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

Abstract

On the basis of a compartment model, the epidemic curve is investigated when the net rate λ of change of the number of infected individuals I is given by an ellipse in the λ-I plane which is supported inwhen a < 1 or I ℓ > 0, oscillation of the infection curve is self-organized and the period of the oscillation is in proportion to the ratio of (I h − I ℓ ) and the geometric mean √ I h I ℓ of I h and I ℓ , (2) when a = 1, the infection curve shows a critical behavior where it decays obeying a power law function with exponent −2 in the long time limit after a peak, and (3) when a > 1, 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 I ℓ < 0.