Unexpected parameter ranges of the 2009 A(H1N1) epidemic for Istanbul and the Netherlands

The data of the 2009 A(H1N1) epidemic in Istanbul, Turkey is unique in terms of the collected data, which include not only the hospitalization but also the fatality information recorded during the pandemic. The analysis of this data displayed an unexpected time shift between the hospital referrals and fatalities. This time shift, which does not conform to the SIR and SEIR models, was explained by multi-stage SIR and SEIR models [21]. In this study we prove that the delay for these models is half of the infectious period within a quadratic approximation, and we determine the epidemic parameters $R_0$, $T$ and $I_0$ of the 2009 A(H1N1) Istanbul and Netherlands epidemics.These epidemic parameters were estimated by comparing the normalized cumulative fatality data with the solutions of the SIR model. Two different error criteria, the $L_2$ norms of the error over the whole observation period and over the initial portion of the data, were used in order to obtain the best-fitting models. It was observed that, with respect to both criteria, the parameters of "good" models were agglomerated along a line in the $T$-$R_0$ plane, instead of being scattered uniformly around a "best" model. As this fact indicates the existence of a nearly invariant quantity, interval estimates for the parameters were given. As the initial phase of the epidemics were less influenced by the effects of medical interventions, the error norm based on the initial portion of the data was preferred. However, the presented parameter ranges are well out of the range for the usual influenza epidemic parameter values. To confirm our observations on the Istanbul data, the same error criteria were also used for the 2009 A(H1N1) epidemic for the Netherlands, which has a similar population density as in Istanbul. As in the Istanbul case, the parameter ranges do not match the usual influenza epidemic parameter values.