论文标题
为什么应使用积分方程代替微分方程来描述流行的动力学
Why integral equations should be used instead of differential equations to describe the dynamics of epidemics
论文作者
论文摘要
了解和跟踪快速展开流行病的动态至关重要。当前共同19-19大流行的健康和经济后果提供了一个令人难以置信的案例。在这里，我们指出，由于它们基于微分方程，因此最广泛使用的流行病模型被近似值所困扰，而在当前的Covid-19-19大流行中，这种近似是没有道理的。以纽约市的数据为例，我们表明目前使用的模型大大低估了最初的基本繁殖编号（$ r_0 $）。基于积分方程式的正确描述可以在大多数报告的模型中实现，并且由于限制性公共会众措施，在$ r_0 $的急剧变化之后，它更准确地说明了流行病的动态。它还提供了一种新的方法来确定孵化期，最重要的是，正如我们在几个国家 /地区所证明的那样，此方法允许对$ R_0 $进行准确的监视，从而对任何限制性措施进行微调。基于积分方程的模型不仅提供了概念上正确的描述，而且它们比基于微分方程的模型具有更多的预测能力，因此我们看不到使用后者的任何理由。
It is of vital importance to understand and track the dynamics of rapidly unfolding epidemics. The health and economic consequences of the current COVID-19 pandemic provide a poignant case. Here we point out that since they are based on differential equations, the most widely used models of epidemic spread are plagued by an approximation that is not justified in the case of the current COVID-19 pandemic. Taking the example of data from New York City, we show that currently used models significantly underestimate the initial basic reproduction number ($R_0$). The correct description, based on integral equations, can be implemented in most of the reported models and it much more accurately accounts for the dynamics of the epidemic after sharp changes in $R_0$ due to restrictive public congregation measures. It also provides a novel way to determine the incubation period, and most importantly, as we demonstrate for several countries, this method allows an accurate monitoring of $R_0$ and thus a fine-tuning of any restrictive measures. Integral equation based models do not only provide the conceptually correct description, they also have more predictive power than differential equation based models, therefore we do not see any reason for using the latter.
