A Susceptible-Exposed-Infected-Removed (Seir) Model For The 2009-2010 A/H1N1 Epidemic In Istanbul

A/H1N1 epidemic data from Istanbul, Turkey during the period June 2009-February 2010 is analyzed with SEIR (Susceptible-Exposed-Infected-Removed) model. The data consist of the daily adult hospitalization numbers and fatalities recorded in various state hospitals serving an adult population of about 1.5-2 million. June 2009-August 2009 period corresponds to the initial stage of the epidemic where the hospitalization rate is nearly %100 and it is excluded from further consideration. The analysis covers the September 2009-February 2010 period, the total number of hospitalizations and fatalities being respectively 869 and 46. It is shown that the maximum correlation between the number of fatalities and hospitalizations occur with a time shift of 9 days and the proportionality constant is {\delta}=0.0537. The SEIR epidemic model is applied to the data by back-shifting the number of fatalities. The determination of the best fitting model is based on the L2 norms of errors between the model and the data and the errors are around %10 and %2.6 for the number of hospitalizations and fatalities, respectively. The parameters in the model are I0, {\eta}, {\epsilon} and {\beta}, where I0 is the percentage of people infected initially, {\eta} and {\epsilon} are related to the inverses of the infection and incubation periods and {\beta}/{\eta} is the representative of the basic reproduction number. These parameters are determined as {\eta}=0.09 (1/{\eta} =11.11days), I0=10^-7.4, {\epsilon}=0.32 (1/{\epsilon} =3.125 days), {\beta}=0.585, {\beta}/{\eta}=6.5.