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Math. Comput. Appl. 2018, 23(3), 33; https://doi.org/10.3390/mca23030033

Qualitative Analysis of a Dengue Fever Model

1
Department of Computer Science, Landmark University, Omu-Aran 251101, Nigeria
2
Department of Ecology and Evolutionary Biology, University of Kansas, Lawrence, KS 66045, USA
3
Department of Mathematical Sciences, University of Zululand, Richards Bay 3900, South Africa
*
Author to whom correspondence should be addressed.
Received: 29 May 2018 / Revised: 19 June 2018 / Accepted: 20 June 2018 / Published: 21 June 2018
(This article belongs to the Section Natural Sciences)
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Abstract

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. View Full-Text
Keywords: Aedes aegypti; A. albopictus; dengue fever; reproduction number; control measures; global stability; aquatic stage; adult stage Aedes aegypti; A. albopictus; dengue fever; reproduction number; control measures; global stability; aquatic stage; adult stage
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).
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MDPI and ACS Style

Gbadamosi, B.; Ojo, M.M.; Oke, S.I.; Matadi, M.B. Qualitative Analysis of a Dengue Fever Model. Math. Comput. Appl. 2018, 23, 33.

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