Table 1 Definition of parameters for the modified epidemic model

á

The isolation rate, i.e. the rate of people moved from the infective group to the hospital isolated group

\(\hat{a}\)

The infection rate, i.e. the rate of the susceptible population get infected

\(\tilde{a}_{E}\)

The outflow rate of early stage infected group, i.e. the rate that early infected people turn advanced infected

\(\tilde{a}_{L}\)

The outflow rate of advanced infected group, i.e. the rate that advanced infected people die of the disease

ό

The outflow rate of the incubation group to the early stage infective group

ù

The outflow rate of the isolation group, that is the rate of isolated patients get cured.

N

The total population

Nc(t)

Number of other household in other countries of one un-hospitalized infected people at time t;

c

Comprehensive treatment and immunization rate

\(\Delta\)

The ratio of the case input (<0) or the output (>0)