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The concept of the effective infection opportunity population (EIOP) wasincorporated into the SIQR model, and it was assumed that this EIOP wouldchange with the spread of infection, and this was named as the effective SIQRmodel. When calculated with this model, the uninfected population S decreaseswith the passage of time. However, when the EIOP N increases because of anyreason, the infection threshold becomes larger than 1. Even after the firstwave seems to have subsided, the infection begins to spread again. Firstly, wefind the curve of EIOP change so that the calculation result by this modelmatches the data of the first and second waves. Then, we use this curve to fitwith only the data of the second wave alone, and the third wave is predicted.In the case of new coronavirus infection, there are various restrictions ondata collection to identify individual coefficients of mathematical models, andthe true value is almost unknown. Therefore, the discussion in this paper isonly about data fitting for predictive calculation. Therefore, the simulationon the true value is not aimed. However, since the data of infected personsreflect the true values, the results of data fitting can be used for theprediction of infected persons, isolated care recipients, inpatients, andseverely ill persons. They are useful for a qualitative understanding ofinfection. The idea of EIOP is important in the sense that it connects themean-field and the non-mean field, but the existence of data is essential, andthe theory alone cannot simulate the non-mean field. We have developed twomethods for treating the non-mean field cases where we don't have enough data.We have briefly introduced them.

Application and Extension of Mean-Field Theory such as SIR to Discuss the Non-Mean Field Problem of COVID-19