Influence of backward bifurcation in a model of hepatitis B and C viruses

In the 1990s, liver transplantation for hepatitis B and C virus (HBV and HCV) related-liver diseases was a very controversial issue since recurrent infection of the graft was inevitable. Significant progress has been made in the prophylaxis and treatment of recurrent hepatitis B/C (or HBV/HCV infect...

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Bibliographic Details
Published in:Mathematical biosciences 2010-04, Vol.224 (2), p.118-125
Main Authors: Qesmi, Redouane, Wu, Jun, Wu, Jianhong, Heffernan, Jane M.
Format: Article
Language:English
Subjects:
Algorithms
Backward bifurcation
Basic Reproduction Number
Biological and medical sciences
Blood cells
Blood Cells - virology
Equilibria
Fundamental and applied biological sciences. Psychology
General aspects
Graft Survival
HBV
HCV
Hepacivirus - physiology
Hepatitis B - prevention & control
Hepatitis B - surgery
Hepatitis B - virology
Hepatitis B virus
Hepatitis B virus - physiology
Hepatitis C - prevention & control
Hepatitis C - surgery
Hepatitis C - virology
Hepatocytes - virology
Human viral diseases
Humans
Infectious diseases
Liver Transplantation
Mathematics in biology. Statistical analysis. Models. Metrology. Data processing in biology (general aspects)
Medical sciences
Models, Biological
Reinfection
Transcritical bifurcation
Transplantation
Viral diseases
Viral hepatitis
Viral Load
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Summary:In the 1990s, liver transplantation for hepatitis B and C virus (HBV and HCV) related-liver diseases was a very controversial issue since recurrent infection of the graft was inevitable. Significant progress has been made in the prophylaxis and treatment of recurrent hepatitis B/C (or HBV/HCV infection) after liver transplantation. In this paper, we propose a mathematical model of ordinary differential equations describing the dynamics of the HBV/HCV and its interaction with both liver and blood cells. A single model is used to describe infection of either virus since the dynamics in-host (infected of the liver) are similar. Analyzing the model, we observe that the system shows either a transcritical or a backward bifurcation. Explicit conditions on the model parameters are given for the backward bifurcation to be present. Consequently, we investigate possible factors that are responsible for HBV/HCV infection and assess control strategies to reduce HBV/HCV reinfection and improve graft survival after liver transplantation.
ISSN:0025-5564
1879-3134
DOI:10.1016/j.mbs.2010.01.002