Stage-Dependent Structured Discrete-Time Models for Mosquito Population Evolution with Survivability: Solution Properties, Equilibrium Points, Oscillations, and Population Feedback Controls

Abstract

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.

On the Properties of a Class of Impulsive Competition Beverton–Holt Equations

“…The results are applied to the study of the coexistence of two competing species subject to Allee effects and contest competition. It can be pointed out that a Beverton-Holt equation type is proposed and studied in [35] for a set with, in general, more than two competing species. It is found that the species with the best fitness outcompete the remaining ones.…”

“…It is found that the species with the best fitness outcompete the remaining ones. For the study of the involvement of two sampling periods for two stages of evolution of mosquito, see, for instance [35] and some of the references therein.…”