Modelling and Solution of Infectious Diseases Using the Extended Laplace Adomian Decomposition Techniques

Bazuaye Frank Etin-Osa; Ezeora Jeremiah

doi:doi:10.11648/j.acm.20211002.11

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Modelling and Solution of Infectious Diseases Using the Extended Laplace Adomian Decomposition Techniques

Bazuaye Frank Etin-Osa, Ezeora Jeremiah

Published in Applied and Computational Mathematics (Volume 10, Issue 2)

Received: 14 December 2020 Accepted: 21 January 2021 Published: 16 April 2021

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Abstract

The use of Mathematical models to describe the transmission of infectious diseases has attracted a lot of interest over the years and serious worldwide effort is accelerating the developments in the establishment of a global efforts for combating pandemics of infectious diseases. Scientists from different fields have teamed up for rapid assessment of potentially immediate situations. Toward this aim, mathematical modeling plays an important role in efforts that focus on predicting, assessing, and controlling potential outbreaks. The recent outbreak of covid 19 pandemic had increased the curiosity for the formulation of Mathematical models to describe and analyze the propagation of the disease. This paper focuses on the modeling and analysis of an infectious diseases model using the extended Laplace Adomian Decomposition (LAD) method. The method is used to obtain solutions in the form of infinite series. The result of the research with the aid of MAPLE indicates that physical contact with an infected person is the major cause of the propagation of any infectious disease in the absence of pharmaceutical and non pharmaceutical safety protocols such as the proper use of face mask, physical and social distancing. It becomes vital to subject the infected persons in isolation and adhere to the necessary protocols by relevance agencies and this will significantly flattened the curve of the spread of the infectious disease.

Published in	Applied and Computational Mathematics (Volume 10, Issue 2)
DOI	10.11648/j.acm.20211002.11
Page(s)	30-39
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

Infectious Disease, Numerical Analysis, Mathematical Model, Susceptible Class, Infected Population

References

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[4]	Sattenspeiel L, Herring DA (2003).. Simulating the effects of quarantine on the spread of 1918 flu in central Canada. Bull Math Biol; 65: 1–26.
[5]	Shil P, Bidaye S, Vidyasagar PB (2008). Analyzing the effects of surface distribution of pores in cell electroporation for a cell membrane containing cholesterol. J Phys D: Appl Phys; 41: 551–557.
[6]	Deguen S, Thomas G, Chau NP (2000). Estimation of the contact rate in a seasonal SEIR model: application to chickenpox incidence in France. Statist. Med.; 19: 1207–1216.
[7]	Wang J, McMichael AJ, Meng B, Becker NG, Han W, Glass K, Wu J, Liu X, Liu J, Li X, Zheng X (2006). Spatial dynamics of an epidemic of severe acute respiratory syndrome in an urban area. Bull. World Health Organization; 84 (12): 965–968.
[8]	Kongnuy R, Pongsumpun P 2011. Mathematical modeling for Dengue transmission with theeffect of season. Int. J Biological Life Sci; 7 (3): 143–147.
[9]	Constatenos S., Cle A, Lucia R. Christos G, Elefterios M. (2015). Modeling the 2014 Ebola Virus Epidemic – Agent-Based Simulations, Temporal Analysis and Future Predictions for Liberia and Sierra Leone. PLoS Currents. 2015: 1-18.
[10]	Ruan S, Xiao D, Beier JC (2008). On the Delayed Ross–Macdonald Model for MalariaTransmission. Bull Math Biol. 70 (4): 1098–1114.
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[13]	Somali S. and Gokmen G. (2007). Adomian Decomposition Method for Non-Linear Sturm-Liouville Problems, Surveys in Mathematics and its Applications, Vol. 2, 11-20.
[14]	Adomian G., Adomian G. E. (1984). A global method for solution of complex systems, Math. Model. 5521-568.
[15]	Adomian G. (1994). Solving Frontier Problems of Physics: The DecompositionMethod, Kluwer Academic Publishers, Dordecht.
[16]	Wazwa A. M. (2000). A new algorithm for calculating Adomian polynomials for non-linear Operators, Appl. Math. Comput. 111: 53-69.

