Application of Homotopy Analysis Method for Solving an SEIRS Epidemic Model

Inyama Simeon Chioma; Ekeamadi Godsgift Ugonna; Uwagboe Osazee Michael; Omame Andrew; Mbachu Hope Ifeyinwa; Uwakwe Joy Ijeoma

doi:doi:10.11648/j.mma.20190403.11

Application of Homotopy Analysis Method for Solving an SEIRS Epidemic Model

Inyama Simeon Chioma, Ekeamadi Godsgift Ugonna, Uwagboe Osazee Michael, Omame Andrew, Mbachu Hope Ifeyinwa, Uwakwe Joy Ijeoma

Published in Mathematical Modelling and Applications (Volume 4, Issue 3)

Received: 10 June 2019 Accepted: 15 July 2019 Published: 3 September 2019

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Abstract

In this paper, we modified the model of [23] and then applied a new semi-analytic technique namely the Homotopy Analysis Method (HAM) in solving the SEIRS Epidemic Mathematical Model. The modified SEIRS model wasfirst formulated and adequately analyzed. We investigated the basic properties of the model by proving the positivity of the solutions and establishing the invariant region. We further obtained the steady states: disease-free equilibrium (DFE) and endemic equilibrium (EE), then we went further to determine the local stability of the DEF and EE using the basic reproduction number which was calculated. We also applied Lyaponuv method to prove the global stability of endemic equilibrium, The HAM was applied to obtain an accurate solution to the model in few iterations. Finally, a numerical solution (simulation) of the model was obtained using MAPLE 15 computation software.

Published in	Mathematical Modelling and Applications (Volume 4, Issue 3)
DOI	10.11648/j.mma.20190403.11
Page(s)	36-48
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), 2019. Published by Science Publishing Group

Keywords

SEIRS Model, Homotopy Analysis Method (HAM), Local Stability, Disease-free Equilibrium, Endemic Equilibrium

References

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[4]	Fallahzadeh, A. and Shakibi, K. (2015) A method to solve Convection-Diffusion equation based on Homotopy Analysis Method; Journal of Interpolation and Approximation in Scientific Computing. No. (1) 1-8.
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[17]	Nirmala, P. Subramanian S. P. et al (2015) SEIR Model of Seasonal Epidemic Diseases using HAM. Applications and Applied Mathematics: An International Journal (AAM) vol. 10, Issue pp. 1066-1081 ISSN: 1932-9466.
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APA Style

Inyama Simeon Chioma, Ekeamadi Godsgift Ugonna, Uwagboe Osazee Michael, Omame Andrew, Mbachu Hope Ifeyinwa, et al. (2019). Application of Homotopy Analysis Method for Solving an SEIRS Epidemic Model. Mathematical Modelling and Applications, 4(3), 36-48. https://doi.org/10.11648/j.mma.20190403.11

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ACS Style

Inyama Simeon Chioma; Ekeamadi Godsgift Ugonna; Uwagboe Osazee Michael; Omame Andrew; Mbachu Hope Ifeyinwa, et al. Application of Homotopy Analysis Method for Solving an SEIRS Epidemic Model. Math. Model. Appl. 2019, 4(3), 36-48. doi: 10.11648/j.mma.20190403.11

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AMA Style

Inyama Simeon Chioma, Ekeamadi Godsgift Ugonna, Uwagboe Osazee Michael, Omame Andrew, Mbachu Hope Ifeyinwa, et al. Application of Homotopy Analysis Method for Solving an SEIRS Epidemic Model. Math Model Appl. 2019;4(3):36-48. doi: 10.11648/j.mma.20190403.11

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@article{10.11648/j.mma.20190403.11,
  author = {Inyama Simeon Chioma and Ekeamadi Godsgift Ugonna and Uwagboe Osazee Michael and Omame Andrew and Mbachu Hope Ifeyinwa and Uwakwe Joy Ijeoma},
  title = {Application of Homotopy Analysis Method for Solving an SEIRS Epidemic Model},
  journal = {Mathematical Modelling and Applications},
  volume = {4},
  number = {3},
  pages = {36-48},
  doi = {10.11648/j.mma.20190403.11},
  url = {https://doi.org/10.11648/j.mma.20190403.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20190403.11},
  abstract = {In this paper, we modified the model of [23] and then applied a new semi-analytic technique namely the Homotopy Analysis Method (HAM) in solving the SEIRS Epidemic Mathematical Model. The modified SEIRS model wasfirst formulated and adequately analyzed. We investigated the basic properties of the model by proving the positivity of the solutions and establishing the invariant region. We further obtained the steady states: disease-free equilibrium (DFE) and endemic equilibrium (EE), then we went further to determine the local stability of the DEF and EE using the basic reproduction number which was calculated. We also applied Lyaponuv method to prove the global stability of endemic equilibrium, The HAM was applied to obtain an accurate solution to the model in few iterations. Finally, a numerical solution (simulation) of the model was obtained using MAPLE 15 computation software.},
 year = {2019}
}

