Before revision:  Moreover, we show it is not expected that vaccination at a slow pace in Japan will  suppress the infection spread sufficiently to extinguish the current  wave within a few months  .
After revision:  Moreover, we show it is not expected that vaccination at a slow pace in Japan will suppress the infection spread sufficiently to extinguish the current wave within a few months . However, a restricted quantity of vaccines can be used efficiently by maximizing a diverted index value ? the conditional entropy ? of vaccination distribution. Furthermore, travel activity across regional borders that accelerated infection spread so far is found to rather sup-press it if vaccination is processed at a high pace .