Global Sensitivity Analysis of Soil Pollution Using Fractal Fractional Order Model

Priya Pichandi; Sabarmathi Ayyavu

doi:doi:10.11648/j.ijees.20240902.12

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Global Sensitivity Analysis of Soil Pollution Using Fractal Fractional Order Model

Priya Pichandi^*

, Sabarmathi Ayyavu

Published in International Journal of Energy and Environmental Science (Volume 9, Issue 2)

Received: 22 March 2024 Accepted: 7 April 2024 Published: 15 August 2024

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Abstract

This research investigates the profound impact of land pollution on soil degradation, stemming from human-made (xenobiotic) chemicals and alterations in soil composition. The framework explains a comprehensive nonlinear fractal fractional order eco-epidemic model, delineating four compartments: Susceptible soil (S), Polluted soil (P), Remediation or recycling of polluted soil (T), and Recovered soil (R). The study rigorously establishes the non-negative and unique existence of solutions using the fixed point theorem while analyzing the local and global stability of equilibrium points under pollution-free equilibrium and pollution extinct equilibrium. Dula’s criterion confirms periodic orbits, while categorizing changes in secondary reproduction numbers provides crucial insights into pollution dynamics, enhancing our understanding of system dynamics. Local and global sensitivity analyses, employing forward sensitivity and the Morris Method, yield essential findings for informed decision-making. Additionally, Adams-Bashforth's method is employed to approximate solutions, facilitating the integration of theoretical concepts with practical applications. Supported by numerical simulations conducted in MATLAB, the study offers a nuanced understanding of parameter roles and validates theoretical propositions, ultimately contributing valuable insights to environmental management and policy formulation.

Published in	International Journal of Energy and Environmental Science (Volume 9, Issue 2)
DOI	10.11648/j.ijees.20240902.12
Page(s)	38-51
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Soil Pollution, Fractional Order Model, Stability, Adams Bashforth Technique, Lyapunov Function, Sensitivity Analysis

References

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APA Style

Pichandi, P., Ayyavu, S. (2024). Global Sensitivity Analysis of Soil Pollution Using Fractal Fractional Order Model. International Journal of Energy and Environmental Science, 9(2), 38-51. https://doi.org/10.11648/j.ijees.20240902.12

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ACS Style

Pichandi, P.; Ayyavu, S. Global Sensitivity Analysis of Soil Pollution Using Fractal Fractional Order Model. Int. J. Energy Environ. Sci. 2024, 9(2), 38-51. doi: 10.11648/j.ijees.20240902.12

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AMA Style

Pichandi P, Ayyavu S. Global Sensitivity Analysis of Soil Pollution Using Fractal Fractional Order Model. Int J Energy Environ Sci. 2024;9(2):38-51. doi: 10.11648/j.ijees.20240902.12

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@article{10.11648/j.ijees.20240902.12,
  author = {Priya Pichandi and Sabarmathi Ayyavu},
  title = {Global Sensitivity Analysis of Soil Pollution Using Fractal Fractional Order Model
},
  journal = {International Journal of Energy and Environmental Science},
  volume = {9},
  number = {2},
  pages = {38-51},
  doi = {10.11648/j.ijees.20240902.12},
  url = {https://doi.org/10.11648/j.ijees.20240902.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijees.20240902.12},
  abstract = {This research investigates the profound impact of land pollution on soil degradation, stemming from human-made (xenobiotic) chemicals and alterations in soil composition. The framework explains a comprehensive nonlinear fractal fractional order eco-epidemic model, delineating four compartments: Susceptible soil (S), Polluted soil (P), Remediation or recycling of polluted soil (T), and Recovered soil (R). The study rigorously establishes the non-negative and unique existence of solutions using the fixed point theorem while analyzing the local and global stability of equilibrium points under pollution-free equilibrium and pollution extinct equilibrium. Dula’s criterion confirms periodic orbits, while categorizing changes in secondary reproduction numbers provides crucial insights into pollution dynamics, enhancing our understanding of system dynamics. Local and global sensitivity analyses, employing forward sensitivity and the Morris Method, yield essential findings for informed decision-making. Additionally, Adams-Bashforth's method is employed to approximate solutions, facilitating the integration of theoretical concepts with practical applications. Supported by numerical simulations conducted in MATLAB, the study offers a nuanced understanding of parameter roles and validates theoretical propositions, ultimately contributing valuable insights to environmental management and policy formulation.
},
 year = {2024}
}

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TY  - JOUR
T1  - Global Sensitivity Analysis of Soil Pollution Using Fractal Fractional Order Model

AU  - Priya Pichandi
AU  - Sabarmathi Ayyavu
Y1  - 2024/08/15
PY  - 2024
N1  - https://doi.org/10.11648/j.ijees.20240902.12
DO  - 10.11648/j.ijees.20240902.12
T2  - International Journal of Energy and Environmental Science
JF  - International Journal of Energy and Environmental Science
JO  - International Journal of Energy and Environmental Science
SP  - 38
EP  - 51
PB  - Science Publishing Group
SN  - 2578-9546
UR  - https://doi.org/10.11648/j.ijees.20240902.12
AB  - This research investigates the profound impact of land pollution on soil degradation, stemming from human-made (xenobiotic) chemicals and alterations in soil composition. The framework explains a comprehensive nonlinear fractal fractional order eco-epidemic model, delineating four compartments: Susceptible soil (S), Polluted soil (P), Remediation or recycling of polluted soil (T), and Recovered soil (R). The study rigorously establishes the non-negative and unique existence of solutions using the fixed point theorem while analyzing the local and global stability of equilibrium points under pollution-free equilibrium and pollution extinct equilibrium. Dula’s criterion confirms periodic orbits, while categorizing changes in secondary reproduction numbers provides crucial insights into pollution dynamics, enhancing our understanding of system dynamics. Local and global sensitivity analyses, employing forward sensitivity and the Morris Method, yield essential findings for informed decision-making. Additionally, Adams-Bashforth's method is employed to approximate solutions, facilitating the integration of theoretical concepts with practical applications. Supported by numerical simulations conducted in MATLAB, the study offers a nuanced understanding of parameter roles and validates theoretical propositions, ultimately contributing valuable insights to environmental management and policy formulation.

