A Logistic Curve in the SEIR Model and the Basic Reproduction Number of COVID-19 in Japan

The SEIR model is one of modified models of SIR, especially taken into account of exposed people. SEIR equations can be solved numerically, but it is hard to obtain analytically. Here, we propose some approximate solutions of SEIR equations, one of which is related with the logistic formula in Biology. As the second aim, the SEIR model is applied to the 7th-wave of COVID-19 in Japan. The basic reproduction number ( α ) in the SEIR model is estimated for the Omicron wave. We make use of data of the removed number R ( t ) rather than that of the infective number, because the latter seems to be ambiguous. This analysis gives α = 10 with γ = 1 and σ = 0.5.