  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.
