ABSTRACT
A new mathematical model called SIIR model is constructed to describe the spread of infection by taking account of the characteristics of COVID-19 and is verified by the data from Japan. The following features of COVID-19: (a) there exist presymptomatic individuals who have infectivity even during the incubation period, (b) there exist asymptomatic individuals who can freely move around and play crucial roles in the spread of infection, and (c) the duration of immunity may be finite, are incorporated into the SIIR model. The SIIR model has the advantage of being able to explicitly handle asymptomatic individuals who are delayed in discovery or are extremely difficult to be discovered in the real world. It is shown that the conditions for herd immunity in the SIIR model become more severe than those in the SIR model; that is, the presence of asymptomatic individuals increases herd immunity threshold (HIT).