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APA Style

Bazuaye Frank Etin-Osa, Ezeora Jeremiah. (2021). Modelling and Solution of Infectious Diseases Using the Extended Laplace Adomian Decomposition Techniques. Applied and Computational Mathematics, 10(2), 30-39. https://doi.org/10.11648/j.acm.20211002.11

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ACS Style

Bazuaye Frank Etin-Osa; Ezeora Jeremiah. Modelling and Solution of Infectious Diseases Using the Extended Laplace Adomian Decomposition Techniques. Appl. Comput. Math. 2021, 10(2), 30-39. doi: 10.11648/j.acm.20211002.11

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AMA Style

Bazuaye Frank Etin-Osa, Ezeora Jeremiah. Modelling and Solution of Infectious Diseases Using the Extended Laplace Adomian Decomposition Techniques. Appl Comput Math. 2021;10(2):30-39. doi: 10.11648/j.acm.20211002.11

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@article{10.11648/j.acm.20211002.11,
  author = {Bazuaye Frank Etin-Osa and Ezeora Jeremiah},
  title = {Modelling and Solution of Infectious Diseases Using the Extended Laplace Adomian Decomposition Techniques},
  journal = {Applied and Computational Mathematics},
  volume = {10},
  number = {2},
  pages = {30-39},
  doi = {10.11648/j.acm.20211002.11},
  url = {https://doi.org/10.11648/j.acm.20211002.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20211002.11},
  abstract = {The use of Mathematical models to describe the transmission of infectious diseases has attracted a lot of interest over the years and serious worldwide effort is accelerating the developments in the establishment of a global efforts for combating pandemics of infectious diseases. Scientists from different fields have teamed up for rapid assessment of potentially immediate situations. Toward this aim, mathematical modeling plays an important role in efforts that focus on predicting, assessing, and controlling potential outbreaks. The recent outbreak of covid 19 pandemic had increased the curiosity for the formulation of Mathematical models to describe and analyze the propagation of the disease. This paper focuses on the modeling and analysis of an infectious diseases model using the extended Laplace Adomian Decomposition (LAD) method. The method is used to obtain solutions in the form of infinite series. The result of the research with the aid of MAPLE indicates that physical contact with an infected person is the major cause of the propagation of any infectious disease in the absence of pharmaceutical and non pharmaceutical safety protocols such as the proper use of face mask, physical and social distancing. It becomes vital to subject the infected persons in isolation and adhere to the necessary protocols by relevance agencies and this will significantly flattened the curve of the spread of the infectious disease.},
 year = {2021}
}

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TY  - JOUR
T1  - Modelling and Solution of Infectious Diseases Using the Extended Laplace Adomian Decomposition Techniques
AU  - Bazuaye Frank Etin-Osa
AU  - Ezeora Jeremiah
Y1  - 2021/04/16
PY  - 2021
N1  - https://doi.org/10.11648/j.acm.20211002.11
DO  - 10.11648/j.acm.20211002.11
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JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
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PB  - Science Publishing Group
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AB  - The use of Mathematical models to describe the transmission of infectious diseases has attracted a lot of interest over the years and serious worldwide effort is accelerating the developments in the establishment of a global efforts for combating pandemics of infectious diseases. Scientists from different fields have teamed up for rapid assessment of potentially immediate situations. Toward this aim, mathematical modeling plays an important role in efforts that focus on predicting, assessing, and controlling potential outbreaks. The recent outbreak of covid 19 pandemic had increased the curiosity for the formulation of Mathematical models to describe and analyze the propagation of the disease. This paper focuses on the modeling and analysis of an infectious diseases model using the extended Laplace Adomian Decomposition (LAD) method. The method is used to obtain solutions in the form of infinite series. The result of the research with the aid of MAPLE indicates that physical contact with an infected person is the major cause of the propagation of any infectious disease in the absence of pharmaceutical and non pharmaceutical safety protocols such as the proper use of face mask, physical and social distancing. It becomes vital to subject the infected persons in isolation and adhere to the necessary protocols by relevance agencies and this will significantly flattened the curve of the spread of the infectious disease.
VL  - 10
IS  - 2
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Author Information

Bazuaye Frank Etin-Osa

Department of Mathematics and Statistics, Faculty of Science, University of Port Harcourt, Port Harcourt, Nigeria
Ezeora Jeremiah

