Table 1.
Constraints and initial–final values of the inversion algorithm.
| Case | Variable → |
α (day−1) |
β1 (day−1) |
β2 (day−1) |
β3 (day−1) |
ϵ−1 (day) |
γ−1 (day) |
E(0) |
I∞ (M) L (day) D∞ |
|---|---|---|---|---|---|---|---|---|---|
| Lower bound | 10−5 | 0.5 | 10−6 | 10−6 | 3 | 3 | 103 | ||
| Upper bound | 10−1 | 0.9 | 103 | 103 | 6 | 6 | 2 × 105 | ||
| Initial value | 0.006 | 0.75 | 0.5 | 0.5 | 5 | 5 | 104/105 | ||
| 1.1 | Final value | 0.00144 | 0.75 | 0.34 | 0.2 | 4.25 | 4.02 | 11,460 | 2.69 |
| 1.2 | IFR | 0.57% | 262–Nov 11 | ||||||
| 1.3 | R0 | 3.00 | 1.36 | 0.80 | 15,652 | ||||
| 2.1 | Final value (*) | 0.0051 | 0.702 | 0.29 | 0.132 | 5.45 | 4.75 | 9,460 | 1.33 |
| 2.2 | IFR | 2.37 % | 264–Nov 13 | ||||||
| 2.3 | R0 | 3.25 | 1.34 | 0.61 | 31,934 | ||||
| 3.1 | Final value (*) | 0.00142 | 0.75 | 0.57 | 0.395 | 5.79 | 3.31 | 99,500 | 6.49 |
| 3.2 | IFR | 0.47% | 236–Oct 16 | ||||||
| 3.3 | R0 | 2.47 | 1.87 | 1.30 | 30,544 | ||||
| Lower bound | 10−5 | 0.5 | 10−6 | 10−6 | 2 | 2 | 103 | ||
| Upper bound | 10−1 | 0.9 | 103 | 103 | 20 | 20 | 2 × 105 | ||
| Initial value | 0.006 | 0.75 | 0.5 | 0.2 | 5/15 | 5/15 | 103/105 | ||
| 4.1 | Final value | 0.00436 | 0.59 | 0.29 | 0.094 | 6.10 | 5.28 | 8,800 | 0.69 |
| 4.2 | IFR | 2.25% | 239–Oct 19 | ||||||
| 4.3 | R0 | 3.04 | 1.50 | 0.48 | 15,652 | ||||
| 5.1 | Final value | 0.0011 | 0.81 | 0.33 | 0.03 | 13 | 5.53 | 91,900 | 2.49 |
| 5.2 | IFR | 0.60% | 247–Oct 27 | ||||||
| 5.3 | R0 | 4.45 | 1.81 | 0.16 | 15,345 | ||||
| 6.1 | Final value | 0.0073 | 0.755 | 0.23 | 0.125 | 4.87 | 5.11 | 170 | 0.44 |
| 6.2 | IFR | 3.59% | 269–Nov 18 | ||||||
| 6.3 | R0 | 3.72 | 1.13 | 0.61 | 16,401 | ||||
| 7.1 | Final value | 0.09 | 0.9 | 0.28 | 0.175 | 2.99 | 6.15 | 32 | 0.04 |
| 7.2 | IFR | 35.62% | 212–Sep 22 | ||||||
| 7.3 | R0 | 3.56 | 1.11 | 0.69 | 16,112 | ||||
| 8.1 | Final value | 0.00674 | 0.83 | 0.006 | 0.01 | 12.79 | 14.93 | 1,270 | 0.18 |
| 8.2 | IFR | 9.15% | 272–Nov 21 | ||||||
| 8.3 | R0 | 11.2 | 0.08 | 0.13 | 16,681 | ||||
| 9.1 | Final value | 0.0055 | 0.506 | 0.044 | 0.01 | 11.08 | 14.97 | 8,960 | 0.22 |
| 9.2 | IFR | 7.60% | 268–Nov 17 | ||||||
| 9.3 | R0 | 7.00 | 0.61 | 0.14 | 16,653 |
Several cases that honor the data. I(0) = 1000, except Case 7, with I(0) = 1.
(*) Doubling the number of casualties.
The values of β refer to the periods (in days): [1, 22], [22, 35], and [35, ∞] (in days).
I∞ (in millions) indicates the total number of infected individuals at the end of the epidemic.
L denotes the day of the last infected individual, obtained when I < 1.
D∞ is the death toll at the end of the epidemic.
Read et al. (18) report the mean values ϵ−1 = 4 days and γ−1 = 3.6 days.
Lauer et al. (19) report ϵ−1 = 5.1 days.
Ferguson et al. (20) estimate an average IFR = 0.9%.