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

TitleInfluence of backward bifurcation in a model of hepatitis B and C viruses.
Publication TypeJournal Article
Year of Publication2010
AuthorsQesmi R, Wu J, Wu J, Heffernan JM
JournalMathematical biosciences
Volume224
Issue2
Pagination118-25
Date Published2010 Apr
ISSN1879-3134
KeywordsAlgorithms, Basic Reproduction Number, Blood Cells, Graft Survival, Hepacivirus, Hepatitis B, Hepatitis B virus, Hepatitis C, Hepatocytes, Humans, Liver Transplantation, Models, Biological, Viral Load
Abstract

In the 1990 s, 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.

DOI10.1016/j.mbs.2010.01.002
Alternate JournalMath Biosci