The interplay between models and public health policies: Regional control for a class of spatially structured epidemics (think globally, act locally)
A review is presented here of the research carried out, by a group including the authors, on the mathematical analysis of epidemic systems. Particular attention is paid to recent analysis of optimal control problems related to spatially structured epidemics driven by environmental pollution. A relev...
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AIMS Press
2018-01-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2018001 |
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| author | Vincenzo Capasso Sebastian AniȚa |
| author_facet | Vincenzo Capasso Sebastian AniȚa |
| author_sort | Vincenzo Capasso |
| collection | DOAJ |
| description | A review is presented here of the research carried out, by a group including the authors, on the mathematical analysis of epidemic systems. Particular attention is paid to recent analysis of optimal control problems related to spatially structured epidemics driven by environmental pollution. A relevant problem, related to the possible eradication of the epidemic, is the so called zero stabilization. In a series of papers, necessary conditions, and sufficient conditions of stabilizability have been obtained. It has been proved that it is possible to diminish exponentially the epidemic process, in the whole habitat, just by reducing the concentration of the pollutant in a nonempty and sufficiently large subset of the spatial domain. The stabilizability with a feedback control of harvesting type is related to the magnitude of the principal eigenvalue of a certain operator. The problem of finding the optimal position (by translation) of the support of the feedback stabilizing control is faced, in order to minimize both the infected population and the pollutant at a certain finite time. |
| format | Article |
| id | doaj-art-3208c730e49b4a3c980affd8ef06591c |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2018-01-01 |
| publisher | AIMS Press |
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| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-3208c730e49b4a3c980affd8ef06591c2025-01-24T02:40:37ZengAIMS PressMathematical Biosciences and Engineering1551-00182018-01-0115112010.3934/mbe.2018001The interplay between models and public health policies: Regional control for a class of spatially structured epidemics (think globally, act locally)Vincenzo Capasso0Sebastian AniȚa1ADAMSS, Universitá degli Studi di Milano, 20133 MILANO, ItalyFaculty of Mathematics, "Alexandru Ioan Cuza" University of Iași, "Octav Mayer" Institute of Mathematics of the Romanian Academy, Iași 700506, RomaniaA review is presented here of the research carried out, by a group including the authors, on the mathematical analysis of epidemic systems. Particular attention is paid to recent analysis of optimal control problems related to spatially structured epidemics driven by environmental pollution. A relevant problem, related to the possible eradication of the epidemic, is the so called zero stabilization. In a series of papers, necessary conditions, and sufficient conditions of stabilizability have been obtained. It has been proved that it is possible to diminish exponentially the epidemic process, in the whole habitat, just by reducing the concentration of the pollutant in a nonempty and sufficiently large subset of the spatial domain. The stabilizability with a feedback control of harvesting type is related to the magnitude of the principal eigenvalue of a certain operator. The problem of finding the optimal position (by translation) of the support of the feedback stabilizing control is faced, in order to minimize both the infected population and the pollutant at a certain finite time.https://www.aimspress.com/article/doi/10.3934/mbe.2018001epidemic systemsnonlinear modelsman-environment epidemicsreaction-diffusion systemsstabilizationprincipal eigenvaluefeedback controloptimal regional control |
| spellingShingle | Vincenzo Capasso Sebastian AniȚa The interplay between models and public health policies: Regional control for a class of spatially structured epidemics (think globally, act locally) Mathematical Biosciences and Engineering epidemic systems nonlinear models man-environment epidemics reaction-diffusion systems stabilization principal eigenvalue feedback control optimal regional control |
| title | The interplay between models and public health policies: Regional control for a class of spatially structured epidemics (think globally, act locally) |
| title_full | The interplay between models and public health policies: Regional control for a class of spatially structured epidemics (think globally, act locally) |
| title_fullStr | The interplay between models and public health policies: Regional control for a class of spatially structured epidemics (think globally, act locally) |
| title_full_unstemmed | The interplay between models and public health policies: Regional control for a class of spatially structured epidemics (think globally, act locally) |
| title_short | The interplay between models and public health policies: Regional control for a class of spatially structured epidemics (think globally, act locally) |
| title_sort | interplay between models and public health policies regional control for a class of spatially structured epidemics think globally act locally |
| topic | epidemic systems nonlinear models man-environment epidemics reaction-diffusion systems stabilization principal eigenvalue feedback control optimal regional control |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2018001 |
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