Analysis of a simple mathematical model describing tuberculous granuloma
This paper discusses a mathematical model describing the formation of tuberculosis(TB) granulomas. The main purpose is to analyze the change trend of Mtb and immune cells in different stages after Mtb invaded the host. The theoretical analysis indicates that the existence and global stability of bac...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Western Libraries
2023-11-01
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| Series: | Mathematics in Applied Sciences and Engineering |
| Subjects: | |
| Online Access: | https://ojs.lib.uwo.ca/index.php/mase/article/view/16678 |
| _version_ | 1827340996431577088 |
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| author | Yuqi Jin Hui Cao Xiaxia Xu |
| author_facet | Yuqi Jin Hui Cao Xiaxia Xu |
| author_sort | Yuqi Jin |
| collection | DOAJ |
| description | This paper discusses a mathematical model describing the formation of tuberculosis(TB) granulomas. The main purpose is to analyze the change trend of Mtb and immune cells in different stages after Mtb invaded the host. The theoretical analysis indicates that the existence and global stability of bacteria-free equilibrium and bacteria-present equilibrium under different conditions. In addition, the sensitivity analysis is performed on the parameters, which determines the parameters that have the greatest impact on Mtb invading the host. The stage of no infection, the latent TB infection(LTBIs) and active TB corresponding to the clearance, survival or growth and reproduction of Mtb are displayed by the numerical simulations. The results suggest that whether the individuals infected with Mtb will be progressed to the active TB depends on the immune system of individuals. |
| first_indexed | 2024-03-07T21:29:34Z |
| format | Article |
| id | doaj.art-3e82d516b1dd460ab63916d91e940dd3 |
| institution | Directory Open Access Journal |
| issn | 2563-1926 |
| language | English |
| last_indexed | 2024-03-07T21:29:34Z |
| publishDate | 2023-11-01 |
| publisher | Western Libraries |
| record_format | Article |
| series | Mathematics in Applied Sciences and Engineering |
| spelling | doaj.art-3e82d516b1dd460ab63916d91e940dd32024-02-26T18:53:22ZengWestern LibrariesMathematics in Applied Sciences and Engineering2563-19262023-11-014424926310.5206/mase/1667810935Analysis of a simple mathematical model describing tuberculous granulomaYuqi JinHui CaoXiaxia XuThis paper discusses a mathematical model describing the formation of tuberculosis(TB) granulomas. The main purpose is to analyze the change trend of Mtb and immune cells in different stages after Mtb invaded the host. The theoretical analysis indicates that the existence and global stability of bacteria-free equilibrium and bacteria-present equilibrium under different conditions. In addition, the sensitivity analysis is performed on the parameters, which determines the parameters that have the greatest impact on Mtb invading the host. The stage of no infection, the latent TB infection(LTBIs) and active TB corresponding to the clearance, survival or growth and reproduction of Mtb are displayed by the numerical simulations. The results suggest that whether the individuals infected with Mtb will be progressed to the active TB depends on the immune system of individuals.https://ojs.lib.uwo.ca/index.php/mase/article/view/16678tuberculous granuloma, immune cell, sensitivity analysis, stability. |
| spellingShingle | Yuqi Jin Hui Cao Xiaxia Xu Analysis of a simple mathematical model describing tuberculous granuloma Mathematics in Applied Sciences and Engineering tuberculous granuloma, immune cell, sensitivity analysis, stability. |
| title | Analysis of a simple mathematical model describing tuberculous granuloma |
| title_full | Analysis of a simple mathematical model describing tuberculous granuloma |
| title_fullStr | Analysis of a simple mathematical model describing tuberculous granuloma |
| title_full_unstemmed | Analysis of a simple mathematical model describing tuberculous granuloma |
| title_short | Analysis of a simple mathematical model describing tuberculous granuloma |
| title_sort | analysis of a simple mathematical model describing tuberculous granuloma |
| topic | tuberculous granuloma, immune cell, sensitivity analysis, stability. |
| url | https://ojs.lib.uwo.ca/index.php/mase/article/view/16678 |
| work_keys_str_mv | AT yuqijin analysisofasimplemathematicalmodeldescribingtuberculousgranuloma AT huicao analysisofasimplemathematicalmodeldescribingtuberculousgranuloma AT xiaxiaxu analysisofasimplemathematicalmodeldescribingtuberculousgranuloma |