There exists the "smartest" movement rate to control the epidemic rather than "city lockdown"

The emergency outbreak and spread of coronavirus disease 2019 (COVID-19) has left great damage to individuals over most of the world. Population mobility is the primary reason for the spread of the epidemic. A delayed stochastic epidemic susceptible-infected-recovered (SIR) model with Gaussian white noise is introduced. Compared with traditional models,this model is characterized by time delay, environmental noise and population mobility among municipalities with the convenient transportation network. The stochastic dynamic behavior of the SIR model is analyzed and the existence of the stochastic bifurcation of the system is proved. The effect of time delay and movement rate are investigated. Numerical simulations are performed to support the theoretical results. It is worth mentioning that the movement rate is not as low as possible and appropriate population mobility is conducive to alleviating the epidemic. Through simulation, we demonstrate the existence of the best movement rate named the "smartest" $$ , which is helpful to control the epidemic. This model is also useful to prevent other infectious diseases.