Table 1 Definitions and values of parameters and variables in Yangzhou and Xi’an

Parameter

   c(t)

\(c_0\)

Contact rate before lockdown

22.90(5.44)

24.70(6.33)

Estimated

\(c_b\)

Minimum contact rate with control strategies

3.31(0.97)

2.38(1.83)

Estimated

\(r_c\)

Exponential decreasing rate of contact rate

1.12(0.48)

0.32(0.24)

Estimated

   \(\beta\)

Transmission probability from I to S per contact

0.09(0.02)

0.06(0.02)

Estimated

   q(t)

\(q_0\)

Quarantined rate before lockdown

0.23(0.06)

0.25(0.05)

Estimated

\(q_b\)

Maximum quarantined rate with control strategies

0.88(0.03)

0.86(0.11)

Estimated

\(r_q\)

Exponential increasing rate of quarantined rate

0.61(0.21)

0.78(0.98)

Estimated

   \(\lambda\)

Releasing rate of quarantined susceptibles

1/14

1/14

[34, 35]

   \(\sigma\)

Transition rate of exposed individuals to the infected class

1/3

1/3

[36]

   \(\delta _I(t)\)

\(\delta _{I0}\)

Diagnose rate of infected individuals before lockdown

0.10(0.02)

0.19(0.05)

Estimated

\(\delta _{Ib}\)

Diagnose rate of infected individuals after lockdown

–

0.02(0.01)

Estimated

   \(\delta _q(t)\)

\(\delta _{q0}\)

Diagnose rate of quarantined individuals before lockdown

0.23(0.02)

0.27(0.08)

Estimated

\(\delta _{qb}\)

Diagnose rate of quarantined individuals after lockdown

–

0.19(0.05)

Estimated

   \(\gamma _I\)

Recovery rate of infected individuals

0.04(0.01)

0.11(0.06)

Estimated

   \(\gamma _H\)

Recovery rate of confirmed and isolated infections

0.12(0.0003)

0.12(0.005)

Estimated

Variable

   S

Susceptible population

\(1.70\times 10^6\)

\(1.29\times 10^7\)

[33]

   E

Exposed population

36.19(15.73)

16.41(7.61)

Estimated

   I

Infected population

18.31(2.94)

1.03(0.27)

Estimated

   \(S_q\)

Quarantined susceptible population

0

0

Data

   \(E_q\)

Quarantined exposed population

0

0

Data

   H

Confirmed and isolated population

2

1

Data

   R

Recovered population

0

0

Data