%0 Journal Article
%J Mathematical biosciences
%D 2010
%T Influence of backward bifurcation in a model of hepatitis B and C viruses.
%A Qesmi, Redouane
%A Wu, Jun
%A Wu, Jianhong
%A Heffernan, Jane M
%K Algorithms
%K Basic Reproduction Number
%K Blood Cells
%K Graft Survival
%K Hepacivirus
%K Hepatitis B
%K Hepatitis B virus
%K Hepatitis C
%K Hepatocytes
%K Humans
%K Liver Transplantation
%K Models, Biological
%K Viral Load
%N 2
%P 118-25
%R 10.1016/j.mbs.2010.01.002
%V 224
%X 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.
%8 2010 Apr