Department of Mathematics and Statistics, Faculty of Science, University of Port Harcourt, Port Harcourt, Nigeria

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APA Style

Bazuaye Frank Etin-Osa, Ezeora Jeremiah. (2021). Modelling and Solution of Infectious Diseases Using the Extended Laplace Adomian Decomposition Techniques. Applied and Computational Mathematics, 10(2), 30-39. https://doi.org/10.11648/j.acm.20211002.11

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ACS Style

Bazuaye Frank Etin-Osa; Ezeora Jeremiah. Modelling and Solution of Infectious Diseases Using the Extended Laplace Adomian Decomposition Techniques. Appl. Comput. Math. 2021, 10(2), 30-39. doi: 10.11648/j.acm.20211002.11

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AMA Style

Bazuaye Frank Etin-Osa, Ezeora Jeremiah. Modelling and Solution of Infectious Diseases Using the Extended Laplace Adomian Decomposition Techniques. Appl Comput Math. 2021;10(2):30-39. doi: 10.11648/j.acm.20211002.11

Copy | Download

@article{10.11648/j.acm.20211002.11,
  author = {Bazuaye Frank Etin-Osa and Ezeora Jeremiah},
  title = {Modelling and Solution of Infectious Diseases Using the Extended Laplace Adomian Decomposition Techniques},
  journal = {Applied and Computational Mathematics},
  volume = {10},
  number = {2},
  pages = {30-39},
  doi = {10.11648/j.acm.20211002.11},
  url = {https://doi.org/10.11648/j.acm.20211002.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20211002.11},
  abstract = {The use of Mathematical models to describe the transmission of infectious diseases has attracted a lot of interest over the years and serious worldwide effort is accelerating the developments in the establishment of a global efforts for combating pandemics of infectious diseases. Scientists from different fields have teamed up for rapid assessment of potentially immediate situations. Toward this aim, mathematical modeling plays an important role in efforts that focus on predicting, assessing, and controlling potential outbreaks. The recent outbreak of covid 19 pandemic had increased the curiosity for the formulation of Mathematical models to describe and analyze the propagation of the disease. This paper focuses on the modeling and analysis of an infectious diseases model using the extended Laplace Adomian Decomposition (LAD) method. The method is used to obtain solutions in the form of infinite series. The result of the research with the aid of MAPLE indicates that physical contact with an infected person is the major cause of the propagation of any infectious disease in the absence of pharmaceutical and non pharmaceutical safety protocols such as the proper use of face mask, physical and social distancing. It becomes vital to subject the infected persons in isolation and adhere to the necessary protocols by relevance agencies and this will significantly flattened the curve of the spread of the infectious disease.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Modelling and Solution of Infectious Diseases Using the Extended Laplace Adomian Decomposition Techniques
AU  - Bazuaye Frank Etin-Osa
AU  - Ezeora Jeremiah
Y1  - 2021/04/16
PY  - 2021
N1  - https://doi.org/10.11648/j.acm.20211002.11
DO  - 10.11648/j.acm.20211002.11
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 30
EP  - 39
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20211002.11
AB  - The use of Mathematical models to describe the transmission of infectious diseases has attracted a lot of interest over the years and serious worldwide effort is accelerating the developments in the establishment of a global efforts for combating pandemics of infectious diseases. Scientists from different fields have teamed up for rapid assessment of potentially immediate situations. Toward this aim, mathematical modeling plays an important role in efforts that focus on predicting, assessing, and controlling potential outbreaks. The recent outbreak of covid 19 pandemic had increased the curiosity for the formulation of Mathematical models to describe and analyze the propagation of the disease. This paper focuses on the modeling and analysis of an infectious diseases model using the extended Laplace Adomian Decomposition (LAD) method. The method is used to obtain solutions in the form of infinite series. The result of the research with the aid of MAPLE indicates that physical contact with an infected person is the major cause of the propagation of any infectious disease in the absence of pharmaceutical and non pharmaceutical safety protocols such as the proper use of face mask, physical and social distancing. It becomes vital to subject the infected persons in isolation and adhere to the necessary protocols by relevance agencies and this will significantly flattened the curve of the spread of the infectious disease.
VL  - 10
IS  - 2
ER  -

Copy | Download