Modeling and analysis of COVID-19 infected persons during repeated waves in Japan

A model for estimating the number of COVID-19 infected persons (infecteds) is proposed based on the exponential function law of the SIR model. This model is composed of several equations expressing the number of infecteds, considering the onset after an incubation period, infectivity, wavy infection persistence with repeated infection spread and convergence with insufficient quarantine. This model is applied to the infection in Japan, which is currently suffering from the 5th wave, and the initial number of infecteds and various related parameters are calculated by curve fitting of the cumulative number of infecteds to the total cases in the database. As a minimum boundary of the number of infecteds for the infection continuation up to the 5th wave, the initial number of infecteds at the outbreak of infection is more than an order of magnitude higher than the actual initial cases. A convergence ratio (cumulative number of infecteds / total cases) at the end of the first wave is obtained as 1.5. The quarantine rate and social distancing ratio based on the SIQR model are evaluated, and the social distancing ratio increases sharply just after the governments declaration of emergency. The quarantine rate closely equals the positive rate by PCR tests, meaning that the number of infecteds, which had been unknown, is on the order of almost the same as the number of tests.