Application of Homotopy Analysis Method for Solving an SEIRS Epidemic Model
Mathematical Modelling and Applications
Volume 4, Issue 3, September 2019, Pages: 36-48
Received: Jun. 10, 2019; Accepted: Jul. 15, 2019; Published: Sep. 3, 2019
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Authors
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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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.
Keywords
SEIRS Model, Homotopy Analysis Method (HAM), Local Stability, Disease-free Equilibrium, Endemic Equilibrium
To cite this article
Inyama Simeon Chioma, Ekeamadi Godsgift Ugonna, Uwagboe Osazee Michael, Omame Andrew, Mbachu Hope Ifeyinwa, Uwakwe Joy Ijeoma, Application of Homotopy Analysis Method for Solving an SEIRS Epidemic Model, Mathematical Modelling and Applications. Vol. 4, No. 3, 2019, pp. 36-48. doi: 10.11648/j.mma.20190403.11
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Copyright © 2019 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/) which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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