Influence of backward bifurcation in a model of hepatitis B and C viruses. (English) Zbl 1188.92017

Qesmi, Redouane; Wu, Jun; Wu, Jianhong; Heffernan, Jane M.

Math. Biosci. 224, No. 2, 118-125 (2010).

Summary: 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. We propose a mathematical model of ordinary differential equations describing the dynamics of the HBV/HCV and its interactions 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.

MSC:

92C50	Medical applications (general)
34C60	Qualitative investigation and simulation of ordinary differential equation models
34D20	Stability of solutions to ordinary differential equations
92C60	Medical epidemiology
37N25	Dynamical systems in biology

Keywords:

HBV; HCV; transplantation; reinfection; equilibria; transcritical bifurcation; backward bifurcation

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