Stay with your community: Bridges between clusters trigger expansion of COVID-19.

In this study, the spread of virus infection was simulated using artificial human networks. Here, real-space urban life was modeled as a modified scale-free network with constraints. To date, the scale-free network has been adopted for modeling online communities in several studies. However, in the present study, it has been modified to represent the social behaviors of people where the generated communities are restricted and reflect spatiotemporal constraints in real life. Furthermore, the networks have been extended by introducing multiple cliques in the initial step of network construction and enabling people to contact hidden (zero-degree) as well as popular (large-degree) people. Consequently, four findings and a policy proposal were obtained. First, "second waves" were observed in some cases of the simulations even without external influence or constraints on people's social contacts or the releasing of the constraints. These waves tend to be lower than the first wave and occur in "fresh" clusters, that is, via the infection of people who are connected in the network but have not been infected previously. This implies that the bridge between infected and fresh clusters may trigger a new spread of the virus. Second, if the network changes its structure on the way of infection spread or after its suppression, a second wave larger than the first can occur. Third, the peak height in the time series of the number of infected cases depends on the difference between the upper bound of the number of people each member actually meets and the number of people they choose to meet during the period of infection spread. This tendency is observed for the two kinds of artificial networks introduced here and implies the impact of bridges between communities on the virus spreading. Fourth, the release of a previously imposed constraint may trigger a second wave higher than the peak of the time series without introducing any constraint so far previously, if the release is introduced at a time close to the peak. Thus, overall, both the government and individuals should be careful in returning to society where people enjoy free inter-community contact.