Um modelo para a competição entre o mexilhão dourado e sua versão geneticamente modificada

Charles Henrique Xavier Barreto Barbosa; Claudia Mazza Dias; Dayse Haime Pastore

doi:10.35819/remat2024v10iespecialid7077

Authors

Charles Henrique Xavier Barreto Barbosa Universidade Federal Rural do Rio de Janeiro (UFRRJ), Programa de Pós-Graduação em Modelagem Matemática e Computacional (PPGMMC), Seropédica, RJ, Brasil https://orcid.org/0000-0001-5926-2126
Claudia Mazza Dias Universidade Federal Rural do Rio de Janeiro (UFRRJ), Programa de Pós-Graduação em Modelagem Matemática e Computacional (PPGMMC), Nova Iguaçu, RJ, Brasil https://orcid.org/0000-0001-7376-1554
Dayse Haime Pastore Centro Federal de Educação Tecnológica Celso Suckow da Fonseca (CEFET-RJ), Programa de Pós-Graduação em Engenharia de Produção e Sistemas (PPPRO), Rio de Janeiro, RJ, Brasil https://orcid.org/0000-0002-0905-0085

DOI:

https://doi.org/10.35819/remat2024v10iespecialid7077

Keywords:

mathematical modeling, competition model, population dynamics, stability analysis, biomathematics

Abstract

The presence of the invasive golden mussel in Brazilian waters brings ecological or economic consequences. An alternative and promising populational control is the immersion of a genetically modified species with the aim of, upon contact with wild mollusks, producing infertile generations. A proposed mathematical model that encompasses such competition becomes important, as it can provide information to guide future experiments. However, the competition model requires a well-established growth dynamics. This work presents two models for the dynamics of wild mussels, studied analytically. The study exposes equilibrium solutions, their local stability at stationary points, and a sensitivity analysis of the basic reproduction numbers (R_0's). Through these results, the most suitable model for incorporating competition components is defined. Numerical simulations are performed to gauge possible competition outcomes, using the fourth-order Runge-Kutta method. The study is able to present two important conclusive points: that eradication can be achieved through planned competition and that there is a need for competitive advantages for the strategy to work. This study highlights the need for competitive advantages for the modified mussel. Among the possible advantages, the study indicates reproductive efficiency and the mortality rate of the modified mussel as the most promising ones. Given such an important topic, this work is necessary for this population control strategy to be studied and tested to assist in the development of the modified species in a way that respects ecology.

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Author Biographies

Charles Henrique Xavier Barreto Barbosa, Universidade Federal Rural do Rio de Janeiro (UFRRJ), Programa de Pós-Graduação em Modelagem Matemática e Computacional (PPGMMC), Seropédica, RJ, Brasil

http://lattes.cnpq.br/4770644090480283
Claudia Mazza Dias, Universidade Federal Rural do Rio de Janeiro (UFRRJ), Programa de Pós-Graduação em Modelagem Matemática e Computacional (PPGMMC), Nova Iguaçu, RJ, Brasil

http://lattes.cnpq.br/3801901177718984
Dayse Haime Pastore, Centro Federal de Educação Tecnológica Celso Suckow da Fonseca (CEFET-RJ), Programa de Pós-Graduação em Engenharia de Produção e Sistemas (PPPRO), Rio de Janeiro, RJ, Brasil

http://lattes.cnpq.br/3142092367803598

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