论文标题
在连续时间图中量化建模Covid-19的大流行中的不准确性
Quantifying Inaccuracies in Modeling COVID-19 Pandemic within a Continuous Time Picture
论文作者
论文摘要
通常，关于COVID-19的大流行预测的数学模拟研究基于确定性微分方程，这些方程式假定各种流行病学类别中的个体的数量（$ n $）以及其依赖的时间（$ t $）的数量是不同的数量。这张照片与$ n $和$ t $的离散表示形成对比，根据每日感染案例报告的实际流行病学数据，为此，基于有限差异方程式的描述将更加足够。采用逻辑增长框架，在本文中，我们对连续时间描述引入的错误进行了定量分析。该分析表明，尽管流行病学曲线最大的高度本质上是不受影响的，但在连续时间表示内获得的位置$ t_ {1/2}^{c} $在$ t_ {1/2}^{d} $ the Invive of Invife n indivet niver inivet nive invireet the Invete timpational in Invive the Invert the Invetiles the Invereptional $ T_ {1/2}^} $ to in Systhy上向后移动。相反，违反直觉的是，这种时间移位的大小$τ\ equiv t_ {1/2}^{c} {c} - t_ {1/2}^{d} <0 $基本上对感染率$κ$的变化基本上不敏感。对于在极端情况下从COVID-19数据中得出的广泛$κ$值（指数增长和完全锁定），我们发现了一个相当强大的估计$τ\ simeq -2.65 \，\ mbox {day}^}^{ - 1} $。在没有任何特定假设的情况下获得的目前数学结果通常适用于逻辑增长，而没有任何限制特定的实际系统。
Typically, mathematical simulation studies on COVID-19 pandemic forecasting are based on deterministic differential equations which assume that both the number ($n$) of individuals in various epidemiological classes and the time ($t$) on which they depend are quantities that vary continuous. This picture contrasts with the discrete representation of $n$ and $t$ underlying the real epidemiological data reported in terms daily numbers of infection cases, for which a description based on finite difference equations would be more adequate. Adopting a logistic growth framework, in this paper we present a quantitative analysis of the errors introduced by the continuous time description. This analysis reveals that, although the height of the epidemiological curve maximum is essentially unaffected, the position $T_{1/2}^{c}$ obtained within the continuous time representation is systematically shifted backwards in time with respect to the position $T_{1/2}^{d}$ predicted within the discrete time representation. Rather counterintuitively, the magnitude of this temporal shift $τ\equiv T_{1/2}^{c} - T_{1/2}^{d} < 0$ is basically insensitive to changes in infection rate $κ$. For a broad range of $κ$ values deduced from COVID-19 data at extreme situations (exponential growth in time and complete lockdown), we found a rather robust estimate $τ\simeq -2.65\,\mbox{day}^{-1}$. Being obtained without any particular assumption, the present mathematical results apply to logistic growth in general without any limitation to a specific real system.
