Qualitative Analysis of a Dengue Fever Model
In this paper, a deterministic mathematical model of the Dengue virus with a nonlinear incidence function in a population is presented and rigorously analysed. The model incorporates control measures at the aquatic and adult stages of the vector (mosquito). The stability of the system is analysed fo...
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| Format: | Article |
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MDPI AG
2018-06-01
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| Series: | Mathematical and Computational Applications |
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| Online Access: | http://www.mdpi.com/2297-8747/23/3/33 |
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| author | Babatunde Gbadamosi Mayowa Micheal Ojo Segun Isaac Oke Maba Boniface Matadi |
| author_facet | Babatunde Gbadamosi Mayowa Micheal Ojo Segun Isaac Oke Maba Boniface Matadi |
| author_sort | Babatunde Gbadamosi |
| collection | DOAJ |
| description | In this paper, a deterministic mathematical model of the Dengue virus with a nonlinear incidence function in a population is presented and rigorously analysed. The model incorporates control measures at the aquatic and adult stages of the vector (mosquito). The stability of the system is analysed for the disease-free equilibrium and the existence of endemic equilibria under certain conditions. The local stability of the Dengue-free equilibrium is investigated via the threshold parameter (reproduction number) that was obtained using the next-generation matrix techniques. The Routh–Hurwitz criterion, along with Descartes’ rule of signs change, established the local asymptotically stability of the model whenever R0<1 and was unstable otherwise. The comparison theorem was used to establish the global asymptomatically stability of the model. |
| first_indexed | 2024-12-12T23:28:44Z |
| format | Article |
| id | doaj.art-fbaba85b115f4f86a50b8767e84ce92c |
| institution | Directory Open Access Journal |
| issn | 2297-8747 |
| language | English |
| last_indexed | 2024-12-12T23:28:44Z |
| publishDate | 2018-06-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematical and Computational Applications |
| spelling | doaj.art-fbaba85b115f4f86a50b8767e84ce92c2022-12-22T00:07:53ZengMDPI AGMathematical and Computational Applications2297-87472018-06-012333310.3390/mca23030033mca23030033Qualitative Analysis of a Dengue Fever ModelBabatunde Gbadamosi0Mayowa Micheal Ojo1Segun Isaac Oke2Maba Boniface Matadi3Department of Computer Science, Landmark University, Omu-Aran 251101, NigeriaDepartment of Ecology and Evolutionary Biology, University of Kansas, Lawrence, KS 66045, USADepartment of Mathematical Sciences, University of Zululand, Richards Bay 3900, South AfricaDepartment of Mathematical Sciences, University of Zululand, Richards Bay 3900, South AfricaIn this paper, a deterministic mathematical model of the Dengue virus with a nonlinear incidence function in a population is presented and rigorously analysed. The model incorporates control measures at the aquatic and adult stages of the vector (mosquito). The stability of the system is analysed for the disease-free equilibrium and the existence of endemic equilibria under certain conditions. The local stability of the Dengue-free equilibrium is investigated via the threshold parameter (reproduction number) that was obtained using the next-generation matrix techniques. The Routh–Hurwitz criterion, along with Descartes’ rule of signs change, established the local asymptotically stability of the model whenever R0<1 and was unstable otherwise. The comparison theorem was used to establish the global asymptomatically stability of the model.http://www.mdpi.com/2297-8747/23/3/33Aedes aegyptiA. albopictusdengue feverreproduction numbercontrol measuresglobal stabilityaquatic stageadult stage |
| spellingShingle | Babatunde Gbadamosi Mayowa Micheal Ojo Segun Isaac Oke Maba Boniface Matadi Qualitative Analysis of a Dengue Fever Model Mathematical and Computational Applications Aedes aegypti A. albopictus dengue fever reproduction number control measures global stability aquatic stage adult stage |
| title | Qualitative Analysis of a Dengue Fever Model |
| title_full | Qualitative Analysis of a Dengue Fever Model |
| title_fullStr | Qualitative Analysis of a Dengue Fever Model |
| title_full_unstemmed | Qualitative Analysis of a Dengue Fever Model |
| title_short | Qualitative Analysis of a Dengue Fever Model |
| title_sort | qualitative analysis of a dengue fever model |
| topic | Aedes aegypti A. albopictus dengue fever reproduction number control measures global stability aquatic stage adult stage |
| url | http://www.mdpi.com/2297-8747/23/3/33 |
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