A pressure model of immune response to mycobacteriumtuberculosis infection in several space dimensions
Mycobacterium tuberculosis (Mtb) is a widely diffused infection. However, in general, the human immune system is able to contain it. In this work, we propose a mathematical model which describes the early immune response to the Mtb infection in the lungs, also including the possible evolution of the...
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AIMS Press
2010-03-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.277 |
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| author | Fabrizio Clarelli Roberto Natalini |
| author_facet | Fabrizio Clarelli Roberto Natalini |
| author_sort | Fabrizio Clarelli |
| collection | DOAJ |
| description | Mycobacterium tuberculosis (Mtb) is a widely diffused infection. However, in general, the human immune system is able to contain it. In this work, we propose a mathematical model which describes the early immune response to the Mtb infection in the lungs, also including the possible evolution of the infection in the formation of a granuloma. The model is based on coupled reaction-diffusion-transport equations with chemotaxis, which take into account the interactions among bacteria, macrophages and chemoattractant. The novelty of this approach is in the modeling of the velocity field, proportional to the gradient of the pressure developed between the cells, which makes possible to deal with a full multidimensional description and efficient numerical simulations. We perform a linear stability analysis of the model and propose a robust implicit-explicit scheme to deal with long time simulations. Both in one and two-dimensions, we find that there are threshold values in the parameters space, between a contained infection and the uncontrolled bacteria growth, and the generation of granuloma-like patterns can be observed numerically. |
| format | Article |
| id | doaj-art-c452536066254b579aafaed65554d1bb |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2010-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-c452536066254b579aafaed65554d1bb2025-01-24T02:00:28ZengAIMS PressMathematical Biosciences and Engineering1551-00182010-03-017227730010.3934/mbe.2010.7.277A pressure model of immune response to mycobacteriumtuberculosis infection in several space dimensionsFabrizio Clarelli0Roberto Natalini1Istituto per le Applicazioni del Calcolo “M. Picone”, CNR, c/o Dip. di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 1; I-00133 RomaIstituto per le Applicazioni del Calcolo “M. Picone”, CNR, c/o Dip. di Matematica, Università di Roma “Tor Vergata”, Via della Ricerca Scientifica, 1; I-00133 RomaMycobacterium tuberculosis (Mtb) is a widely diffused infection. However, in general, the human immune system is able to contain it. In this work, we propose a mathematical model which describes the early immune response to the Mtb infection in the lungs, also including the possible evolution of the infection in the formation of a granuloma. The model is based on coupled reaction-diffusion-transport equations with chemotaxis, which take into account the interactions among bacteria, macrophages and chemoattractant. The novelty of this approach is in the modeling of the velocity field, proportional to the gradient of the pressure developed between the cells, which makes possible to deal with a full multidimensional description and efficient numerical simulations. We perform a linear stability analysis of the model and propose a robust implicit-explicit scheme to deal with long time simulations. Both in one and two-dimensions, we find that there are threshold values in the parameters space, between a contained infection and the uncontrolled bacteria growth, and the generation of granuloma-like patterns can be observed numerically.https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.277internal velocity.reaction-diffusion-advectionmulti-dimensional modelmycobacterium tuberculosischemotaxis |
| spellingShingle | Fabrizio Clarelli Roberto Natalini A pressure model of immune response to mycobacteriumtuberculosis infection in several space dimensions Mathematical Biosciences and Engineering internal velocity. reaction-diffusion-advection multi-dimensional model mycobacterium tuberculosis chemotaxis |
| title | A pressure model of immune response to mycobacteriumtuberculosis infection in several space dimensions |
| title_full | A pressure model of immune response to mycobacteriumtuberculosis infection in several space dimensions |
| title_fullStr | A pressure model of immune response to mycobacteriumtuberculosis infection in several space dimensions |
| title_full_unstemmed | A pressure model of immune response to mycobacteriumtuberculosis infection in several space dimensions |
| title_short | A pressure model of immune response to mycobacteriumtuberculosis infection in several space dimensions |
| title_sort | pressure model of immune response to mycobacteriumtuberculosis infection in several space dimensions |
| topic | internal velocity. reaction-diffusion-advection multi-dimensional model mycobacterium tuberculosis chemotaxis |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.277 |
| work_keys_str_mv | AT fabrizioclarelli apressuremodelofimmuneresponsetomycobacteriumtuberculosisinfectioninseveralspacedimensions AT robertonatalini apressuremodelofimmuneresponsetomycobacteriumtuberculosisinfectioninseveralspacedimensions AT fabrizioclarelli pressuremodelofimmuneresponsetomycobacteriumtuberculosisinfectioninseveralspacedimensions AT robertonatalini pressuremodelofimmuneresponsetomycobacteriumtuberculosisinfectioninseveralspacedimensions |