  We consider the pandemic spreading of COVID-19 for some selected countries
after the outbreak of the coronavirus in Wuhan City, China. We estimated the
infection rate and the initial infected individuals of COVID-19 by using the
officially reported data at the early stage of the epidemic for the susceptible
(S), infectable (I), quarantined (Q), and the cofirmed recovered (Rk)
population model, so called SIQRk model. In the reported data we know the
quarantined cases and the recovered cases. We can not know the recovered cases
from the asymptomatic cases. In the SIQRk model we can estimated the model
parameters and the initial infecting cases (confirmed ans asymtomatic cases)
from the data fits. We obtained the infection rate in the range between 0.233
and 0.462, the basic reproduction number Ro in the range between 1.8 and 3.5,
and the initial number of infected individuals in the range betwee 10 and 8409
for some selected countries. By using fitting parameters we estimated the
maximum time of the infection for Germany when the government are performing
the quarantine policy. The disease is undergoing to the calm state about six
months after first patients were identified.
