Table 1 Parameter estimates for the COVID-19 epidemic in Kazakhstan and Pakistan

β

Probability of transmission per contact

0.089

0.0713

Estimated

µ

Release rate of quarantined uninfected contact

1/14

1/14

[19]

c₀

Contact rate at the initial time

20.3

23.9

Estimate

c₁(c₃)

Minimum contact rate in stage I (III)

6.8(19.1)

12(9)

Estimated

c₂

Maximum contact rate in stage II

16.5

18.3

Estimated

\(r_{1}^{c} \left( {r_{2}^{c} ,r_{3}^{c} } \right)\)

Exponential rate of contact rate under stage I (II, III)

0.01(0.02, 0.2)

0.08(0.04,0.25)

Estimated

q₀

Quarantined rate of exposed individuals at the initial time

0.009

0.005

Estimated

q₁(q₃)

Maximum quarantined rate of exposed individuals in stage I (III)

0.8(0.62)

0.5(0.6)

Estimated

q₂

Minimum quarantined rate of exposed individuals in stage II

0.2

0.25

Estimated

\(r_{1}^{q} \left( {r_{2}^{q} ,r_{3}^{q} } \right)\)

Exponential rate of quarantined rate of exposed individuals under stage I (II, III)

0.08(0.01,0.04)

0.05(0.04,0.1)

Estimated

b

Detection rate of the quarantined suspected class

0.2

0.2

Estimated

P

Transition rate of quarantined suspected class to the confirmed class

0.9

0.9

Estimated

δ

Transition rate of exposed individuals to the infected class

1/3.42

1/3.42

[23]

τ₀

Initial diagnosis rate at initial time

0.0214

0.07

Estimated

τ₁(τ₃)

Fastest diagnosis rate in stage I (III)

0.8(0.43)

0.6(0.3)

Estimated

τ₂

Fastest diagnosis rate in stage II

0.1

0.12

Estimated

\(r_{1}^{\tau } \left( {r_{2}^{\tau } ,r_{3}^{\tau } } \right)\)

Exponential rate of diagnosis rate in stage I (II, III)

0.2(0.1,0.1)

0.2(0.09,0.001)

Estimated

γ_I

Recovery rate of infected individuals

0.28

0.228

Estimated

d_I

Disease-induced death rate of infected individuals

0.00002

0.00005

Estimated

γ_C

Recovery rate of confirmed individuals

0.08

0.06

Estimated

d_C

Disease-induced death rate of confirmed individuals

0.000145

0.000366

Estimated

t₀(t₁)

The starting time of stage II(III)

71(193)

113(170)

Data

N (0)

Initial total population

1.9 × 10⁷

2.21 × 10⁸

Data

S(0)

Initial susceptible population

1.792 × 10⁷

2.197 × 10⁸

Estimated

E(0)

Initial exposed population

2750

1950

Estimated

I(0)

Initial infected population

1220

1120

Estimated

S_q(0)

Initial quarantined susceptible population

4976

10,707

Estimated

Q(0)

Initial quarantined suspected population

420

180

Estimated

C(0)

Initial confirmed population

94,945

6521

Data

R(o)

Initial recovered population

961,806

1.263 × 10⁶

Data