Table 2 Resulting estimates for a range of scenarios varying delta-to-variant cross-immunity (\(\epsilon\)), preimmunized populations proportion (a) and generation time (GT). The table displays \(\hat{R}_{\textrm{omicron}}/\hat{R}_{\textrm{delta}}\) values (weighted mean across regions). Further minimum and maximum values for variance across regions as well as means of the loss function (6), both weighted by population size, are outlined at the bottom of each generation-time associated scenario .

GT (delta 5, omicron 3) days

 \(\epsilon\) = 0.25

1.589

1.591

1.595

1.607

 \(\epsilon\) = 0.5

1.592

1.565

1.594

1.608

\(\epsilon\) = 0.75

1.590

1.590

1.593

1.603

 \(\epsilon\) = 1.0

1.588

1.587

1.585

1.580

 Variance

\(\sigma ^2 = [0.006-0.022]\)

 Loss

\(L = [1.26-1.85]\)

GT (delta 5, omicron 3.5) days

 \(\epsilon\) = 0.25

1.705

1.707

1.711

1.724

 \(\epsilon\) = 0.5

1.704

1.706

1.711

1.725

 \(\epsilon\) = 0.75

1.705

1.705

1.707

1.720

 \(\epsilon\) = 1.0

1.704

1.704

1.702

1.696

 Variance

\(\sigma ^2 = [0.008-0.009]\)

 Loss

\(L = [1.39-1.42]\)

GT (delta 5, omicron 4) days

 \(\epsilon\) = 0.25

1.823

1.824

1.827

1.838

 \(\epsilon\) = 0.5

1.823

1.823

1.826

1.838

 \(\epsilon\) = 0.75

1.823

1.823

1.824

1.835

 \(\epsilon\) = 1.0

1.823

1.822

1.820

1.814

 Variance

\(\sigma ^2 = [0.012-0.013]\)

 Loss

\(L = [1.48-1.54]\)

GT (delta 5, omicron 6) days

 \(\epsilon\) = 0.25

2.317

2.321

2.328

2.344

 \(\epsilon\) = 0.5

2.317

2.319

2.325

2.343

 \(\epsilon\) = 0.75

2.317

2.324

2.340

2.340

 \(\epsilon\) = 1.0

2.316

2.315

2.312

2.307

 Variance

\(\sigma ^2 = [0.018-0.019]\)

 Loss

\(L = [1.65-1.73]\)