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.
| Published in | American Journal of Mathematical and Computer Modelling (Volume 4, Issue 3) |
| DOI | 10.11648/j.ajmcm.20190403.12 |
| Page(s) | 58-65 |
| 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. |
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Copyright © The Author(s), 2019. Published by Science Publishing Group |
HCV Cellular Model, Differential System, Therapy, Local and Global Solution, Invariant Set, Stability
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APA Style
Alexis Nangue. (2019). Global Stability Analysis of the Original Cellular Model of Hepatitis C Virus Infection Under Therapy. American Journal of Mathematical and Computer Modelling, 4(3), 58-65. https://doi.org/10.11648/j.ajmcm.20190403.12
ACS Style
Alexis Nangue. Global Stability Analysis of the Original Cellular Model of Hepatitis C Virus Infection Under Therapy. Am. J. Math. Comput. Model. 2019, 4(3), 58-65. doi: 10.11648/j.ajmcm.20190403.12
AMA Style
Alexis Nangue. Global Stability Analysis of the Original Cellular Model of Hepatitis C Virus Infection Under Therapy. Am J Math Comput Model. 2019;4(3):58-65. doi: 10.11648/j.ajmcm.20190403.12
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Download@article{10.11648/j.ajmcm.20190403.12,
author = {Alexis Nangue},
title = {Global Stability Analysis of the Original Cellular Model of Hepatitis C Virus Infection Under Therapy},
journal = {American Journal of Mathematical and Computer Modelling},
volume = {4},
number = {3},
pages = {58-65},
doi = {10.11648/j.ajmcm.20190403.12},
url = {https://doi.org/10.11648/j.ajmcm.20190403.12},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajmcm.20190403.12},
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.},
year = {2019}
}
TY - JOUR T1 - Global Stability Analysis of the Original Cellular Model of Hepatitis C Virus Infection Under Therapy AU - Alexis Nangue Y1 - 2019/08/29 PY - 2019 N1 - https://doi.org/10.11648/j.ajmcm.20190403.12 DO - 10.11648/j.ajmcm.20190403.12 T2 - American Journal of Mathematical and Computer Modelling JF - American Journal of Mathematical and Computer Modelling JO - American Journal of Mathematical and Computer Modelling SP - 58 EP - 65 PB - Science Publishing Group SN - 2578-8280 UR - https://doi.org/10.11648/j.ajmcm.20190403.12 AB - 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. VL - 4 IS - 3 ER -
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