Eikenberry Steffen, Hews Sarah, Nagy John D, Kuang Yang
Department of Mathematics and Statistics, Arizona State University, Tempe, AZ 85287, United States.
Math Biosci Eng. 2009 Apr;6(2):283-99. doi: 10.3934/mbe.2009.6.283.
Chronic HBV affects 350 million people and can lead to death through cirrhosis-induced liver failure or hepatocellular carcinoma. We analyze the dynamics of a model considering logistic hepatocyte growth and a standard incidence function governing viral infection. This model also considers an explicit time delay in virus production. With this model formulation all model parameters can be estimated from biological data; we also simulate a course of lamivudine therapy and find that the model gives good agreement with clinical data. Previous models considering constant hepatocyte growth have permitted only two dynamical possibilities: convergence to a virus free or a chronic steady state. Our model admits a third possibility of sustained oscillations. We show that when the basic reproductive number is greater than 1 there exists a biologically meaningful chronic steady state, and the stability of this steady state is dependent upon both the rate of hepatocyte regeneration and the virulence of the disease. When the chronic steady state is unstable, simulations show the existence of an attracting periodic orbit. Minimum hepatocyte populations are very small in the periodic orbit, and such a state likely represents acute liver failure. Therefore, the often sudden onset of liver failure in chronic HBV patients can be explained as a switch in stability caused by the gradual evolution of parameters representing the disease state.
慢性乙肝病毒感染影响着3.5亿人，可导致因肝硬化引起的肝衰竭或肝细胞癌而死亡。我们分析了一个模型的动力学，该模型考虑了逻辑斯蒂肝细胞生长和控制病毒感染的标准发生率函数。该模型还考虑了病毒产生中的明确时间延迟。通过这种模型公式，所有模型参数都可以从生物学数据中估计出来；我们还模拟了拉米夫定治疗过程，发现该模型与临床数据吻合良好。之前考虑恒定肝细胞生长的模型只允许两种动力学可能性：收敛到无病毒或慢性稳态。我们的模型允许第三种持续振荡的可能性。我们表明，当基本繁殖数大于1时，存在一个具有生物学意义的慢性稳态，并且该稳态的稳定性取决于肝细胞再生速率和疾病的毒力。当慢性稳态不稳定时，模拟显示存在一个吸引周期轨道。在周期轨道中最小肝细胞群体非常小，这种状态可能代表急性肝衰竭。因此，慢性乙肝患者肝衰竭通常突然发作可以解释为代表疾病状态的参数逐渐演变导致的稳定性转变。
