Optimal control analysis of malaria-schistosomiasis co-infection dynamics
This paper presents a mathematical model for malaria-schistosom-iasis co-infection in order to investigate their synergistic relationship in the presence of treatment. We first analyse the single infection steady states, then investigate the existence and stability of equilibria and then calculate t...
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| Language: | English |
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AIMS Press
2017-03-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2017024 |
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| author | Kazeem Oare Okosun Robert Smith? |
| author_facet | Kazeem Oare Okosun Robert Smith? |
| author_sort | Kazeem Oare Okosun |
| collection | DOAJ |
| description | This paper presents a mathematical model for malaria-schistosom-iasis co-infection in order to investigate their synergistic relationship in the presence of treatment. We first analyse the single infection steady states, then investigate the existence and stability of equilibria and then calculate the basic reproduction numbers. Both the single-infection models and the co-infection model exhibit backward bifurcations. We carrying out a sensitivity analysis of the co-infection model and show that schistosomiasis infection may not be associated with an increased risk of malaria. Conversely, malaria infection may be associated with an increased risk of schistosomiasis. Furthermore, we found that effective treatment and prevention of schistosomiasis infection would also assist in the effective control and eradication of malaria. Finally, we apply Pontryagin's Maximum Principle to the model in order to determine optimal strategies for control of both diseases. |
| format | Article |
| id | doaj-art-766feddd033f42149328dd35e15f22a9 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2017-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-766feddd033f42149328dd35e15f22a92025-01-24T02:39:37ZengAIMS PressMathematical Biosciences and Engineering1551-00182017-03-0114237740510.3934/mbe.2017024Optimal control analysis of malaria-schistosomiasis co-infection dynamicsKazeem Oare Okosun0Robert Smith?1Department of Mathematics, Vaal University of Technology, Andries Potgieter Boulevard, Vanderbijlpark, 1911, South AfricaDepartment of Mathematics, The University of Ottawa, 585 King Edward Ave, Ottawa ON K1N6N5, CanadaThis paper presents a mathematical model for malaria-schistosom-iasis co-infection in order to investigate their synergistic relationship in the presence of treatment. We first analyse the single infection steady states, then investigate the existence and stability of equilibria and then calculate the basic reproduction numbers. Both the single-infection models and the co-infection model exhibit backward bifurcations. We carrying out a sensitivity analysis of the co-infection model and show that schistosomiasis infection may not be associated with an increased risk of malaria. Conversely, malaria infection may be associated with an increased risk of schistosomiasis. Furthermore, we found that effective treatment and prevention of schistosomiasis infection would also assist in the effective control and eradication of malaria. Finally, we apply Pontryagin's Maximum Principle to the model in order to determine optimal strategies for control of both diseases.https://www.aimspress.com/article/doi/10.3934/mbe.2017024malariaschistosomiasisoptimal control |
| spellingShingle | Kazeem Oare Okosun Robert Smith? Optimal control analysis of malaria-schistosomiasis co-infection dynamics Mathematical Biosciences and Engineering malaria schistosomiasis optimal control |
| title | Optimal control analysis of malaria-schistosomiasis co-infection dynamics |
| title_full | Optimal control analysis of malaria-schistosomiasis co-infection dynamics |
| title_fullStr | Optimal control analysis of malaria-schistosomiasis co-infection dynamics |
| title_full_unstemmed | Optimal control analysis of malaria-schistosomiasis co-infection dynamics |
| title_short | Optimal control analysis of malaria-schistosomiasis co-infection dynamics |
| title_sort | optimal control analysis of malaria schistosomiasis co infection dynamics |
| topic | malaria schistosomiasis optimal control |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2017024 |
| work_keys_str_mv | AT kazeemoareokosun optimalcontrolanalysisofmalariaschistosomiasiscoinfectiondynamics AT robertsmith optimalcontrolanalysisofmalariaschistosomiasiscoinfectiondynamics |