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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Manuel De la Sen & Asier Ibeas & Aitor J. Garrido, 2019. "Stage-Dependent Structured Discrete-Time Models for Mosquito Population Evolution with Survivability: Solution Properties, Equilibrium Points, Oscillations, and Population Feedback Controls," Mathematics, MDPI, vol. 7(12), pages 1-29, December.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:12:p:1181-:d:293704
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    References listed on IDEAS

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    1. Flores, J.C., 2003. "A mathematical model for wild and sterile species in competition: immigration," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 328(1), pages 214-224.
    2. Stevo Stevic, 2006. "A short proof of the Cushing-Henson conjecture," Discrete Dynamics in Nature and Society, Hindawi, vol. 2006, pages 1-5, November.
    3. Ruchi Verma & Vivek Kumar Sehgal & Nitin, 2016. "Computational Stochastic Modelling to Handle the Crisis Occurred During Community Epidemic," Annals of Data Science, Springer, vol. 3(2), pages 119-133, June.
    4. M. De La Sen & S. Alonso-Quesada, 2008. "Model-Matching-Based Control of the Beverton-Holt Equation in Ecology," Discrete Dynamics in Nature and Society, Hindawi, vol. 2008, pages 1-21, February.
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