Analysis of a mathematical model for golden mussels infestation

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 a...

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Bibliographic Details
Published in:	Ecological modelling Vol. 486; p. 110502
Main Authors:	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.
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01-12-2023
Subjects:	Algae-mussel interaction model Biologic invasion Differential equations Mathematical modeling Algae-mussel interaction model Mathematical modeling Differential equations Biologic invasion
Online Access:	Get full text
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Summary:	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. •Mussel-algae interaction model.•Stability analysis of stationary solutions of the model.•Basal reproduction rate for the golden mussel model.
ISSN:	0304-3800 1872-7026
DOI:	10.1016/j.ecolmodel.2023.110502