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

• 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
• ISSN: 0025-5564; 1879-3134
• DOI: 10.1016/j.mbs.2010.01.002

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.