Committed toProf. Dr. Dr.h.c. Herbert Zeitler at the celebration of his eightieth birthdayProf. Dr. Dr.h.c. Helmut Karzel at the party of his seventy fifth birthdayProf. Dr. Dr.h.c Grozio Stanilov at the social gathering of his seventieth birthdayVarna (Bulgaria), September 5-10, 2003
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4 Discussion The ﬁndings in this study promote two Gaussian–type of regression models that assess inﬂuenza outbreak trends. Unlike the well–known cyclical Serﬂing model, 44 M. Nu˜ no and M. Pagano Table 2. Fit results implementing Model 1 and Model 2 for ILI data that is grouped according to the subtype–speciﬁc strains (H1N1, H3N2, and B) dominating in each season. Note that a1 describes the model baseline, a2 and a3 the intensity of peaks 1 and 2, with peak times at b2 and b3 , and corresponding duration given by c1 and c2 .
4. Residual plots for Model 1 (a) and Model 2 (b) for French ILI data from 19852005. Solid, dotted and boxed notches denote the residuals corresponding to H3N2, H1N1 and B type strains. We ﬁnd strong evidence that Model 2 ﬁts the data better than Model 1. The goodness of ﬁt of each of these models was assessed by analyzing their residuals A Model for Characterizing Annual Flu Cases 43 for each of the years ﬁtted. We illustrate the goodness of ﬁt of these model for the 1990-1991 ﬂu season. Figure 3 illustrates the ﬁts obtained with Model 2 (top–panel), Model 1 (bottom–panel) for these ﬁts.
Network simulation is particularly useful when we have only a little knowledge about the investigated disease. For example, Meyers et al.  used three different networks, urban, power law, and Poisson, to study how contact patterns influence SARS transmission and found that in the same network settings, different contact patterns yield totally different epidemiological outcomes. 3 Incorporating Geographical Contacts into SNA The studies of SNA in epidemiology primarily use only personal contacts to construct social networks.
6th International conference on geometry and applications