论文标题
sir型系统中不确定性的路径积分方法
Path Integral Approach to Uncertainties in SIR-type Systems
论文作者
论文摘要
在本文中，我展示了如何使用路径积分技术来对“易感性抗病恢复”（SIR）型系统的历史进行衡量。标准的SIR解决方案作为描述该度量的动作的经典马鞍出现。然后，可以在背景解决方案周围进行扰动，然后本文继续解决背景解决方案周围波动的协方差。使用绿色的功能类型方法，只需要求解其他普通微分方程即可。不需要明确的矩阵反转。计算的协方差矩阵应该在构建快速可能性的构建中，以将SIR型模型的参数拟合到数据中。提出了对模拟集合方法的预测的比较。
In this paper I show how path integral techniques can be used to put measures on histories in "susceptible-infectious-recovered" (SIR)-type systems. The standard SIR solution emerges as the classical saddle point of the action describing the measure. One can then expand perturbatively around the background solution, and this paper goes on to work out the covariance of fluctuations around the background solution. Using a Green's function type approach, one simply needs to solve additional ordinary differential equations; an explicit matrix inversion is not required. The computed covariance matrix should be useful in the construction of fast likelihoods for fitting the parameters of SIR-type models to data. A comparison of the predictions of the approach to an ensemble of simulations is presented.
