  The SEIRS model, an extension of the SEIR model for analyzing and predicting
the spread of virus infection, was further extended to consider the movement of
people across regions. In contrast to previous models that con-sider the risk
of travelers from/to other regions, we consider two factors. First, we consider
the movements of susceptible (S), exposed (E), and recovered (R) individuals
who may get infected and infect others in the destination region, as well as
infected (I) individuals. Second, people living in a region and moving from
other regions are dealt as separate but interacting groups with respect to
their states, S, E, R, or I. This enables us to consider the potential
influence of movements before individuals become infected, difficult to detect
by testing at the time of immigration, on the spread of infection. In this
paper, we show the results of the simulation where individuals travel across
regions, which means prefectures here, and the government chooses regions to
vaccinate with priority. We found a general law that a quantity of vaccines can
be used efficiently by maximizing an index value, the conditional entropy Hc,
when we distribute vaccines to regions. The efficiency of this strategy, which
maximizes Hc, was found to outperform that of vaccinating regions with a larger
effective re-generation number. This law also explains the surprising result
that travel activities across regional borders may suppress the spread if
vaccination is processed at a sufficiently high pace, introducing the concept
of social muddling.
