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Oscillatory regimes in a mosquito population model with larval feedback on egg hatching. (English) Zbl 1448.92251
Summary: Understanding mosquitoes life cycle is of great interest presently because of the increasing impact of vector borne diseases in several countries. There is evidence of oscillations in mosquito populations independent of seasonality, still unexplained, based on observations both in laboratories and in nature. We propose a simple mathematical model of egg hatching enhancement by larvae which produces such oscillations that conveys a possible explanation. We propose both a theoretical analysis, based on slow-fast dynamics and Hopf bifurcation, and numerical investigations in order to shed some light on the mechanisms at work in this model.
MSC:
92D25 Population dynamics (general)
34C23 Bifurcation theory for ordinary differential equations
Software:
Maple; XPPAUT
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