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Oscillations Induced by Quiescent Adult Female in a Reaction–Diffusion Model of Wild Aedes Aegypti Mosquitoes

Ibn Zohr University, CST Campus Universitaire Ait Melloul Agadir, Morocco

Laboratory of Analysis, Geometry and Applications (LAGA), Department of Mathematics Faculty of Sciences, Ibn Tofail University, Campus Universitaire BP 133, Kenitra, Morocco

E-mail Address: yafia1@yahoo.fr

Corresponding author.

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M. A. Aziz Alaoui

Normandie Univ, France

ULH, LMAH, F-76600 Le Havre, France

FR-CNRS-3335, ISCN, 25 rue Ph. Lebon, 76600 Le Havre, France

E-mail Address: aziz.alaoui@univ-lehavre.fr

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A. Tridane

Department of Mathematical Sciences, United Arab Emirates University Al Ain, Abu Dhabi, UAE

E-mail Address: a-tridane@uaeu.ac.ae

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, and

F. A. Rihan

Department of Mathematical Sciences, United Arab Emirates University Al Ain, Abu Dhabi, UAE

E-mail Address: frihan@uaeu.ac.ae

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https://doi.org/10.1142/S021812741950189XCited by:5 (Source: Crossref)

Abstract

This paper takes the reaction–diffusion approach to deal with the quiescent females phase, so as to describe the dynamics of invasion of aedes aegypti mosquitoes, which are divided into three subpopulations: eggs, pupae and female. We mainly investigate whether the time of quiescence (delay) in the females phase can induce Hopf bifurcation. By means of analyzing the eigenvalue spectrum, we show that the persistent positive equilibrium is asymptotically stable in the absence of time delay, but loses its stability via Hopf bifurcation when time delay crosses some critical value. Using normal form and center manifold theory, we investigate the stability of the bifurcating branches of periodic solutions and the direction of the Hopf bifurcation. Numerical simulations are carried out to support our theoretical results.

Keywords:

References

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