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In this paper a Feynman-type path integral control approach is used for arecursive formulation of a health objective function subject to a fatiguedynamics, a forward-looking stochastic multi-risksusceptible-infective-recovered (SIR) model with risk-group's Bayesian opiniondynamics towards vaccination against COVID-19. My main interest lies in solvinga minimization of a policy-maker's social cost which depends on somedeterministic weight. I obtain an optimal lock-down intensity from aWick-rotated Schrodinger-type equation which is analogous to aHamiltonian-Jacobi-Bellman (HJB) equation. My formulation is based on pathintegral control and dynamic programming tools facilitates the analysis andpermits the application of algorithm to obtain numerical solution for pandemiccontrol model. Feynman path integral is a quantization method which uses thequantum Lagrangian function, while Schrodinger's quantization uses theHamiltonian function. These two methods are believed to be equivalent but, thisequivalence has not fully proved mathematically. As the complexity and memoryrequirements of grid-based partial differential equation (PDE) solvers increaseexponentially as the dimension of the system increases, this method becomesimpractical in the case with high dimensions. As an alternative path integralcontrol solves a class a stochastic control problems with a Monte Carlo methodfor a HJB equation and this approach avoids the need of a global grid of thedomain of the HJB equation.

On Lock-down Control of a Pandemic Model