We study a stochastic behavior of aerosols by the non-equilibrium statistical mechanics approach using the analytical approach of the Langevin equation. We firstly show that superdiffusion can possibly occur right after the emission, which may be attributed to the physical mechanism of the outbreak of the COVID-19 pandemic. We also provide clear evidence of the least required distance to prevent infections occurred by aerosols. In particular, the required distance to prevent aerosol infections is derived to be about 42 m when we assume Cauchy distribution as an initial velocity distribution. This fact implies that due to superdiffusion the aerosol infection can occur even far away from a long distance as compared to the previous considerations.