title: Influence of backward bifurcation in a model of hepatitis B and C viruses.
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.
authors.affiliation: Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada. rqesm@mathstat.yorku.ca
authors.forename: Redouane
authors.initials: R
authors.lastname: Qesmi
authors.forename: Jun
authors.initials: J
authors.lastname: Wu
authors.forename: Jianhong
authors.initials: J
authors.lastname: Wu
authors.forename: Jane M
authors.initials: JM
authors.lastname: Heffernan
mesh_terms: D000465:Algorithms; D050936:Basic Reproduction Number; D001773:Blood Cells / Q000821:virology; D006085:Graft Survival; D016174:Hepacivirus / Q000502:physiology; D006509:Hepatitis B / Q000517:prevention & control / Q000601:surgery / Q000821:virology*; D006515:Hepatitis B virus / Q000502:physiology; D006526:Hepatitis C / Q000517:prevention & control / Q000601:surgery / Q000821:virology*; D022781:Hepatocytes / Q000821:virology; D006801:Humans; D016031:Liver Transplantation; D008954:Models, Biological; D019562:Viral Load