Mathematical analysis of the transmission dynamics of HIV/TB coinfection in the presence of treatment
This paper addresses the synergistic interaction between HIV andmycobacterium tuberculosis using a deterministic model, which incorporatesmany of the essential biological and epidemiological features of the two dis-eases. In the absence of TB infection, the model (HIV-only model) is shownto have a g...
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AIMS Press
2007-12-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.145 |
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| author | Oluwaseun Sharomi Chandra N. Podder Abba B. Gumel Baojun Song |
| author_facet | Oluwaseun Sharomi Chandra N. Podder Abba B. Gumel Baojun Song |
| author_sort | Oluwaseun Sharomi |
| collection | DOAJ |
| description | This paper addresses the synergistic interaction between HIV andmycobacterium tuberculosis using a deterministic model, which incorporatesmany of the essential biological and epidemiological features of the two dis-eases. In the absence of TB infection, the model (HIV-only model) is shownto have a globally asymptotically stable, disease-free equilibrium whenever theassociated reproduction number is less than unity and has a unique endemicequilibrium whenever this number exceeds unity. On the other hand, themodel with TB alone (TB-only model) undergoes the phenomenon of back-ward bifurcation, where the stable disease-free equilibrium co-exists with astable endemic equilibrium when the associated reproduction threshold is lessthan unity. The analysis of the respective reproduction thresholds shows thatthe use of a targeted HIV treatment (using anti-retroviral drugs) strategy canlead to effective control of HIV provided it reduces the relative infectiousnessof individuals treated (in comparison to untreated HIV-infected individuals)below a certain threshold. The full model, with both HIV and TB, is simu-lated to evaluate the impact of the various treatment strategies. It is shownthat the HIV-only treatment strategy saves more cases of the mixed infectionthan the TB-only strategy. Further, for low treatment rates, the mixed-onlystrategy saves the least number of cases (of HIV, TB, and the mixed infection)in comparison to the other strategies. Thus, this study shows that if resourcesare limited, then targeting such resources to treating one of the diseases ismore beneficial in reducing new cases of the mixed infection than targetingthe mixed infection only diseases. Finally, the universal strategy saves morecases of the mixed infection than any of the other strategies. |
| format | Article |
| id | doaj-art-bd7dfa6d67274dd0a0eb0a82a1eca8dd |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2007-12-01 |
| publisher | AIMS Press |
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| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-bd7dfa6d67274dd0a0eb0a82a1eca8dd2025-01-24T01:57:50ZengAIMS PressMathematical Biosciences and Engineering1551-00182007-12-015114517410.3934/mbe.2008.5.145Mathematical analysis of the transmission dynamics of HIV/TB coinfection in the presence of treatmentOluwaseun Sharomi0Chandra N. Podder1Abba B. Gumel2Baojun Song3Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, R3T 2N2Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, R3T 2N2Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, R3T 2N2Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, R3T 2N2This paper addresses the synergistic interaction between HIV andmycobacterium tuberculosis using a deterministic model, which incorporatesmany of the essential biological and epidemiological features of the two dis-eases. In the absence of TB infection, the model (HIV-only model) is shownto have a globally asymptotically stable, disease-free equilibrium whenever theassociated reproduction number is less than unity and has a unique endemicequilibrium whenever this number exceeds unity. On the other hand, themodel with TB alone (TB-only model) undergoes the phenomenon of back-ward bifurcation, where the stable disease-free equilibrium co-exists with astable endemic equilibrium when the associated reproduction threshold is lessthan unity. The analysis of the respective reproduction thresholds shows thatthe use of a targeted HIV treatment (using anti-retroviral drugs) strategy canlead to effective control of HIV provided it reduces the relative infectiousnessof individuals treated (in comparison to untreated HIV-infected individuals)below a certain threshold. The full model, with both HIV and TB, is simu-lated to evaluate the impact of the various treatment strategies. It is shownthat the HIV-only treatment strategy saves more cases of the mixed infectionthan the TB-only strategy. Further, for low treatment rates, the mixed-onlystrategy saves the least number of cases (of HIV, TB, and the mixed infection)in comparison to the other strategies. Thus, this study shows that if resourcesare limited, then targeting such resources to treating one of the diseases ismore beneficial in reducing new cases of the mixed infection than targetingthe mixed infection only diseases. Finally, the universal strategy saves morecases of the mixed infection than any of the other strategies.https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.145equilibriahiv/tbtreatment.stabilitybifurcation |
| spellingShingle | Oluwaseun Sharomi Chandra N. Podder Abba B. Gumel Baojun Song Mathematical analysis of the transmission dynamics of HIV/TB coinfection in the presence of treatment Mathematical Biosciences and Engineering equilibria hiv/tb treatment. stability bifurcation |
| title | Mathematical analysis of the transmission dynamics of HIV/TB coinfection in the presence of treatment |
| title_full | Mathematical analysis of the transmission dynamics of HIV/TB coinfection in the presence of treatment |
| title_fullStr | Mathematical analysis of the transmission dynamics of HIV/TB coinfection in the presence of treatment |
| title_full_unstemmed | Mathematical analysis of the transmission dynamics of HIV/TB coinfection in the presence of treatment |
| title_short | Mathematical analysis of the transmission dynamics of HIV/TB coinfection in the presence of treatment |
| title_sort | mathematical analysis of the transmission dynamics of hiv tb coinfection in the presence of treatment |
| topic | equilibria hiv/tb treatment. stability bifurcation |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2008.5.145 |
| work_keys_str_mv | AT oluwaseunsharomi mathematicalanalysisofthetransmissiondynamicsofhivtbcoinfectioninthepresenceoftreatment AT chandranpodder mathematicalanalysisofthetransmissiondynamicsofhivtbcoinfectioninthepresenceoftreatment AT abbabgumel mathematicalanalysisofthetransmissiondynamicsofhivtbcoinfectioninthepresenceoftreatment AT baojunsong mathematicalanalysisofthetransmissiondynamicsofhivtbcoinfectioninthepresenceoftreatment |