Geodesic
Global stability of a delayed mosquito-transmitted disease model with stage structure
Electronic Journal of Differential Equations, Tome 2015 (2015).

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Summary: This article presents a new eco-epidemiological deterministic delay differential equation model considering a biological controlling approach on mosquitoes, for endemic dengue disease with variable host (human) and variable vector (Aedes aegypti) populations, and stage structure for mosquitoes. In this model, predator-prey interaction is considered by using larvae as prey and mosquito-fish as predator. We give a complete classification of equilibria of the model, and sufficient conditions for global stability/global attractivity of some equilibria are given by constructing suitable Lyapunov functionals and using Lyapunov-LaSalle invariance principle. Also, numerical simulations are presented to show the validity of our results.
Classification : 92D25, 34D23, 92B05, 93C23
Keywords: epidemic model, time delay, Lyapunov functional, global stability, nonlinear response 
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     author = {Pradeep, B.G.Sampath Aruna and Ma, Wanbiao},
     title = {Global stability of a delayed mosquito-transmitted disease model with stage structure},
     journal = {Electronic Journal of Differential Equations},
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     volume = {2015},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a26/}
}
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Pradeep, B.G.Sampath Aruna; Ma, Wanbiao. Global stability of a delayed mosquito-transmitted disease model with stage structure. Electronic Journal of Differential Equations, Tome 2015 (2015). http://geodesic.mathdoc.fr/item/EJDE_2015__2015__a26/