Inverse proportionality between height and duration of epidemic peaks not observed for the COVID-19 epidemic in Japan

The height of the epidemic peaks varied ten-fold, but the duration was almost constant independent of the peak height in the six times COVID-19 epidemics in Japan over the past two years. The observed relation between the peak height and duration contradicts the inverse proportionality, which is the essential conclusion derived from mathematical models for infectious diseases. We found that the peak height was inversely proportional to the number of rhinovirus patients. The literature has revealed the mechanism behind our found power of rhinovirus suppressing COVID-19. We discuss that the critical flaw of current mathematical models originates in the absence of the 0th power term of the number of infected people in the Kermack and McKendrick equation.