Author Correction: Development of a model-inference system for estimating epidemiological characteristics of SARS-CoV-2 variants of concern

Correction to: Nature Communications 10.1038/s41467-021-25913-9, published online 22 September 2021.

The original version of this article contained errors in the Supplementary Information, equations S3 and S5.

Equation S3, line 4, was missing a term. The original read:

$$\left\{\begin{array}{c}\hfill \frac{dS}{dt}=\frac{R}{L}-\frac{{b_t{e}_t{m}_t\beta }_{t}IS}{N}-\epsilon -v_1\left(t\right)-v_2\left(t\right)\hfill \\ \hfill \frac{dE}{dt}=\frac{{b_t{e}_t{m}_t\beta }_{t}IS}{N}-\frac{E}{Z}+\epsilon \hfill \\ \hfill \frac{dI}{dt}=\frac{E}{Z}-\frac{I}{D}\hfill \\ \hfill \frac{dR}{dt}=\frac{I}{D}+v_1\left(t\right)+v_2\left(t\right)\hfill \end{array}\right)$$

This has been corrected to:

$$\left\{\begin{array}{c}\hfill \frac{dS}{dt}=\frac{R}{L}-\frac{{b_t{e}_t{m}_t\beta }_{t}IS}{N}-\epsilon -v_1\left(t\right)-v_2\left(t\right)\hfill \\ \hfill \frac{dE}{dt}=\frac{{b_t{e}_t{m}_t\beta }_{t}IS}{N}-\frac{E}{Z}+\epsilon \hfill \\ \hfill \frac{dI}{dt}=\frac{E}{Z}-\frac{I}{D}\hfill \\ \hfill \frac{dR}{dt}=\frac{I}{D}-\frac{R}{L}+v_1\left(t\right)+v_2\left(t\right)\hfill \end{array}\right)$$

Equation S5, line 2 was incorrectly written; the original read:

$$\left\{\begin{array}{c}\hfill \frac{{dS}_i^A}{dt}=\frac{R_i^A}{L_i^A}-\sum _j{b_t{e}_t{m}_{t}c}_{ij}\sum _a\frac{{\beta }_j^{Aa}{S}_j^A{I}_j^a}{N^a}-{\epsilon }_i-v_{i,1}^A\left(t\right)-v_{i,2}^A\left(t\right)\hfill \\ \hfill \frac{{dE}_i^A}{dt}=\sum _j{b}_t{e}_t{m}_t\sum _a\frac{{\beta }_j^{Aa}{S}_j^A{I}_j^a}{N^a}-\frac{E_i^A}{Z_i^A}+{\epsilon }_i\hfill \\ \hfill \frac{{dI}_i^A}{dt}=\frac{E_i^A}{Z_i^A}-\frac{I_i^A}{D_i^A}\hfill \\ \hfill \frac{{dR}_i^A}{dt}=\frac{I_i^A}{D_i^A}-\frac{R_i^A}{L_i^A}+v_{i,1}^A\left(t\right)+v_{i,2}^A\left(t\right)\hfill \end{array}\right)$$

This has been corrected to:

$$\left\{\begin{array}{c}\hfill \frac{{dS}_i^A}{dt}=\frac{R_i^A}{L_i^A}-\sum _j{b_t{e}_t{m}_{t}c}_{ij}\sum _a\frac{{\beta }_j^{Aa}{S}_j^A{I}_j^a}{N^a}-{\epsilon }_i-v_{i,1}^A\left(t\right)-v_{i,2}^A\left(t\right)\hfill \\ \hfill \frac{{dE}_i^A}{dt}=b_t{e}_t{m}_t\sum _a\frac{{\beta }_i^{Aa}{S}_i^A{I}_i^a}{N^a}-\frac{E_i^A}{Z_i^A}+{\epsilon }_i\hfill \\ \hfill \frac{{dI}_i^A}{dt}=\frac{E_i^A}{Z_i^A}-\frac{I_i^A}{D_i^A}\hfill \\ \hfill \frac{{dR}_i^A}{dt}=\frac{I_i^A}{D_i^A}-\frac{R_i^A}{L_i^A}+v_{i,1}^A\left(t\right)+v_{i,2}^A\left(t\right)\hfill \end{array}\right)$$

These corrections have been made to the Supplementary Information pdf.

Supplementary information

The online version contains supplementary material available at 10.1038/s41467-021-27703-9.