  The SEIR model, widely used for analyzing and predicting the spread of virus
infection, is here extended to considering the movement of people across
regions. In contrast to previous models considering the risk due to the
travelers from and to other regions, here we consider two factors. First, we
con-sider the movements of susceptible (S), exposed (E), and recovered (R)
people as well as infected (I) who can get infected after movement. Second, the
infectious contacts between people from different regions are considered and
dealt with separately from the first factor. By this, we can reflect the
potential risk of future infections that are not out of the range of inspection
of infection without over/under-estimating the ratio of E or I among the entire
number of people moving. 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 high effective regeneration
number should be vaccinated with priority and that frequent travels tend to
cause an influence to enhance the spread especially in the up-trend stage of
infections and in regions of smaller populations. 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.
