Deterministic Models in Dengue Transmission Dynamics
Adeterministic model for monitoring the impact of treatment on the transmission dynamics of dengue in the human and vector populations is presented. In addition to having a locally-asymptotically stable disease-free equilibrium (OFE) whenever the basic reproduction number is less than unity, it...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English English |
| Published: |
Institute for Mathematical Research
2008
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| Online Access: | http://psasir.upm.edu.my/id/eprint/12463/1/Artikel_5_vol2_no1.pdf |
| _version_ | 1796968240822353920 |
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| author | Abu Bakar, Mohd Rizam Mohammed, Salisu Garba Ibrahim, Noor Akma Monsi, Mansor |
| author_facet | Abu Bakar, Mohd Rizam Mohammed, Salisu Garba Ibrahim, Noor Akma Monsi, Mansor |
| author_sort | Abu Bakar, Mohd Rizam |
| collection | UPM |
| description | Adeterministic model for monitoring the impact of
treatment on the transmission dynamics of dengue
in the human and vector populations is presented.
In addition to having a locally-asymptotically
stable disease-free equilibrium (OFE) whenever
the basic reproduction number is less than unity, it
is shown, llsing a Lyapunov function and LaSalle
Invariance Principle that the DFE of both
treatment~frcc and treatment model, in the absence
of dengue-induced 1ll00tality, IS globallyasymptotically
stable whenever the reproduction
number is less than unity. Each oftbe models has a
unique endemic equilibrium whenever its
reproduction number excceds unity. Numerical
simulations of thc model show that for high
treatment rates, the disease can be controled within
a community. |
| first_indexed | 2024-03-06T07:25:33Z |
| format | Article |
| id | upm.eprints-12463 |
| institution | Universiti Putra Malaysia |
| language | English English |
| last_indexed | 2024-03-06T07:25:33Z |
| publishDate | 2008 |
| publisher | Institute for Mathematical Research |
| record_format | dspace |
| spelling | upm.eprints-124632013-05-27T07:52:25Z http://psasir.upm.edu.my/id/eprint/12463/ Deterministic Models in Dengue Transmission Dynamics Abu Bakar, Mohd Rizam Mohammed, Salisu Garba Ibrahim, Noor Akma Monsi, Mansor Adeterministic model for monitoring the impact of treatment on the transmission dynamics of dengue in the human and vector populations is presented. In addition to having a locally-asymptotically stable disease-free equilibrium (OFE) whenever the basic reproduction number is less than unity, it is shown, llsing a Lyapunov function and LaSalle Invariance Principle that the DFE of both treatment~frcc and treatment model, in the absence of dengue-induced 1ll00tality, IS globallyasymptotically stable whenever the reproduction number is less than unity. Each oftbe models has a unique endemic equilibrium whenever its reproduction number excceds unity. Numerical simulations of thc model show that for high treatment rates, the disease can be controled within a community. Institute for Mathematical Research 2008-12 Article PeerReviewed application/pdf en http://psasir.upm.edu.my/id/eprint/12463/1/Artikel_5_vol2_no1.pdf Abu Bakar, Mohd Rizam and Mohammed, Salisu Garba and Ibrahim, Noor Akma and Monsi, Mansor (2008) Deterministic Models in Dengue Transmission Dynamics. Math Digest : Research Bulletin Institute for Mathematical Research, 2 (1). pp. 21-33. ISSN 1985-2436 English |
| spellingShingle | Abu Bakar, Mohd Rizam Mohammed, Salisu Garba Ibrahim, Noor Akma Monsi, Mansor Deterministic Models in Dengue Transmission Dynamics |
| title | Deterministic Models in Dengue Transmission Dynamics |
| title_full | Deterministic Models in Dengue Transmission Dynamics |
| title_fullStr | Deterministic Models in Dengue Transmission Dynamics |
| title_full_unstemmed | Deterministic Models in Dengue Transmission Dynamics |
| title_short | Deterministic Models in Dengue Transmission Dynamics |
| title_sort | deterministic models in dengue transmission dynamics |
| url | http://psasir.upm.edu.my/id/eprint/12463/1/Artikel_5_vol2_no1.pdf |
| work_keys_str_mv | AT abubakarmohdrizam deterministicmodelsindenguetransmissiondynamics AT mohammedsalisugarba deterministicmodelsindenguetransmissiondynamics AT ibrahimnoorakma deterministicmodelsindenguetransmissiondynamics AT monsimansor deterministicmodelsindenguetransmissiondynamics |