciences, University of the Free State South Africa2. Department of Mathematics Education, Akenten Appiah-Menka University of Skills Training and Entrepreneurial Development, Kumasi, Ghana3. College of Mathematics and Finance, Xiangnan University, Chenzhou 423000, China4. Department of Mathematics, College of Sciences, King Khalid University, Abha 61413, Saudi Arabia5. Department of Mathematics, Vaal University of Technology, Vanderbijlpark, South AfricaBuruli is a neglected tropical disease that can now be found in many countries including developed countries like Australia. It is a skin disorder that usually occurs in the arms and legs. The disease has been identified in a number of mammals, particularly possum. Adequate eradication and control programs are needed to minimize infection and its spread to less developed countries before it becomes an epidemic. In this work, a SIR type possum epidemic model is proposed. The properties of the model are thoroughly studied and obtained its stability results. We determine the stability of the model at its fixed points and show that the model is locally and globally asymptomatically stable. The stability of the disease-free case is shown for $ \mathcal{R}_0 < 1 $ and the endemic case is examined for $ \mathcal{R}_0 > 1$. We further extend the model using the control variables and obtain an optimal control system and using the optimal control theory to characterize the necessary condition for controlling the spread of Buruli ulcer (BU). The model results are plotted to determine the best strategies for disease elimination. Numerical simulation has shown that the useful strategy consists in implementing all suggested controls.https://aimspress.com/article/doi/10.3934/math.2021572?viewType=HTMLpossum mammaloptimal controlburuli ulcermycobacterium ulceransstability analysis |
| spellingShingle | Muhammad Altaf Khan E. Bonyah Yi-Xia Li Taseer Muhammad K. O. Okosun Mathematical modeling and optimal control strategies of Buruli ulcer in possum mammals AIMS Mathematics possum mammal optimal control buruli ulcer mycobacterium ulcerans stability analysis |
| title | Mathematical modeling and optimal control strategies of Buruli ulcer in possum mammals |
| title_full | Mathematical modeling and optimal control strategies of Buruli ulcer in possum mammals |
| title_fullStr | Mathematical modeling and optimal control strategies of Buruli ulcer in possum mammals |
| title_full_unstemmed | Mathematical modeling and optimal control strategies of Buruli ulcer in possum mammals |
| title_short | Mathematical modeling and optimal control strategies of Buruli ulcer in possum mammals |
| title_sort | mathematical modeling and optimal control strategies of buruli ulcer in possum mammals |
| topic | possum mammal optimal control buruli ulcer mycobacterium ulcerans stability analysis |
| url | https://aimspress.com/article/doi/10.3934/math.2021572?viewType=HTML |
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