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TY  - JOUR
T1  - Application of Homotopy Analysis Method for Solving an SEIRS Epidemic Model
AU  - Inyama Simeon Chioma
AU  - Ekeamadi Godsgift Ugonna
AU  - Uwagboe Osazee Michael
AU  - Omame Andrew
AU  - Mbachu Hope Ifeyinwa
AU  - Uwakwe Joy Ijeoma
Y1  - 2019/09/03
PY  - 2019
N1  - https://doi.org/10.11648/j.mma.20190403.11
DO  - 10.11648/j.mma.20190403.11
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 36
EP  - 48
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20190403.11
AB  - In this paper, we modified the model of [23] and then applied a new semi-analytic technique namely the Homotopy Analysis Method (HAM) in solving the SEIRS Epidemic Mathematical Model. The modified SEIRS model wasfirst formulated and adequately analyzed. We investigated the basic properties of the model by proving the positivity of the solutions and establishing the invariant region. We further obtained the steady states: disease-free equilibrium (DFE) and endemic equilibrium (EE), then we went further to determine the local stability of the DEF and EE using the basic reproduction number which was calculated. We also applied Lyaponuv method to prove the global stability of endemic equilibrium, The HAM was applied to obtain an accurate solution to the model in few iterations. Finally, a numerical solution (simulation) of the model was obtained using MAPLE 15 computation software.
VL  - 4
IS  - 3
ER  -

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Author Information

Inyama Simeon Chioma

Department of Mathematics, Federal University of Technology, Owerri, Nigeria
Ekeamadi Godsgift Ugonna

Department of Mathematics, Federal University of Technology, Owerri, Nigeria
Uwagboe Osazee Michael

Department of Mathematics, Federal University of Technology, Owerri, Nigeria
Omame Andrew

Department of Mathematics, Federal University of Technology, Owerri, Nigeria
Mbachu Hope Ifeyinwa

Department of Statistics, Imo State University, Owerri, Nigeria
Uwakwe Joy Ijeoma

Alvan Ikoku College of Education, Owerri, Nigeria

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APA Style

Inyama Simeon Chioma, Ekeamadi Godsgift Ugonna, Uwagboe Osazee Michael, Omame Andrew, Mbachu Hope Ifeyinwa, et al. (2019). Application of Homotopy Analysis Method for Solving an SEIRS Epidemic Model. Mathematical Modelling and Applications, 4(3), 36-48. https://doi.org/10.11648/j.mma.20190403.11

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ACS Style

Inyama Simeon Chioma; Ekeamadi Godsgift Ugonna; Uwagboe Osazee Michael; Omame Andrew; Mbachu Hope Ifeyinwa, et al. Application of Homotopy Analysis Method for Solving an SEIRS Epidemic Model. Math. Model. Appl. 2019, 4(3), 36-48. doi: 10.11648/j.mma.20190403.11

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AMA Style

Inyama Simeon Chioma, Ekeamadi Godsgift Ugonna, Uwagboe Osazee Michael, Omame Andrew, Mbachu Hope Ifeyinwa, et al. Application of Homotopy Analysis Method for Solving an SEIRS Epidemic Model. Math Model Appl. 2019;4(3):36-48. doi: 10.11648/j.mma.20190403.11

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@article{10.11648/j.mma.20190403.11,
  author = {Inyama Simeon Chioma and Ekeamadi Godsgift Ugonna and Uwagboe Osazee Michael and Omame Andrew and Mbachu Hope Ifeyinwa and Uwakwe Joy Ijeoma},
  title = {Application of Homotopy Analysis Method for Solving an SEIRS Epidemic Model},
  journal = {Mathematical Modelling and Applications},
  volume = {4},
  number = {3},
  pages = {36-48},
  doi = {10.11648/j.mma.20190403.11},
  url = {https://doi.org/10.11648/j.mma.20190403.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mma.20190403.11},
  abstract = {In this paper, we modified the model of [23] and then applied a new semi-analytic technique namely the Homotopy Analysis Method (HAM) in solving the SEIRS Epidemic Mathematical Model. The modified SEIRS model wasfirst formulated and adequately analyzed. We investigated the basic properties of the model by proving the positivity of the solutions and establishing the invariant region. We further obtained the steady states: disease-free equilibrium (DFE) and endemic equilibrium (EE), then we went further to determine the local stability of the DEF and EE using the basic reproduction number which was calculated. We also applied Lyaponuv method to prove the global stability of endemic equilibrium, The HAM was applied to obtain an accurate solution to the model in few iterations. Finally, a numerical solution (simulation) of the model was obtained using MAPLE 15 computation software.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Application of Homotopy Analysis Method for Solving an SEIRS Epidemic Model
AU  - Inyama Simeon Chioma
AU  - Ekeamadi Godsgift Ugonna
AU  - Uwagboe Osazee Michael
AU  - Omame Andrew
AU  - Mbachu Hope Ifeyinwa
AU  - Uwakwe Joy Ijeoma
Y1  - 2019/09/03
PY  - 2019
N1  - https://doi.org/10.11648/j.mma.20190403.11
DO  - 10.11648/j.mma.20190403.11
T2  - Mathematical Modelling and Applications
JF  - Mathematical Modelling and Applications
JO  - Mathematical Modelling and Applications
SP  - 36
EP  - 48
PB  - Science Publishing Group
SN  - 2575-1794
UR  - https://doi.org/10.11648/j.mma.20190403.11
AB  - In this paper, we modified the model of [23] and then applied a new semi-analytic technique namely the Homotopy Analysis Method (HAM) in solving the SEIRS Epidemic Mathematical Model. The modified SEIRS model wasfirst formulated and adequately analyzed. We investigated the basic properties of the model by proving the positivity of the solutions and establishing the invariant region. We further obtained the steady states: disease-free equilibrium (DFE) and endemic equilibrium (EE), then we went further to determine the local stability of the DEF and EE using the basic reproduction number which was calculated. We also applied Lyaponuv method to prove the global stability of endemic equilibrium, The HAM was applied to obtain an accurate solution to the model in few iterations. Finally, a numerical solution (simulation) of the model was obtained using MAPLE 15 computation software.
VL  - 4
IS  - 3
ER  -

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