Self-organization of oscillation in an epidemic model for COVID-19.

On the basis of a compartment model, the epidemic curve is investigated when the net rate of change of the number of infected individuals is given by an ellipse in the - plane which is supported in . With , it is shown that (1) when , oscillation of the infection curve is self-organized and the period of the oscillation is in proportion to the ratio of the difference and the geometric mean of and , (2) when , the infection curve shows a critical behavior where it decays obeying a power law function with exponent in the long time limit after a peak, and (3) when , the infection curve decays exponentially in the long time limit after a peak. The present result indicates that the pandemic can be controlled by a measure which makes .