Fig. 1

Schematic diagrams illustrate the construction of the Bootstrap samples using Ensemble Method 1 (a) and Ensemble Method 2 (b). Suppose we have I models under consideration. Given the training data, let \( {\hat{\varTheta}}_i \) denote the set of estimated parameters and \( {f}_i\left(t,{\hat{\varTheta}}_i\right) \) denote the estimated mean incident curve, for the i-th model. Based on the quality of the model fit measured by the MSE or criteria such as AIC, we compute the weight w_i for the i-th model, i = 1, ..., I, where ∑w_i = 1. For Method 1, we generate a random variable y_i from Poisson distribution with mean \( {f}_{ens}\left({t}_j\right)=\sum \limits_{i=1}^I{w}_i{f}_i\left(t,{\hat{\Theta}}_i\right) \) to generate a bootstrap sample. In contrast, to generate the Bootstrap samples based on Method 2, we assume that at each time point the epidemic follows the i-th model with probability w_i