Table 2. Cross-protection parameter estimates by province.
| Province | |||
|---|---|---|---|
| Beijing | 21 (9, 25) | 1.00 (0.65, 1.00) | 21.00 (8.25, 25.00) |
| Tianjin | 22 (2, 31) | 1.00 (0.40, 1.00) | 22.00 (1.80, 31.00) |
| Hebei | 4 (3, 4) | 1.00 (0.80, 1.00) | 4.00 (2.85, 3.80) |
| Shanxi | 0 (0, 52) | 0.05 (0.00, 1.00) | 0.00 (0.00, 5.20) |
| Inner Mongolia | 2 (0, 52) | 0.05 (0.00, 1.00) | 0.10 (0.00, 33.80) |
| Liaoning | 4 (3, 8) | 1.00 (0.70, 1.00) | 4.00 (3.00, 8.00) |
| Jilin | 2 (0, 52) | 0.95 (0.00, 1.00) | 1.90 (0.00, 3.20) |
| Heilongjiang | 52 (0, 52) | 0.10 (0.00, 1.00) | 5.20 (0.00, 13.00) |
| Shanghai | 9 (6, 18) | 1.00 (0.60, 1.00) | 9.00 (5.20, 18.00) |
| Jiangsu | 8 (1, 14) | 0.40 (0.10, 1.00) | 3.20 (0.55, 7.65) |
| Zhejiang | 8 (3, 9) | 0.65 (0.40, 1.00) | 5.20 (2.55, 8.00) |
| Anhui | 9 (1, 16) | 0.30 (0.05, 1.00) | 2.70 (0.05, 7.65) |
| Fujian | 6 (3, 8) | 1.00 (0.80, 1.00) | 6.00 (3.00, 8.00) |
| Jiangxi | 0 (0, 52) | 0.05 (0.00, 1.00) | 0.00 (0.00, 4.50) |
| Shandong | 4 (3, 7) | 1.00 (0.65, 1.00) | 4.00 (2.25, 7.00) |
| Henan | 6 (4, 6) | 1.00 (0.60, 1.00) | 6.00 (3.00, 5.70) |
| Hubei | 2 (0, 52) | 1.00 (0.00, 1.00) | 2.00 (0.00, 9.00) |
| Hunan | 6 (5, 8) | 0.35 (0.15, 0.55) | 2.10 (0.90, 3.30) |
| Guangdong | 11 (11, 12) | 1.00 (1.00, 1.00) | 11.00 (11.00, 12.00) |
| Guangxi | 9 (8, 14) | 1.00 (0.95, 1.00) | 9.00 (8.00, 14.00) |
| Hainan | 0 (0, 52) | 0.05 (0.00, 1.00) | 0.00 (0.00, 3.25) |
| Chongqing | 3 (2, 52) | 1.00 (0.05, 1.00) | 3.00 (1.20, 6.90) |
| Sichuan | 6 (5, 8) | 1.00 (0.30, 1.00) | 6.00 (1.80, 8.00) |
| Guizhou | 52 (2, 52) | 0.15 (0.05, 1.00) | 7.80 (1.20, 15.60) |
| Yunnan | 26 (6, 32) | 0.20 (0.15, 0.55) | 5.20 (2.25, 7.80) |
| Tibet | 3 (2, 31) | 1.00 (0.40, 1.00) | 3.00 (1.40, 20.15) |
| Shaanxi | 1 (0, 52) | 0.75 (0.00, 1.00) | 0.75 (0.00, 1.50) |
| Gansu | 0 (0, 52) | 0.05 (0.00, 1.00) | 0.00 (0.00, 31.20) |
| Qinghai | 26 (0, 52) | 0.05 (0.00, 1.00) | 1.30 (0.00, 13.75) |
| Ningxia | 4 (1, 29) | 0.75 (0.20, 1.00) | 3.00 (0.40, 13.05) |
| Xinjiang | 52 (0, 52) | 0.15 (0.00, 1.00) | 7.80 (0.00, 52.00) |
| National Average | 9.95 (3.31, 23.40) | 0.68 (0.37, 0.96) | 6.77 (2.50, 10.03) |
δ is the proportion of those infected with one serotype who are cross-protected against infection from all other serotypes for a fixed duration of k time steps, and the product k ⋅ δ represents the average duration of cross-protection. 95% CIs for the individual parameters are derived from the profile likelihood using the χ2 distribution with 1 degree of freedom.