Table 1 Model parameters, description, source and the basic reproduction number in China, 2015–2018

S(0)*

Number of susceptible children under 5

Fixed [1]

95,920,000

96,490,000

98,290,000

94,386,870

V(0)

Vaccinated

Fixed [16]

0

0

0

5,110,000

E(0) in [500,5 ×10⁴]

Number of exposed under incubation periods

MSS [17]

3000

1800

2000

1200

I_N(0) in [500,5 ×10⁴]

Infectious but not hospitalized

MSS [17]

1000

1200

1800

800

I₂(0)

Infectious with pathogens other than EV71 or CVA16 / other than EV71

Calculated, 0.3/0.55 × reported cases in January/30**

577.5

795

1419

638

I₃(0)

Infectious with EV71-HFMD or CVA16-HFMD / EV71-HFMD

Calculated, 0.7/0.45 × reported cases in January/30**

1347.5

1855

1161

522

R(0)

Recovered

Assumed

0

0

0

0

α

Progression rate

Assumed

1

1

1

1

β in [0.01,50]

Transmission rate, Contact frequency × Infection efficiency

MSS [17,18,19]

0.9387

0.7098

1.1188

0.8429

P₁ in [0.01,1]

Proportion of I_N

MSS [17]

0.9627

0.9663

0.8644

0.9333

P₂

Proportion of I₂

Calculated, 0.3/0.55 × (1-P₁) **

0.0112

0.0101

0.0746

0.0367

P₃

Proportion of I₃

Calculated, 0.7/0.45 × (1-P₁) **

0.0261

0.0236

0.0610

0.0300

γ₁ in [0.1,1]

Recovery rate of I_N

MSS[18]

0.8932

0.6441

1.0721

0.7573

γ₂ in [0.1,1]

Recovery rate of I₂

MSS[18]

0.8852

0.7127

0.2619

0.3612

γ₃ in [0.1,1]

Recovery rate of I₃

MSS[18]

0.4583

0.5497

0.4907

0.5264

γ in [0.0001,1]

Relapse rate

MSS*** [17]

0.0125

0.0136

0.0064

0.0139

π

Birth rate

Fixed [1]

0.01207/365

0.01295/365

0.01243/365

0.01094/365

μ

Death rate of children under 5

Fixed [1]

0.0107/365

0.0102/365

0.00905/365

0.00832/365

v

The number of vaccinated people per day

Fixed [16]

0

0

14,000

24,000

VE

Vaccine efficacy

Fixed [12]

–

–

95%

95%

R₀

Basic reproductive number

Calculated

2.02

1.82

2.35

1.97