Table 2 Description and source of parameters in the age-specific model

β_ii ^*

Transmission relative rate among age group i

Individuals^-1·days^-1

–

 ≥ 0

Curve fitting

β_ij ^*

Transmission relative rate from age group i to j

Individuals^-1·days^-1

–

 ≥ 0

Curve fitting

β_ji ^*

Transmission relative rate from age group j to i

Individuals^-1·days^-1

–

 ≥ 0

Curve fitting

β_jj ^*

Transmission relative rate among age group i

Individuals^-1·days^-1

–

 ≥ 0

Curve fitting

κ

Relative transmissibility rate of asymptomatic to symptomatic individuals

1

0.65

0–1

[12, 21, 22]

p

Proportion of the asymptomatic

1

0.36

0.016–0.78

[23, 24]

ω

Incubation relative rate

Days^-1

0.2

0.05556–0.5

[20, 25,26,27]

ω'

Latent relative rate

Days^-1

0.2

0.05556–0.5

[20, 25,26,27]

γ

Recovered/Removed rate of the infectious

Days^-1

0.2

0.1111–0.3333

[27,28,29,30,31]

γ'

Recovered/Removed rate of the asymptomatic

Days^-1

0.1

0.04762–1

[32]

f_i

Fatality of the disease of age group i

1

–

0–1

Analysis of data

δ

Vaccination rate

Days^-1

–

0–1

Assumption

φ

Immune relative rate

1

–

0–1

[33,34,35,36,37]

λ

Vaccine efficacy

1

–

0–1

[38,39,40,41,42,43,44,45,46,47,48,49,50]

θ

Proportion of herd immunity

1

0

0–1

Assumption

x

Decreasing proportion of vaccine efficacy against susceptibility

1

0.6

0–1

[18]

y

Decreasing proportion of vaccine efficacy against infectivity

1

0.6

0–1

[18]

z

Decreasing proportion of vaccine efficacy against pathogenicity

1

0.33

0–1

[18]