On Lock-down Control of a Pandemic Model

TL;DR

This paper applies a path integral control approach to optimize pandemic lock-down policies within a complex stochastic SIR model incorporating fatigue and Bayesian opinion dynamics, providing a novel numerical solution method.

Contribution

It introduces a path integral control framework for pandemic policy optimization, linking quantum-inspired methods with stochastic control in high-dimensional models.

Findings

Derived an optimal lock-down intensity using a Schrödinger-type equation.

Implemented a Monte Carlo algorithm for high-dimensional stochastic control.

Demonstrated the approach's applicability to COVID-19 pandemic modeling.

Abstract

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.