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Analysis of a mathematical model for golden mussels infestation

Author

Listed:
  • Barbosa, Charles H.X.B.
  • Dias, Claudia M.
  • Pastore, Dayse H.
  • Silva, José C.R.
  • Costa, Anna R.C.
  • Santos, Isaac P.
  • Azevedo, Ramoni Z.S.
  • Figueira, Raquel M.A.
  • Fortunato, Humberto F.M.

Abstract

The presence of the golden mussel in Brazil is a matter of great concern and causes harm to the country, particularly affecting the power generation sector. Infestation control represents a challenge, and there is a need to mathematically describe the dynamics of the problem. This work proposes to analyze a mathematical model based on differential equations that relate the populations of larvae, mussels, and algae. For this model, the critical points and stationary states are determined, seeking steady-state conditions stability, through the basic reproduction rate. In addition, it presents the sensitivity analysis of the parameters involved. The paper results are relevant as they allow mathematical interpretation of the golden mussel infestation potential through the basic reproduction rate. Furthermore, the sensitivity analysis suggests how important the parameters are for this potential. For that matter, this work can provide baseline information to guide future control strategies as it provides quantification of the species involved over time as well as a condition for infestation.

Suggested Citation

  • Barbosa, Charles H.X.B. & Dias, Claudia M. & Pastore, Dayse H. & Silva, José C.R. & Costa, Anna R.C. & Santos, Isaac P. & Azevedo, Ramoni Z.S. & Figueira, Raquel M.A. & Fortunato, Humberto F.M., 2023. "Analysis of a mathematical model for golden mussels infestation," Ecological Modelling, Elsevier, vol. 486(C).
    • Handle: RePEc:eee:ecomod:v:486:y:2023:i:c:s0304380023002326
    DOI: 10.1016/j.ecolmodel.2023.110502
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    References listed on IDEAS

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    1. Ndaïrou, Faïçal & Area, Iván & Nieto, Juan J. & Torres, Delfim F.M., 2020. "Mathematical modeling of COVID-19 transmission dynamics with a case study of Wuhan," Chaos, Solitons & Fractals, Elsevier, vol. 135(C).
    2. Melo-Merino, Sara M. & Reyes-Bonilla, Héctor & Lira-Noriega, Andrés, 2020. "Ecological niche models and species distribution models in marine environments: A literature review and spatial analysis of evidence," Ecological Modelling, Elsevier, vol. 415(C).
    3. de Ávila-Simas, Sunshine & Morato, Marcelo M. & Reynalte-Tataje, David A. & Silveira, Hector B. & Zaniboni-Filho, Evoy & E. Normey-Rico, Julio, 2019. "Model-based predictive control for the regulation of the golden mussel Limnoperna fortunei (Dunker, 1857)," Ecological Modelling, Elsevier, vol. 406(C), pages 84-97.
    4. Kassa, Semu M. & Njagarah, John B.H. & Terefe, Yibeltal A., 2020. "Analysis of the mitigation strategies for COVID-19: From mathematical modelling perspective," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
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