Electron. J. Diff. Equ.,
Vol. 2015 (2015), No. 10, pp. 1-19.
Global stability of a delayed mosquito-transmitted disease
model with stage structure
B. G. Sampath Aruna Pradeep, Wanbiao Ma
Abstract:
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.
Submitted April 22, 2014. Published January 7, 2015.
Math Subject Classifications: 92D25, 34D23, 92B05, 93C23.
Key Words: Epidemic model; time delay; Lyapunov functional;
global stability; nonlinear response.
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B. G. Sampath Aruna Pradeep
Department of Applied Mathematics
School of Mathematics and Physics
University of Science and Technology Beijing
Beijing 100083, China
email: sampath@maths.ruh.ac.lk
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Wanbiao Ma
Department of Applied Mathematics
School of Mathematics and Physics
University of Science and Technology Beijing
Beijing 100083, China
email: wanbiao_ma@ustb.edu.cn
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