Analysis of a Tuberculosis Infection Model considering the Influence of Saturated Recovery (Treatment)
Tuberculosis (TB) is a serious global health threat that is caused by the bacterium Mycobacterium tuberculosis, is extremely infectious, and has a high mortality rate. In this paper, we developed a model of TB infection to predict the impact of saturated recovery. The existence of equilibrium and it...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2021/1805651 |
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| _version_ | 1832561451130159104 |
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| author | Fatima Sulayman Farah Aini Abdullah |
| author_facet | Fatima Sulayman Farah Aini Abdullah |
| author_sort | Fatima Sulayman |
| collection | DOAJ |
| description | Tuberculosis (TB) is a serious global health threat that is caused by the bacterium Mycobacterium tuberculosis, is extremely infectious, and has a high mortality rate. In this paper, we developed a model of TB infection to predict the impact of saturated recovery. The existence of equilibrium and its stability has been investigated based on the effective reproduction number RC. The model displays interesting dynamics, including backward bifurcation and Hopf bifurcation, which further results in the stable disease-free and stable endemic equilibria to be coexisting. Bifurcation analysis demonstrates that the saturation parameter is accountable for the phenomenon of backward bifurcation. We derive a condition that guarantees that the model is globally asymptotically stable using the Lyapunov function approach to global stability. The numerical simulation also reveals that the extent of saturation of TB infection is the mechanism that is fuelling TB disease in the population. |
| format | Article |
| id | doaj-art-b04091ea7ba2482793f138a47cf3af03 |
| institution | Kabale University |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-b04091ea7ba2482793f138a47cf3af032025-02-03T01:25:02ZengWileyComplexity1076-27871099-05262021-01-01202110.1155/2021/18056511805651Analysis of a Tuberculosis Infection Model considering the Influence of Saturated Recovery (Treatment)Fatima Sulayman0Farah Aini Abdullah1School of Mathematical Sciences, Universiti Sains Malaysia USM, 11800 Penang, MalaysiaSchool of Mathematical Sciences, Universiti Sains Malaysia USM, 11800 Penang, MalaysiaTuberculosis (TB) is a serious global health threat that is caused by the bacterium Mycobacterium tuberculosis, is extremely infectious, and has a high mortality rate. In this paper, we developed a model of TB infection to predict the impact of saturated recovery. The existence of equilibrium and its stability has been investigated based on the effective reproduction number RC. The model displays interesting dynamics, including backward bifurcation and Hopf bifurcation, which further results in the stable disease-free and stable endemic equilibria to be coexisting. Bifurcation analysis demonstrates that the saturation parameter is accountable for the phenomenon of backward bifurcation. We derive a condition that guarantees that the model is globally asymptotically stable using the Lyapunov function approach to global stability. The numerical simulation also reveals that the extent of saturation of TB infection is the mechanism that is fuelling TB disease in the population.http://dx.doi.org/10.1155/2021/1805651 |
| spellingShingle | Fatima Sulayman Farah Aini Abdullah Analysis of a Tuberculosis Infection Model considering the Influence of Saturated Recovery (Treatment) Complexity |
| title | Analysis of a Tuberculosis Infection Model considering the Influence of Saturated Recovery (Treatment) |
| title_full | Analysis of a Tuberculosis Infection Model considering the Influence of Saturated Recovery (Treatment) |
| title_fullStr | Analysis of a Tuberculosis Infection Model considering the Influence of Saturated Recovery (Treatment) |
| title_full_unstemmed | Analysis of a Tuberculosis Infection Model considering the Influence of Saturated Recovery (Treatment) |
| title_short | Analysis of a Tuberculosis Infection Model considering the Influence of Saturated Recovery (Treatment) |
| title_sort | analysis of a tuberculosis infection model considering the influence of saturated recovery treatment |
| url | http://dx.doi.org/10.1155/2021/1805651 |
| work_keys_str_mv | AT fatimasulayman analysisofatuberculosisinfectionmodelconsideringtheinfluenceofsaturatedrecoverytreatment AT farahainiabdullah analysisofatuberculosisinfectionmodelconsideringtheinfluenceofsaturatedrecoverytreatment |