How does the outbreak of 2019-nCoV spread in mainland China? A retrospective analysis of the dynamic transmission routes

Xiandeng Jiang; Le Chang; Yanlin Shi

) is the matrix of kernel weights calculated based on the bandwidth b i , i = 1, . . . , N , and K b i (τ s − τ ) = K( τs−τ b i )/b i with τ s defined as a scaled time s T −1 . We use the Epanechnikov kernel K(x) = 0.75(1 − x 2 ) + and a unified bandwidth for each i (b i ≡ b) to avoid a large number of tuning parameters. The coefficients β i,j,t denotes the ij th entry of the Granger causality matrix B t , and λ is the tuning parameter that aims to shrink insignificant β i,j,t to zero and thus controls the sparsity of B t . Another essential feature of our proposed model is that the adaptive weights w i,j,t are employed to penalize β i,j,t differently in the lasso (L1) penalty [39, 40] . The choice of weights w i,j,t takes account of the prior knowledge about the transmissions and can be specified by the users. In this study, we consider w i,j,t as the reciprocal of the accumulated confirmed in province i on day t − 1. That is, the growth rate of a province with a smaller accumulated confirmed cases is less likely to influence the growth rates of others, and thus, more likely to be shrunk to zero. The final sparsity structure of B t is still data-driven.