Smith Amber M, Adler Frederick R, Perelson Alan S
Department of Mathematics, University of Utah, Salt Lake City, UT 84112, USA.
J Math Biol. 2010 May;60(5):711-26. doi: 10.1007/s00285-009-0281-8. Epub 2009 Jul 25.
During an acute viral infection, virus levels rise, reach a peak and then decline. Data and numerical solutions suggest the growth and decay phases are linear on a log scale. While viral dynamic models are typically nonlinear with analytical solutions difficult to obtain, the exponential nature of the solutions suggests approximations can be found. We derive a two-phase approximate solution to the target cell limited influenza model and illustrate its accuracy using data and previously established parameter values of six patients infected with influenza A. For one patient, the fall in virus concentration from its peak was not consistent with our predictions during the decay phase and an alternate approximation is derived. We find expressions for the rate and length of initial viral growth in terms of model parameters, the extent each parameter is involved in viral peaks, and the single parameter responsible for virus decay. We discuss applications of this analysis in antiviral treatments and in investigating host and virus heterogeneities.
在急性病毒感染期间，病毒水平上升、达到峰值然后下降。数据和数值解表明，在对数尺度上，生长和衰减阶段是线性的。虽然病毒动力学模型通常是非线性的，难以获得解析解，但解的指数性质表明可以找到近似解。我们推导了靶细胞受限流感模型的两阶段近似解，并使用感染甲型流感的六名患者的数据和先前确定的参数值来说明其准确性。对于一名患者，病毒浓度从峰值下降在衰减阶段与我们的预测不一致，因此推导了另一种近似解。我们根据模型参数、每个参数参与病毒峰值的程度以及负责病毒衰减的单个参数，得出了初始病毒生长速率和长度的表达式。我们讨论了该分析在抗病毒治疗以及研究宿主和病毒异质性方面的应用。