VL  - 9
IS  - 2
ER  -

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Author Information

Priya Pichandi

PG and Research Department of Mathematics, Auxilium College (Autonomous), Affiliated to Thiruvalluvar University, Vellore, India

Contact Email

http://orcid.org/0000-0002-6841-909X
Sabarmathi Ayyavu

PG and Research Department of Mathematics, Auxilium College (Autonomous), Affiliated to Thiruvalluvar University, Vellore, India

Contact Email

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Plain Text BibTeX RIS

APA Style

Pichandi, P., Ayyavu, S. (2024). Global Sensitivity Analysis of Soil Pollution Using Fractal Fractional Order Model. International Journal of Energy and Environmental Science, 9(2), 38-51. https://doi.org/10.11648/j.ijees.20240902.12

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ACS Style

Pichandi, P.; Ayyavu, S. Global Sensitivity Analysis of Soil Pollution Using Fractal Fractional Order Model. Int. J. Energy Environ. Sci. 2024, 9(2), 38-51. doi: 10.11648/j.ijees.20240902.12

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AMA Style

Pichandi P, Ayyavu S. Global Sensitivity Analysis of Soil Pollution Using Fractal Fractional Order Model. Int J Energy Environ Sci. 2024;9(2):38-51. doi: 10.11648/j.ijees.20240902.12

Copy | Download

@article{10.11648/j.ijees.20240902.12,
  author = {Priya Pichandi and Sabarmathi Ayyavu},
  title = {Global Sensitivity Analysis of Soil Pollution Using Fractal Fractional Order Model
},
  journal = {International Journal of Energy and Environmental Science},
  volume = {9},
  number = {2},
  pages = {38-51},
  doi = {10.11648/j.ijees.20240902.12},
  url = {https://doi.org/10.11648/j.ijees.20240902.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijees.20240902.12},
  abstract = {This research investigates the profound impact of land pollution on soil degradation, stemming from human-made (xenobiotic) chemicals and alterations in soil composition. The framework explains a comprehensive nonlinear fractal fractional order eco-epidemic model, delineating four compartments: Susceptible soil (S), Polluted soil (P), Remediation or recycling of polluted soil (T), and Recovered soil (R). The study rigorously establishes the non-negative and unique existence of solutions using the fixed point theorem while analyzing the local and global stability of equilibrium points under pollution-free equilibrium and pollution extinct equilibrium. Dula’s criterion confirms periodic orbits, while categorizing changes in secondary reproduction numbers provides crucial insights into pollution dynamics, enhancing our understanding of system dynamics. Local and global sensitivity analyses, employing forward sensitivity and the Morris Method, yield essential findings for informed decision-making. Additionally, Adams-Bashforth's method is employed to approximate solutions, facilitating the integration of theoretical concepts with practical applications. Supported by numerical simulations conducted in MATLAB, the study offers a nuanced understanding of parameter roles and validates theoretical propositions, ultimately contributing valuable insights to environmental management and policy formulation.
},
 year = {2024}
}

Copy | Download

TY  - JOUR
T1  - Global Sensitivity Analysis of Soil Pollution Using Fractal Fractional Order Model

AU  - Priya Pichandi
AU  - Sabarmathi Ayyavu
Y1  - 2024/08/15
PY  - 2024
N1  - https://doi.org/10.11648/j.ijees.20240902.12
DO  - 10.11648/j.ijees.20240902.12
T2  - International Journal of Energy and Environmental Science
JF  - International Journal of Energy and Environmental Science
JO  - International Journal of Energy and Environmental Science
SP  - 38
EP  - 51
PB  - Science Publishing Group
SN  - 2578-9546
UR  - https://doi.org/10.11648/j.ijees.20240902.12
AB  - This research investigates the profound impact of land pollution on soil degradation, stemming from human-made (xenobiotic) chemicals and alterations in soil composition. The framework explains a comprehensive nonlinear fractal fractional order eco-epidemic model, delineating four compartments: Susceptible soil (S), Polluted soil (P), Remediation or recycling of polluted soil (T), and Recovered soil (R). The study rigorously establishes the non-negative and unique existence of solutions using the fixed point theorem while analyzing the local and global stability of equilibrium points under pollution-free equilibrium and pollution extinct equilibrium. Dula’s criterion confirms periodic orbits, while categorizing changes in secondary reproduction numbers provides crucial insights into pollution dynamics, enhancing our understanding of system dynamics. Local and global sensitivity analyses, employing forward sensitivity and the Morris Method, yield essential findings for informed decision-making. Additionally, Adams-Bashforth's method is employed to approximate solutions, facilitating the integration of theoretical concepts with practical applications. Supported by numerical simulations conducted in MATLAB, the study offers a nuanced understanding of parameter roles and validates theoretical propositions, ultimately contributing valuable insights to environmental management and policy formulation.

VL  - 9
IS  - 2
ER  -

Copy | Download