Model Selection and Evaluation Based on Emerging Infectious Disease Data Sets including A/H1N1 and Ebola

Liu, Wendi; Tang, Sanyi; Xiao, Yanni

In particular, for West Africa, the selection results are given in the second line of Table 3 and Figure 3 (a). It follows from Table 3 = 1 here). To further confirm the model selection results for West Africa, the AIC values are calculated and given by 5200, 49500, 1872800, and 5400 for models 1 , 2 , 3 , and 4 , respectively. The AIC values for both Logistic model and Richards model further indicate that these two models are the best. In Figure 3(a) , the numbers of four models which have been selected in the last 2000 runs are 1168, 0, 0, and 832 for models 1 , 2 , 3 , and 4 , respectively. It is interesting to notice that the probability for Logistic model is the biggest one and Richards model is the second one, which further confirms that Logistic model is the best model for West Africa data set. In Figure 4 Table 4 and basic reproduction number 0 and turning point based on West Africa data are shown in the second line of Table 5 . The mean estimated generation interval = 12 days given by Chowell and Nishiura [12] is used to calculate the basic reproduction number 0 . Based on Logistic model 0 is estimated to be 1.3522 (95% CI (1.3506, 1.3537)) and the variation in 0 with different generation intervals is shown in Figure 5 For Guinea, the selection results are given in the third line of Table 3 and Figure 3 (b). From Table 3 , Bayes factorŝ 12 ,̂1 3 are infinite (>100 naturally), which confirm that there exists decisive evidence for model 1 (i.e., Logistic model) compared with models 2 and 3 . Moreover, both 1 <̂1 4 = 1.25 < 3 and 1/3 <̂4 1 = 0.8 < 1 mean that the selection of the Logistic model and the Richards model is uniform and alternating. The AIC values are 1991, 3427, 18476, and 1998 for models 1 , 2 , 3 , and 4 , respectively. The AIC values for both Logistic model and Richards model further indicate that these two models are the best for us to fit Guinea data. In Figure 3 The curves represent the fitting to the data for four models, respectively. The grey areas are the 95% confidence interval of each curves. Cyan curve represents Logistic model; blue curve represents Gompertz model; red curve represents Rosenzweig model; black curve represents Richards model. 1028, 0, 0, and 972 for models 1 , 2 , 3 , and 4 , respectively, which further shows that the Logistic model and the Richards model are the best model for Guinea data set, as shown In Figure 4 (b). Compared with the selection results for West Africa we conclude that the outbreak pattern of West Africa follows Guinea.