Table 2.
Summary of the numerical results for the longer cut-off times. Here, the values of T are 9 for θ1, 6 for θ2 and 7 for θ3 such that T is near the end of the epidemic process (also see figure 8). Method 3 yields accurate estimates without requiring knowledge of the size of the susceptible population n. Values in italics indicate the results corresponding to the best performing method.
|
β |
γ |
ρ | |||||||
|---|---|---|---|---|---|---|---|---|---|
| n | statistics | Method 1 | Method 2 | Method 3 | Method 1 | Method 2 | Method 3 | Method 3 | |
| β = 2 | 104 | Avg. | 2.0067 | 2.0067 | 2.0032 | 0.5002 | 0.5002 | 0.4980 | 0.0492 |
| (MSE) | (0.00046) | (0.00046) | (0.00082) | (0.00002) | (0.00002) | (0.00004) | (0.00001) | ||
| γ = 0.5 | 103 | Avg. | 2.0033 | 2.0033 | 1.9868 | 0.4996 | 0.4997 | 0.4974 | 0.0521 |
| (MSE) | (0.00334) | (0.00334) | (0.00883) | (0.00024) | (0.00024) | (0.00028) | (0.00014) | ||
| ρ = 0.05 | 102 | Avg. | 2.0433 | 2.0432 | 1.8890 | 0.5055 | 0.5055 | 0.4950 | 0.0636 |
| (MSE) | (0.04238) | (0.04236) | (0.07655) | (0.07502) | (0.00284) | (0.00230) | (0.00178) | ||
| β = 2 | 104 | Avg. | 2.0026 | 2.0007 | 2.0000 | 1.0003 | 0.9999 | 1.0002 | 0.0501 |
| (MSE) | (0.00046) | (0.00044) | (0.00101) | (0.00012) | (0.00013) | (0.00013) | (0.00001) | ||
| γ = 1 | 103 | Avg. | 1.9942 | 1.9942 | 2.0027 | 0.9961 | 0.9960 | 0.9963 | 0.0505 |
| (MSE) | (0.00489) | (0.00489) | (0.01151) | (0.00107) | (0.00108) | (0.00172) | (0.00015) | ||
| ρ = 0.05 | 102 | Avg. | 2.0002 | 2.0005 | 1.8997 | 1.0425 | 1.0431 | 1.0056 | 0.0702 |
| (MSE) | (0.06295) | (0.0628) | (0.14231) | (0.02772) | (0.02748) | (0.03915) | (0.00402) | ||
| β = 1.5 | 104 | Avg | 1.5003 | 1.5003 | 1.5016 | 0.9992 | 0.9993 | 1.0024 | 0.0497 |
| (MSE) | (0.00037) | (0.00037) | (0.00078) | (0.00018) | (0.00018) | (0.00022) | (0.00002) | ||
| γ = 1 | 103 | Avg. | 1.4940 | 1.4941 | 1.4911 | 1.0094 | 1.0092 | 0.9957 | 0.0493 |
| (MSE) | (0.00362) | (0.00362) | (0.00615) | (0.00180) | (0.00177) | (0.00245) | (0.00014) | ||
| ρ = 0.05 | 102 | Avg. | 1.4126 | 1.4127 | 1.3362 | 1.1211 | 1.1199 | 1.0090 | 0.1087 |
| (MSE) | (0.0796) | (0.07962) | (0.15705) | (0.10955) | (0.10715) | (0.04502) | (0.01313) | ||