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 [Formula: see text] of change of the number of infected individuals [Formula: see text] is given by an ellipse in the [Formula: see text]- [Formula: see text] plane which is supported in [Formula: see text]. With [Formula: see text] , it is shown that (1) when [Formula: see text] , oscillation of the infection curve is self-organized and the period of the oscillation is in proportion to the ratio of the difference [Formula: see text] and the geometric mean [Formula: see text] of [Formula: see text] and [Formula: see text] , (2) when [Formula: see text] , the infection curve shows a critical behavior where it decays obeying a power law function with exponent [Formula: see text] in the long time limit after a peak, and (3) when [Formula: see text] , 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 [Formula: see text].