A two strain tuberculosis transmission model with therapy and quarantine
A two strain tuberculosis model with treatment which allows TB patients with the drug sensitive of strain Mycobacterium tuberculosis to be cured is presented. The model is further extended to incorporate quarantine for active TB cases with multi‐drug resistant TB strains. The model assumes that late...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2009-09-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/6550 |
| _version_ | 1818903361682931712 |
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| author | Claver P. Bhunu Winston Garira |
| author_facet | Claver P. Bhunu Winston Garira |
| author_sort | Claver P. Bhunu |
| collection | DOAJ |
| description | A two strain tuberculosis model with treatment which allows TB patients with the drug sensitive of strain Mycobacterium tuberculosis to be cured is presented. The model is further extended to incorporate quarantine for active TB cases with multi‐drug resistant TB strains. The model assumes that latently infected individuals develop active disease as a result of endogenous activation and exogenous reinfection. Qualitative analysis of the model including positivity, boundedness and persistence of solutions are presented. The thresholds and equilibria quantities for the models are determined and stability of the solution is analyzed. From the study we conclude that quarantine of the multi‐drug resistant tuberculosis cases reduces the multi‐drug resistant tuberculosis induced reproduction number to values below unit, thus this intervention strategy can control the development of multi‐drug resistant tuberculosis epidemic. Also effective chemoprophylaxis and treatment of infectives result in a reduction of multi‐drug resistant tuberculosis cases since most multi‐drug resistant tuberculosis cases are a result of inappropriate treatment.
First published online: 14 Oct 2010 |
| first_indexed | 2024-12-19T20:50:20Z |
| format | Article |
| id | doaj.art-7f59ad957cfe439fae7baec3bf043b81 |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-12-19T20:50:20Z |
| publishDate | 2009-09-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-7f59ad957cfe439fae7baec3bf043b812022-12-21T20:06:08ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102009-09-0114310.3846/1392-6292.2009.14.291-312A two strain tuberculosis transmission model with therapy and quarantineClaver P. Bhunu0Winston Garira1Modelling Biomedical Systems Research Group, Department of Applied Mathematics, National University of Science and Technology; P. O. Box AC 939 Ascot, Bulawayo, ZimbabweModelling Biomedical Systems Research Group, Department of Applied Mathematics, National University of Science and Technology; Department of Mathematics and Applied Mathematics, University of Venda, South AfricaA two strain tuberculosis model with treatment which allows TB patients with the drug sensitive of strain Mycobacterium tuberculosis to be cured is presented. The model is further extended to incorporate quarantine for active TB cases with multi‐drug resistant TB strains. The model assumes that latently infected individuals develop active disease as a result of endogenous activation and exogenous reinfection. Qualitative analysis of the model including positivity, boundedness and persistence of solutions are presented. The thresholds and equilibria quantities for the models are determined and stability of the solution is analyzed. From the study we conclude that quarantine of the multi‐drug resistant tuberculosis cases reduces the multi‐drug resistant tuberculosis induced reproduction number to values below unit, thus this intervention strategy can control the development of multi‐drug resistant tuberculosis epidemic. Also effective chemoprophylaxis and treatment of infectives result in a reduction of multi‐drug resistant tuberculosis cases since most multi‐drug resistant tuberculosis cases are a result of inappropriate treatment. First published online: 14 Oct 2010https://journals.vgtu.lt/index.php/MMA/article/view/6550Tuberculosis modelchemoprophylaxistreatmentquarantineexogenous re‐infectionmulti‐drug resistant |
| spellingShingle | Claver P. Bhunu Winston Garira A two strain tuberculosis transmission model with therapy and quarantine Mathematical Modelling and Analysis Tuberculosis model chemoprophylaxis treatment quarantine exogenous re‐infection multi‐drug resistant |
| title | A two strain tuberculosis transmission model with therapy and quarantine |
| title_full | A two strain tuberculosis transmission model with therapy and quarantine |
| title_fullStr | A two strain tuberculosis transmission model with therapy and quarantine |
| title_full_unstemmed | A two strain tuberculosis transmission model with therapy and quarantine |
| title_short | A two strain tuberculosis transmission model with therapy and quarantine |
| title_sort | two strain tuberculosis transmission model with therapy and quarantine |
| topic | Tuberculosis model chemoprophylaxis treatment quarantine exogenous re‐infection multi‐drug resistant |
| url | https://journals.vgtu.lt/index.php/MMA/article/view/6550 |
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