Mathematical Modelling and Optimal Control of Anthracnose
In this paper we propose two nonlinear models for the control of anthracnose disease. The first one is an ordinary differential equation (ODE) model which represents the whithin host evolution of the disease. The second model includes spatial diffusion of the disease in a bounded domain Ω. We show w...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
Bulgarian Academy of Sciences, Institute of Mathematics and Informatics
2014-06-01
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| Series: | Biomath |
| Subjects: | |
| Online Access: | http://www.biomathforum.org/biomath/index.php/biomath/article/view/216 |
| _version_ | 1797766622038982656 |
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| author | David Fotsa Elvis Houpa David Bekolle Christopher Thron Michel Ndoumbe |
| author_facet | David Fotsa Elvis Houpa David Bekolle Christopher Thron Michel Ndoumbe |
| author_sort | David Fotsa |
| collection | DOAJ |
| description | In this paper we propose two nonlinear models for the control of anthracnose disease. The first one is an ordinary differential equation (ODE) model which represents the whithin host evolution of the disease. The second model includes spatial diffusion of the disease in a bounded domain Ω. We show well formulation of those models checking existence of solutions for given initial conditions and positive invariance of positive cone. Considering a quadratic cost functional and applying maximum principle we construct a feedback optimal control for the EDO model which is evaluated through numerical simulations with scientific software Scilab®. For the diffusion model we establish under some conditions existence of unique optimal control with respect to a generalized version of cost functional mentioned before. We also provide a characterization for existing optimal control. Finally we discuss a family of nonlinear controlled systems. |
| first_indexed | 2024-03-12T20:27:48Z |
| format | Article |
| id | doaj.art-e3a16823fb9843af9f00636942423f78 |
| institution | Directory Open Access Journal |
| issn | 1314-684X 1314-7218 |
| language | English |
| last_indexed | 2024-03-12T20:27:48Z |
| publishDate | 2014-06-01 |
| publisher | Bulgarian Academy of Sciences, Institute of Mathematics and Informatics |
| record_format | Article |
| series | Biomath |
| spelling | doaj.art-e3a16823fb9843af9f00636942423f782023-08-02T00:24:06ZengBulgarian Academy of Sciences, Institute of Mathematics and InformaticsBiomath1314-684X1314-72182014-06-013110.11145/j.biomath.2014.04.161235Mathematical Modelling and Optimal Control of AnthracnoseDavid Fotsa0Elvis HoupaDavid BekolleChristopher ThronMichel NdoumbeThe Univerty of NgaoundereIn this paper we propose two nonlinear models for the control of anthracnose disease. The first one is an ordinary differential equation (ODE) model which represents the whithin host evolution of the disease. The second model includes spatial diffusion of the disease in a bounded domain Ω. We show well formulation of those models checking existence of solutions for given initial conditions and positive invariance of positive cone. Considering a quadratic cost functional and applying maximum principle we construct a feedback optimal control for the EDO model which is evaluated through numerical simulations with scientific software Scilab®. For the diffusion model we establish under some conditions existence of unique optimal control with respect to a generalized version of cost functional mentioned before. We also provide a characterization for existing optimal control. Finally we discuss a family of nonlinear controlled systems.http://www.biomathforum.org/biomath/index.php/biomath/article/view/216Anthracnose modelling, nonlinear systems, optimal control |
| spellingShingle | David Fotsa Elvis Houpa David Bekolle Christopher Thron Michel Ndoumbe Mathematical Modelling and Optimal Control of Anthracnose Biomath Anthracnose modelling, nonlinear systems, optimal control |
| title | Mathematical Modelling and Optimal Control of Anthracnose |
| title_full | Mathematical Modelling and Optimal Control of Anthracnose |
| title_fullStr | Mathematical Modelling and Optimal Control of Anthracnose |
| title_full_unstemmed | Mathematical Modelling and Optimal Control of Anthracnose |
| title_short | Mathematical Modelling and Optimal Control of Anthracnose |
| title_sort | mathematical modelling and optimal control of anthracnose |
| topic | Anthracnose modelling, nonlinear systems, optimal control |
| url | http://www.biomathforum.org/biomath/index.php/biomath/article/view/216 |
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