bdb5b752f84ce4301e7a2f65866df95d mathematics_a2019v7p1181.pdf 81e3a846bc7698c38c9698608d0eda8ac1de0225 mathematics_a2019v7p1181.pdf 84920f1535d532d0dbaaeb8916c981747a16d82ae7dbed72141047cf5d3409af mathematics_a2019v7p1181.pdf Title: Stage-Dependent Structured Discrete-Time Models for Mosquito Population Evolution with Survivability: Solution Properties, Equilibrium Points, Oscillations, and Population Feedback Controls Subject: This paper relied on the investigation of the properties of the stage-structured model of coupled larvae and adult mosquito populations’ evolution when parameterized, in general, by time-varying (or stage-dependent) sequences. In particular, the investigated properties were the non-negativity of the solution under non-negative initial conditions, the boundedness of the sequence solutions under any finite non-negative initial conditions, the equilibrium points, and the convergence conditions to them in the event that the parameterizing sequences converge to finite limits. Some further properties that were investigated relied on deriving the oscillation conditions of the solutions under certain conditions of the parameterizations. The use of feedback controls to decrease the foreseen numbers of alive mosquitoes in future evolution stages is also proposed. The proposed control actions are exerted on the birth rate and/or the maximum progression rate sequences. Some illustrative examples are also given. Keywords: equilibrium points; Beverton–Holt equation; mosquito evolution solution stages; population controls; asymptotic stability; stability; oscillatory solutions Author: Manuel De la Sen, Asier Ibeas and Aitor J. 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