Mathematical analysis of a model for HIV-malaria co-infection
A deterministic model for the co-interaction of HIV and malaria in acommunity is presented and rigorously analyzed. Two sub-models,namely the HIV-only and malaria-only sub-models, areconsidered first of all. Unlike the HIV-only sub-model, which has aglobally-asymptotically stable disease-free equil...
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AIMS Press
2009-02-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.333 |
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| author | Zindoga Mukandavire Abba B. Gumel Winston Garira Jean Michel Tchuenche |
| author_facet | Zindoga Mukandavire Abba B. Gumel Winston Garira Jean Michel Tchuenche |
| author_sort | Zindoga Mukandavire |
| collection | DOAJ |
| description | A deterministic model for the co-interaction of HIV and malaria in acommunity is presented and rigorously analyzed. Two sub-models,namely the HIV-only and malaria-only sub-models, areconsidered first of all. Unlike the HIV-only sub-model, which has aglobally-asymptotically stable disease-free equilibrium whenever theassociated reproduction number is less than unity, the malaria-onlysub-model undergoes the phenomenon of backward bifurcation, where astable disease-free equilibrium co-exists with a stable endemicequilibrium, for a certain range of the associated reproductionnumber less than unity. Thus, for malaria, the classical requirementof having the associated reproduction number to be less than unity,although necessary, is not sufficient for its elimination. It isalso shown, using centre manifold theory, that the full HIV-malariaco-infection model undergoes backward bifurcation. Simulations ofthe full HIV-malaria model show that the two diseases co-existwhenever their reproduction numbers exceed unity (with nocompetitive exclusion occurring). Further, the reduction in sexualactivity of individuals with malaria symptoms decreases the numberof new cases of HIV and the mixed HIV-malaria infection whileincreasing the number of malaria cases. Finally, these simulationsshow that the HIV-induced increase in susceptibility to malariainfection has marginal effect on the new cases of HIV and malariabut increases the number of new cases of the dual HIV-malariainfection. |
| format | Article |
| id | doaj-art-e56f3cf4293847588e53516c8b7dc618 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2009-02-01 |
| publisher | AIMS Press |
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| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-e56f3cf4293847588e53516c8b7dc6182025-01-24T01:59:06ZengAIMS PressMathematical Biosciences and Engineering1551-00182009-02-016233336210.3934/mbe.2009.6.333Mathematical analysis of a model for HIV-malaria co-infectionZindoga Mukandavire0Abba B. Gumel1Winston Garira2Jean Michel Tchuenche3Department of Applied Mathematics, National University of Science and Technology, Box AC 939 Ascot, BulawayoDepartment of Applied Mathematics, National University of Science and Technology, Box AC 939 Ascot, BulawayoDepartment of Applied Mathematics, National University of Science and Technology, Box AC 939 Ascot, BulawayoDepartment of Applied Mathematics, National University of Science and Technology, Box AC 939 Ascot, BulawayoA deterministic model for the co-interaction of HIV and malaria in acommunity is presented and rigorously analyzed. Two sub-models,namely the HIV-only and malaria-only sub-models, areconsidered first of all. Unlike the HIV-only sub-model, which has aglobally-asymptotically stable disease-free equilibrium whenever theassociated reproduction number is less than unity, the malaria-onlysub-model undergoes the phenomenon of backward bifurcation, where astable disease-free equilibrium co-exists with a stable endemicequilibrium, for a certain range of the associated reproductionnumber less than unity. Thus, for malaria, the classical requirementof having the associated reproduction number to be less than unity,although necessary, is not sufficient for its elimination. It isalso shown, using centre manifold theory, that the full HIV-malariaco-infection model undergoes backward bifurcation. Simulations ofthe full HIV-malaria model show that the two diseases co-existwhenever their reproduction numbers exceed unity (with nocompetitive exclusion occurring). Further, the reduction in sexualactivity of individuals with malaria symptoms decreases the numberof new cases of HIV and the mixed HIV-malaria infection whileincreasing the number of malaria cases. Finally, these simulationsshow that the HIV-induced increase in susceptibility to malariainfection has marginal effect on the new cases of HIV and malariabut increases the number of new cases of the dual HIV-malariainfection.https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.333stability.equilibriumbasic reproductionnumberhiv-malaria modelco-infection |
| spellingShingle | Zindoga Mukandavire Abba B. Gumel Winston Garira Jean Michel Tchuenche Mathematical analysis of a model for HIV-malaria co-infection Mathematical Biosciences and Engineering stability. equilibrium basic reproductionnumber hiv-malaria model co-infection |
| title | Mathematical analysis of a model for HIV-malaria co-infection |
| title_full | Mathematical analysis of a model for HIV-malaria co-infection |
| title_fullStr | Mathematical analysis of a model for HIV-malaria co-infection |
| title_full_unstemmed | Mathematical analysis of a model for HIV-malaria co-infection |
| title_short | Mathematical analysis of a model for HIV-malaria co-infection |
| title_sort | mathematical analysis of a model for hiv malaria co infection |
| topic | stability. equilibrium basic reproductionnumber hiv-malaria model co-infection |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2009.6.333 |
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