The analysis of viral kinetics models is mostly achieved by numerical methods. We present an approach via a Magnus expansion that allows us to give an approximate solution to the interferon-dependent viral infection model of influenza which is compared with numerical results. The time of peak viral load is calculated from the approximation and stays within 10% in the studied range of interferon (IFN) efficacy ϵ ∈ [0, 1000]. We utilize our solution to interpret the effect of varying IFN efficacy, suggesting a competition between virions and interferon that can cause an additional peak in the usually exponential increase in the viral load.

中文翻译：

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流感病毒干扰素依赖性病毒动力学模型的近似解。

病毒动力学模型的分析主要通过数值方法来实现。我们提出了一种通过Magnus扩展的方法，该方法使我们能够对流感病毒的干扰素依赖性病毒感染模型提供近似解决方案，并与数值结果进行比较。病毒载量峰值的时间是根据近似值计算的，并且在干扰素（IFN）功效ϵ∈[0，1000]的研究范围内保持在10％以内。我们利用我们的解决方案来解释不同IFN功效的影响，这表明病毒体和干扰素之间的竞争可能导致病毒载量通常呈指数增加的另一个峰值。