Effects of Interregional Travels and Vaccination in Infection Spreads Simulated by Lattice of SEIRS Circuits

Abstract

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.