IDEAS home Printed from https://ideas.repec.org/a/eee/ecomod/v486y2023ics0304380023002326.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304380023002326
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ecolmodel.2023.110502?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Caraballo, T. & Settati, A. & Lahrouz, A. & Boutouil, S. & Harchaoui, B., 2024. "On the stochastic threshold of the COVID-19 epidemic model incorporating jump perturbations," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    2. Pitchaimani, M. & Brasanna Devi, M., 2021. "Stochastic probical strategies in a delay virus infection model to combat COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. Koutou, Ousmane & Diabaté, Abou Bakari & Sangaré, Boureima, 2023. "Mathematical analysis of the impact of the media coverage in mitigating the outbreak of COVID-19," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 205(C), pages 600-618.
    4. Mishra, Bimal Kumar & Keshri, Ajit Kumar & Saini, Dinesh Kumar & Ayesha, Syeda & Mishra, Binay Kumar & Rao, Yerra Shankar, 2021. "Mathematical model, forecast and analysis on the spread of COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 147(C).
    5. Masum, Mohammad & Masud, M.A. & Adnan, Muhaiminul Islam & Shahriar, Hossain & Kim, Sangil, 2022. "Comparative study of a mathematical epidemic model, statistical modeling, and deep learning for COVID-19 forecasting and management," Socio-Economic Planning Sciences, Elsevier, vol. 80(C).
    6. Asamoah, Joshua Kiddy K. & Owusu, Mark A. & Jin, Zhen & Oduro, F. T. & Abidemi, Afeez & Gyasi, Esther Opoku, 2020. "Global stability and cost-effectiveness analysis of COVID-19 considering the impact of the environment: using data from Ghana," Chaos, Solitons & Fractals, Elsevier, vol. 140(C).
    7. Basnarkov, Lasko, 2021. "SEAIR Epidemic spreading model of COVID-19," Chaos, Solitons & Fractals, Elsevier, vol. 142(C).
    8. Cooper, Ian & Mondal, Argha & Antonopoulos, Chris G., 2020. "Dynamic tracking with model-based forecasting for the spread of the COVID-19 pandemic," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    9. Cooper, Ian & Mondal, Argha & Antonopoulos, Chris G., 2020. "A SIR model assumption for the spread of COVID-19 in different communities," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    10. Mishra, A.M. & Purohit, S.D. & Owolabi, K.M. & Sharma, Y.D., 2020. "A nonlinear epidemiological model considering asymptotic and quarantine classes for SARS CoV-2 virus," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    11. Memon, Zaibunnisa & Qureshi, Sania & Memon, Bisharat Rasool, 2021. "Assessing the role of quarantine and isolation as control strategies for COVID-19 outbreak: A case study," Chaos, Solitons & Fractals, Elsevier, vol. 144(C).
    12. Amaral, Marco A. & Oliveira, Marcelo M. de & Javarone, Marco A., 2021. "An epidemiological model with voluntary quarantine strategies governed by evolutionary game dynamics," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    13. Ullah, Mohammad Sharif & Higazy, M. & Kabir, K.M. Ariful, 2022. "Dynamic analysis of mean-field and fractional-order epidemic vaccination strategies by evolutionary game approach," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    14. Bedilu Alamirie Ejigu & Manalebish Debalike Asfaw & Lisa Cavalerie & Tilahun Abebaw & Mark Nanyingi & Matthew Baylis, 2021. "Assessing the impact of non-pharmaceutical interventions (NPI) on the dynamics of COVID-19: A mathematical modelling study of the case of Ethiopia," PLOS ONE, Public Library of Science, vol. 16(11), pages 1-21, November.
    15. Rafiq, Danish & Suhail, Suhail Ahmad & Bazaz, Mohammad Abid, 2020. "Evaluation and prediction of COVID-19 in India: A case study of worst hit states," Chaos, Solitons & Fractals, Elsevier, vol. 139(C).
    16. Faïçal Ndaïrou & Iván Area & Delfim F. M. Torres, 2020. "Mathematical Modeling of Japanese Encephalitis under Aquatic Environmental Effects," Mathematics, MDPI, vol. 8(11), pages 1-14, October.
    17. Swapnarekha, H. & Behera, Himansu Sekhar & Nayak, Janmenjoy & Naik, Bighnaraj, 2020. "Role of intelligent computing in COVID-19 prognosis: A state-of-the-art review," Chaos, Solitons & Fractals, Elsevier, vol. 138(C).
    18. Li, Tingting & Guo, Youming, 2022. "Optimal control and cost-effectiveness analysis of a new COVID-19 model for Omicron strain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 606(C).
    19. Vincent Bian & Merrick Cai & Christopher L. Follett, 2023. "Understanding opposing predictions of Prochlorococcus in a changing climate," Nature Communications, Nature, vol. 14(1), pages 1-10, December.
    20. Florian Dorn & Sahamoddin Khailaie & Marc Stoeckli & Sebastian C. Binder & Tanmay Mitra & Berit Lange & Stefan Lautenbacher & Andreas Peichl & Patrizio Vanella & Timo Wollmershäuser & Clemens Fuest & , 2023. "The common interests of health protection and the economy: evidence from scenario calculations of COVID-19 containment policies," The European Journal of Health Economics, Springer;Deutsche Gesellschaft für Gesundheitsökonomie (DGGÖ), vol. 24(1), pages 67-74, February.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ecomod:v:486:y:2023:i:c:s0304380023002326. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/ecological-modelling .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.