Oscillations induced by quiescent adult female in a model of wild \textit{aedes aegypti} mosquitoes (Q2206329)

The authors present a delayed mathematical model to describe the dynamics of the life cycle of mosquitos. The model is governed by a system of three delay first-order differential equations taking into account the interactions between three stages of the mosquito life cycle (females, eggs, and pupae). The authors first undertake the stability analysis (stability and local stability) of the system and then prove the existence of a bifurcating branch of small amplitude periodic solutions. An algorithm determining the direction of the bifurcation and the stability of bifurcating periodic solutions is proposed. Finally, some numerical simulations are carried out to support the theoretical results.