1 IM response accuracy for the fixed virality value (without data assimilation) Number of responses Fix $$\Delta t$$, $$n$$. Calculate $$n$$. values of the predicted parameter (predicted parameter should be measured and be saved). Calculate $$MAE\left( n \right)$$, $$MAPE\left( n \right)$$. Calculate mean value of the metrics of accuracy er $$p$$ IMs.
2 IM response accuracy with data assimilation Number of responses Fix $$T, n$$ (in Fig. 7$$n = 9$$). A series of forecasts for $$n$$. iterations is carried out: a) at the time of IM generation; b) after each batch from the set $$b \in A$$. batch of assimilation (with the adjustment of the model parameters from the obtained data). Figure 7 shows assimilation of three batches. Additionally, batches of evaluation $$b \in C$$. must be collected to ensure verification predicted values for all $$\left| A \right| + 1$$ forecasts. The averaged values of the forecast accuracy metrics for different assimilation batch are calculated.
3 Impact of the batches’ frequency on the forecast accuracy Number of responses Calculate a series of averaged values of forecast accuracy metrics using the method (2) with a fixed length of the forecast period $$T$$, varying the length of the time interval $$l$$ between batches
4 A number of batches required to achieve desired accuracy Number of batches Fix the desired accuracy $$\varepsilon$$, $$p$$, $$\Delta t$$, $$l$$, $$T$$, the maximum number of batches of evaluation $$A_{ \hbox{max} }$$. The assimilation of the batch is performed while the batch accuracy is less than $$\varepsilon$$ or the maximum number of batches is exceeded $$A_{ \hbox{max} }$$. Accuracy assessment is made by the method (3)
5 Accuracy of the aggregated dynamics reproduction for the period Number of responses Fix, $$p$$, $$l$$, $$T$$. The response is predicted for $$p$$ IMs for the period $$T$$. The numbers of responses in the model and the actual number of responses are measured. The value of $$\lambda$$ is calculated by the Eq. (6). If$$\lambda < \lambda_{0.05}^{ '} = 1.36$$, then the null hypothesis of sample homogeneity is accepted
6 Earliness Forecast time Fix $$\Delta t$$, $$l, T$$, the number batches of assimilation $$k$$. For the moment of IMs generation ($$t = 0)$$ and for each assimilation batch, the forecast is made for the period $$T - l \cdot b$$. The time of the forecast calculation $$\tau_{0} , \ldots ,\tau_{k}$$, is measured. The series of values for the forecast earliness $$z_{0} , \ldots ,z_{k}$$ is calculated using Eqs. (7, 8)