The contributions of our study are to verify the impact of a small-world network on the phenomenon of infection and to reproduce the number of new cases in Japan by simulation with real data. Until July 2022, infectious disease control measures in Japan had kept the daily number of new, confirmed COVID-19 cases per million people at a low level relative to other developed countries. However, the highly infectious Omicron variant BA.5 progressed from around July 2022, and the infection spread rapidly. In the summer of 2022, Japan ranked first worldwide in the daily number of new COVID-19 cases. Thus, a natural infectious phenomenon involves two aspects. First, it is difficult for the infection to propagate if people apply self-restraint on their movements. On the other hand, the infection spreads all at once with increased movement resulting from self-restraint fatigue and quantitative changes in movement. Hence, it is essential to clarify why an infection phenomenon involves these two aspects. Small-world networks give two properties: tightly coupled clusters and weak connections between clusters. When an agent moves in a small-world network, the overall phenomenon changes significantly depending on which of these two properties appears more explicitly. The above two properties should thus appear in an infection phenomenon as people move and come into contact with each other in a network. Tightly connected clusters have a kind of “centripetal force”: As long as infected people do not leave their clusters, the infection is contained only within those clusters and is unlikely to spread. On the other hand, as more infected people move via weak connections, the infection spreads to other clusters and quickly spreads to the entire population. Our study confirms these properties through a multi-agent simulation that reproduces a human travel network with small-world characteristics. Among our findings, a favorable property of the small-world network structure in an infection phenomenon is that herd immunity can be achieved even at low vaccination rates. This combination of the small-world structure and vaccination coverage is a vital feature of our study, and we find it to be effective in lowering the peak of an infection phenomenon.