论文标题
关于大流行模型的锁定控制
On Lock-down Control of a Pandemic Model
论文作者
论文摘要
在本文中,Feynman-type路径积分控制方法用于递归制定健康目标功能,但要遵守疲劳动力学,这是一种前瞻性的随机多风险多风险易感性感应反射(SIR)模型,具有风险群体的贝叶斯舆论动力学,以触发Covid-19。我的主要兴趣在于解决政策制定者的社会成本的最小化,这取决于确定性的体重。我从灯芯旋转的schrodinger-type方程中获得了最佳的锁定强度,该方程类似于汉密尔顿 - 雅各比 - 贝尔曼(HJB)方程。我的公式基于路径积分控制和动态编程工具,促进了分析,并允许应用算法为大流行控制模型获得数值解决方案。 Feynman路径积分是一种使用量子拉格朗日函数的量化方法,而Schrodinger的量化使用了哈密顿函数。人们认为这两种方法是等效的,但是这种等效性并未在数学上得到完全证明。随着基于网格的偏微分方程(PDE)求解器的复杂性和内存需求随着系统尺寸的增加而呈指数增加,因此在高尺寸的情况下,此方法变得不切实际。作为替代路径积分控制,用蒙特卡洛方法解决了HJB方程的A级随机控制问题,此方法避免了HJB方程域的全局网格的需求。
In this paper a Feynman-type path integral control approach is used for a recursive formulation of a health objective function subject to a fatigue dynamics, a forward-looking stochastic multi-risk susceptible-infective-recovered (SIR) model with risk-group's Bayesian opinion dynamics towards vaccination against COVID-19. My main interest lies in solving a minimization of a policy-maker's social cost which depends on some deterministic weight. I obtain an optimal lock-down intensity from a Wick-rotated Schrodinger-type equation which is analogous to a Hamiltonian-Jacobi-Bellman (HJB) equation. My formulation is based on path integral control and dynamic programming tools facilitates the analysis and permits the application of algorithm to obtain numerical solution for pandemic control model. Feynman path integral is a quantization method which uses the quantum Lagrangian function, while Schrodinger's quantization uses the Hamiltonian function. These two methods are believed to be equivalent but, this equivalence has not fully proved mathematically. As the complexity and memory requirements of grid-based partial differential equation (PDE) solvers increase exponentially as the dimension of the system increases, this method becomes impractical in the case with high dimensions. As an alternative path integral control solves a class a stochastic control problems with a Monte Carlo method for a HJB equation and this approach avoids the need of a global grid of the domain of the HJB equation.