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Description and analysis of a mathematical model of population growth of Aedes aegypti

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Abstract

This article proposes a mathematical model based on ordinary nonlinear differential equations that describes the dynamics of population growth of the mosquito Aedes aegypti throughout its life cycle. Then, a modification is made to the model by implementing a time delay, initially constant and then distributed over time. In addition, h, the population growth threshold, is established, the equilibrium points (trivial equilibrium, coexistence equilibrium) of the population are found and an analysis of local stability of the coexistence equilibrium is performed. If \(h>1\), this results in the population of adult aquatic mosquitoes persisting in the environment, approaching a equilibrium of coexistence, regardless of whether the time delay is considered or not. Finally, numerical simulations are carried out using Matlab software using the functions ode45 and dde23, with a value of \( h>1 \), which allow the solutions of the initial model of ordinary differential equations to be compared to the solutions when the delay is implemented.

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Acknowledgements

The authors would like to thank the Department of Basic Sciences of the University CESMAG and the Department of Mathematics and Statistics of the University of Nariño.

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Authors and Affiliations

  1. Basic Science Department, CESMAG University, Carrera 20A 14-54, Pasto, Colombia

    Ana María Pulecio-Montoya

  2. Department of Mathematics and Statistics, University of Nariño, Torobajo, Calle 18 Carrera 50, Pasto, Colombia

    Luis Eduardo López-Montenegro & Jeniffer Yinet Medina-García

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  1. Ana María Pulecio-Montoya
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  2. Luis Eduardo López-Montenegro
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  3. Jeniffer Yinet Medina-García
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Correspondence to Ana María Pulecio-Montoya.

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Pulecio-Montoya, A.M., López-Montenegro, L.E. & Medina-García, J.Y. Description and analysis of a mathematical model of population growth of Aedes aegypti. J. Appl. Math. Comput. 65, 335–349 (2021). https://doi.org/10.1007/s12190-020-01394-9

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  • DOI: https://doi.org/10.1007/s12190-020-01394-9

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