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

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), 2021. Published by Science Publishing Group

Keywords

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

References
[1] Wu J. T, Leung K, Leung GM (2020). Now casting and forecasting the potential domestic and international spread of the 2019-nCoV outbreak originating in Wuhan, China: a modeling study. Lancet; 395: 689-97.
[2] Rui-Zing M, Jiming L, William K. W, Cheung, Xiang W. (2017). Stochastic modelling of infectious diseases for heterogeneous populations. Infectious diseases of poverty. 5 (107): 1-11.
[3] Gurav YK, Pawar SD, Chadha MS, Potdar VA, Deshpande AS, Koratkar (2010). Pandemic influenza A (H1N1) 2009 outbreak in a residential school in Panchgani, Maharashtra, India. Indian J Med Res; 132: 67–71.
[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.
[11] Massad E, Coutinho FAB, Burattini M. N, Amaku M (2010). Estimation of R from the initial phase of an 0 outbreak of a vector borne infection. E. Tropical Medicine Intl Health.; 15 (1): 120–126.
[12] Adomian G, (1988). A Review of the Decomposition Method in Applied Mathematics, J. Math. Anal. Appl. 135: 501-544.
[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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    AU  - Bazuaye Frank Etin-Osa
    AU  - Ezeora Jeremiah
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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.
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Author Information
  • Department of Mathematics and Statistics, Faculty of Science, University of Port Harcourt, Port Harcourt, Nigeria

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

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