Area Theorem of Infection Curves for Large Basic Reproduction Number

Abstract

A remarkable theorem is established in the SIR model in Epidemiology, that is, when the basic reproduction number α is larger than 5, the area of any infection curve is constant given by 1/c, where c is the removed ratio. From this theorem we see that as α gets bigger, the infection curve raises sharply, but its half width decreases inversely. Accordingly, the wave of Omicron will end with a shorter life-time than that of the wave of Delta, because α for Omicron is larger than Delta’s which is regarded as 5<α<9. A rough estimation of the 5-wave area of infection in Japan tells us that the 6-wave will reach a peak on early in Feb., then it will be controlled around early in March.