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
Date Published2010 Apr
KeywordsAlgorithms, Basic Reproduction Number, Blood Cells, Graft Survival, Hepacivirus, Hepatitis B, Hepatitis B virus, Hepatitis C, Hepatocytes, Humans, Liver Transplantation, Models, Biological, Viral Load

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.

Alternate JournalMath Biosci