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

Manuel De la Sen, Asier Ibeas and Aitor J. Garrido
Additional contact information
Manuel De la Sen: Institute of Research and Development of Processes IIDP, University of the Basque Country, Campus of Leioa, Barrio Sarriena, 48940 Leioa, Bizkaia, Spain
Asier Ibeas: Department of Telecommunications and Systems Engineering, Universitat Autònoma de Barcelona, Campus de Bellaterra, Bellaterra, Cerdanyola del Vallès, 08193 Barcelona, Spain
Aitor J. Garrido: Department of Automatic Control and Systems Engineering, Faculty of Engineering of Bilbao, University of the Basque Country, Paseo Rafael Moreno 3, 48013 Bilbao, Spain

Mathematics, 2019, vol. 7, issue 12, 1-29

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.

Keywords: equilibrium points; Beverton–Holt equation; mosquito evolution solution stages; population controls; asymptotic stability; stability; oscillatory solutions (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/7/12/1181/pdf (application/pdf)
https://www.mdpi.com/2227-7390/7/12/1181/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:7:y:2019:i:12:p:1181-:d:293704

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().