Before revision:  As a result , we show the results of simulation where the influence of traveling across regions, which mean prefectures here, and of the choice of regions to vaccinate with priority , on the risk of infection spread. We find the regions of large population or large effective regeneration number should be vaccinated with priority and that frequent travels tend to cause an influence to enhance the spread especially in the uptrend stage of infections and in regions of smaller populations. Moreover, we show vaccination at a slow pace in Japan will not suppress the infection spread sufficiently to extinguish the current 4th wave within a few months. However, a restricted quantity of vaccines can be used efficiently by maximizing a diverted index value?
After revision:  As a result , we show the results of simulation where the influence of traveling across regions, which mean prefectures here, and of the choice of regions to vaccinate with priority . We found a general law that a quantity of vaccines can be used efficiently by maximizing a diverted index value?