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  .
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 / to other regions, here we consider two factors. First, we consider the movements of susceptible (S), exposed (E), and recovered (R) individuals who may get infected after movement, as well as infected (I) . Second, the infectious contacts between people from different regions are dealt with separately from the first factor. By this, we can reflect the potential future influence on the infection spread due to the movements of S and E that are hard to detect by the infection test at the time of immigration . 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 ? 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 .
R
and
/
R
con-sider
consider
R
people
individuals who may get infected after movement,
D
who can get infected after movement
D
considered and
R
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
future influence on the infection spread due to the movements of S and E that are hard to detect by the infection test at the time of immigration
R
high
large
R
up-trend
uptrend
D
it is not expected that
A
not
A
4th
A
. 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