Table 1.
Model parameters, description, source and the basic reproduction number in China, 2015–2018
| Parameters | Description | Source | 2015 | 2016 | 2017 | 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 |
| IN(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 [17–19] | 0.9387 | 0.7098 | 1.1188 | 0.8429 |
| P1 in [0.01,1] | Proportion of IN | 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 IN | 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 |
*(0) denotes the initial number of different compartments
**: The proportions of EV71, CV-A16 and other Enteroviruses are 45, 25 and 30% [20]. Therefore, the proportion of I2 (No EV71 or CVA16) and I3 (EV71 + CVA16) is 30 and 70% in 2015, 2016. While the proportion of I2 (No EV71) and I3 (EV71) is 55 and 45% in 2017 and 2018 due to the launch of EV71 vaccine
***: MSS minimum sum of square