Optimal (Control of) Intervention Strategies for Malaria Epidemic in Karonga District, Malawi
Malaria is a public health problem for more than 2 billion people globally. About 219 million cases of malaria occur worldwide and 660,000 people die, mostly (91%) in the African Region despite decades of efforts to control the disease. Although the disease is preventable, it is life-threatening and...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/594256 |
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| author | Peter M. Mwamtobe Shirley Abelman J. Michel Tchuenche Ansley Kasambara |
| author_facet | Peter M. Mwamtobe Shirley Abelman J. Michel Tchuenche Ansley Kasambara |
| author_sort | Peter M. Mwamtobe |
| collection | DOAJ |
| description | Malaria is a public health problem for more than 2 billion people globally. About 219
million cases of malaria occur worldwide and 660,000 people die, mostly (91%) in the African
Region despite decades of efforts to control the disease. Although the disease is preventable, it
is life-threatening and parasitically transmitted by the bite of the female Anopheles mosquito.
A deterministic mathematical model with intervention strategies is developed in order to
investigate the effectiveness and optimal control strategies of indoor residual spraying (IRS),
insecticide treated nets (ITNs) and treatment on the transmission dynamics of malaria in
Karonga District, Malawi. The effective reproduction number is analytically computed,
and the existence and stability conditions of the equilibria are explored. The model does
not exhibit backward bifurcation. Pontryagin’s Maximum Principle which uses both the
Lagrangian and Hamiltonian principles with respect to a time dependent constant is used to
derive the necessary conditions for the optimal control of the disease. Numerical simulations
indicate that the prevention strategies lead to the reduction of both the mosquito population
and infected human individuals. Effective treatment consolidates the prevention strategies.
Thus, malaria can be eradicated in Karonga District by concurrently applying vector control via ITNs and IRS complemented with timely treatment of infected
people. |
| format | Article |
| id | doaj-art-d8f8b1ed4e6d4721817842473867ba3e |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-d8f8b1ed4e6d4721817842473867ba3e2025-02-03T05:46:27ZengWileyAbstract and Applied Analysis1085-33751687-04092014-01-01201410.1155/2014/594256594256Optimal (Control of) Intervention Strategies for Malaria Epidemic in Karonga District, MalawiPeter M. Mwamtobe0Shirley Abelman1J. Michel Tchuenche2Ansley Kasambara3School of Computational and Applied Mathematics, University of Witwatersrand, Private Bag 3, Wits, Johannesburg 2050, South AfricaSchool of Computational and Applied Mathematics, University of Witwatersrand, Private Bag 3, Wits, Johannesburg 2050, South Africa3253 Flowers Road South, Atlanta, GA 30341, USADepartment of Mathematics and Statistics, University of Malawi, The Malawi Polytechnic, Private Bag 303, Chichiri, Blantyre 3, MalawiMalaria is a public health problem for more than 2 billion people globally. About 219 million cases of malaria occur worldwide and 660,000 people die, mostly (91%) in the African Region despite decades of efforts to control the disease. Although the disease is preventable, it is life-threatening and parasitically transmitted by the bite of the female Anopheles mosquito. A deterministic mathematical model with intervention strategies is developed in order to investigate the effectiveness and optimal control strategies of indoor residual spraying (IRS), insecticide treated nets (ITNs) and treatment on the transmission dynamics of malaria in Karonga District, Malawi. The effective reproduction number is analytically computed, and the existence and stability conditions of the equilibria are explored. The model does not exhibit backward bifurcation. Pontryagin’s Maximum Principle which uses both the Lagrangian and Hamiltonian principles with respect to a time dependent constant is used to derive the necessary conditions for the optimal control of the disease. Numerical simulations indicate that the prevention strategies lead to the reduction of both the mosquito population and infected human individuals. Effective treatment consolidates the prevention strategies. Thus, malaria can be eradicated in Karonga District by concurrently applying vector control via ITNs and IRS complemented with timely treatment of infected people.http://dx.doi.org/10.1155/2014/594256 |
| spellingShingle | Peter M. Mwamtobe Shirley Abelman J. Michel Tchuenche Ansley Kasambara Optimal (Control of) Intervention Strategies for Malaria Epidemic in Karonga District, Malawi Abstract and Applied Analysis |
| title | Optimal (Control of) Intervention Strategies for Malaria Epidemic in Karonga District, Malawi |
| title_full | Optimal (Control of) Intervention Strategies for Malaria Epidemic in Karonga District, Malawi |
| title_fullStr | Optimal (Control of) Intervention Strategies for Malaria Epidemic in Karonga District, Malawi |
| title_full_unstemmed | Optimal (Control of) Intervention Strategies for Malaria Epidemic in Karonga District, Malawi |
| title_short | Optimal (Control of) Intervention Strategies for Malaria Epidemic in Karonga District, Malawi |
| title_sort | optimal control of intervention strategies for malaria epidemic in karonga district malawi |
| url | http://dx.doi.org/10.1155/2014/594256 |
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