  On the basis of a compartment model, the epidemic curve is investigated when
the net rate $\lambda$ of change of the number of infected individuals $I$ is
given by an ellipse in the $\lambda$-$I$ plane which is supported in
$[I_{\ell}, I_h]$. With $a \equiv (I_h - I_{\ell})/(I_h + I_{\ell})$, it is
shown that (1) when $a < 1$ or $I_{\ell} >0$, oscillation of the infection
curve is self-organized and the period of the oscillation is in proportion to
the ratio of the difference $ (I_h - I_{\ell})$ and the geometric mean
$\sqrt{I_h I_{\ell}}$ of $I_h$ and $I_{\ell}$, (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 $I_{\ell} < 0$.
