Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada.
Math Biosci. 2010 Apr;224(2):118-25. doi: 10.1016/j.mbs.2010.01.002. Epub 2010 Jan 18.
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.
在 20 世纪 90 年代，肝移植治疗乙型肝炎和丙型肝炎病毒（HBV 和 HCV）相关肝病是一个非常有争议的问题，因为移植后不可避免地会发生复发性感染。在肝移植后预防和治疗乙型肝炎/丙型肝炎（或 HBV/HCV 感染）方面已经取得了重大进展。在本文中，我们提出了一个常微分方程的数学模型，用于描述 HBV/HCV 的动力学及其与肝和血细胞的相互作用。由于宿主内（肝脏感染）的动力学相似，因此使用单个模型来描述任一病毒的感染。通过分析模型，我们观察到系统表现出转临界或反向分岔。给出了模型参数上的显式条件，以存在反向分岔。因此，我们研究了可能导致 HBV/HCV 感染的因素，并评估了控制策略，以减少肝移植后 HBV/HCV 的再感染并提高移植物的存活率。
