Department of Mathematics, University of Surrey, Guildford, Surrey, UK.
J Biol Dyn. 2008 Apr;2(2):140-53. doi: 10.1080/17513750701769873.
We formulate and systematically study the global dynamics of a simple model of hepatitis B virus in terms of delay differential equations. This model has two important and novel features compared to the well-known basic virus model in the literature. Specifically, it makes use of the more realistic standard incidence function and explicitly incorporates a time delay in virus production. As a result, the infection reproduction number is no longer dependent on the patient liver size (number of initial healthy liver cells). For this model, the existence and the component values of the endemic steady state are explicitly dependent on the time delay. In certain biologically interesting limiting scenarios, a globally attractive endemic equilibrium can exist regardless of the time delay length.
我们以时滞微分方程的形式构建并系统地研究了乙型肝炎病毒的一个简单模型的全局动力学。与文献中著名的基本病毒模型相比，该模型具有两个重要的新颖特征。具体来说，它利用了更现实的标准发病率函数，并明确包含了病毒产生的时间延迟。因此，感染繁殖数不再依赖于患者的肝脏大小（初始健康肝细胞的数量）。对于这个模型，地方病平衡点的存在和组成值明确取决于时滞。在某些生物学上有趣的极限情况下，即使时滞长度存在，也可以存在全局吸引的地方病平衡点。
