Department of Mathematics and Statistics, University of South Alabama, 411 University Boulevard North, Mobile, AL, 36688-0002, USA.
Theory Biosci. 2023 Jun;142(2):107-142. doi: 10.1007/s12064-023-00388-y. Epub 2023 Mar 11.
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 toward 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 Schrödinger-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.
本文使用费曼型路径积分控制方法，针对疲劳动力学，前瞻性随机多风险易感染-感染-恢复（SIR）模型，以及针对 COVID-19 疫苗接种的风险群体贝叶斯意见动态，对健康目标函数进行递归公式化。我的主要兴趣在于解决决策者社会成本的最小化问题，该成本取决于一些确定性权重。我从 Wick 旋转的薛定谔型方程中获得了最佳封锁强度，该方程类似于哈密顿-雅可比-贝尔曼（HJB）方程。我的公式基于路径积分控制和动态规划工具，便于分析，并允许应用算法为大流行控制模型获得数值解。
