Before revision:  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 .
After revision:  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 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 the infection test at the time of immigration .