Global Stability Analysis of the Original Cellular Model of Hepatitis C Virus Infection Under Therapy
American Journal of Mathematical and Computer Modelling
Volume 4, Issue 3, September 2019, Pages: 58-65
Received: Jun. 12, 2019; Accepted: Jul. 27, 2019; Published: Aug. 29, 2019
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Author
Alexis Nangue, Department of Mathematics, Higher Teachers' Training College, University of Maroua, Maroua, Cameroon
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Abstract
In this work, we investigate the hepatitis C virus infection under treatment. We first derive a nonlinear ordinary differential equation model for the studied biological phenomenon. The obtained initial value problem is completely analysed. To begin with the analysis of the model, we use the standard theory of ordinary differential equations to prove existence, uniqueness and boundedness of the solution. Morever, the basic reproduction number R0 determining the extinction or the persistence of the HCV infection is computed and used to express the equilibrium points. Also the global asymptotic stability of the HCV-uninfected equilibrium point and the HCV-infected equilibrium point of the model are derived by means of appropriate Lyapunov functions. Finally numerical simulations are carried out to confirm theoretical results obtained at HCV-unfected equilibrium.
Keywords
HCV Cellular Model, Differential System, Therapy, Local and Global Solution, Invariant Set, Stability
To cite this article
Alexis Nangue, Global Stability Analysis of the Original Cellular Model of Hepatitis C Virus Infection Under Therapy, American Journal of Mathematical and Computer Modelling. Vol. 4, No. 3, 2019, pp. 58-65. doi: 10.11648/j.ajmcm.20190403.12
Copyright
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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