Optimal lock-down intensity: A stochastic pandemic control approach of path integral

Abstract

Abstract The aim of this article is to determine the optimal intensity of lock-down measures and vaccination rates to control the spread of coronavirus disease 2019. The study uses a stochastic susceptible-infected-recovered (SIR) model with infection dynamics. A Feynman-type path integral control approach is used to derive a forward Fokker-Plank-type equation for the system, which helps in performing a stochastic control analysis. The simulation study concludes that increasing the diffusion coefficients leads to a downward trend in the susceptible and recovery curves, while the infection curve becomes ergodic. Additionally, the study shows that the optimal lock-down intensity is stable around zero, and the vaccination rate increases over time.