The age-dependent hospitalization rates and per contact transmission probability in the last four rows (in bold) in Table 2 were obtained by least-squared curve-fitting with the 2004-2005 Taiwan winter P&I (Pneumonia and Influenza) mortality data from October 9, 2004 to March 5, 2005 for age groups 6 (age 22-64) and 7 (>64) using MATLAB software. ν 7 (τ) and ν 1 (τ) are piecewise linear (by week) approximations of the respective weekly vaccination data for elderly (>64) and young children in Taiwan during this time period. To simply our data fitting, we first fitted the data by assuming the per contact transmission probability of the infectees in i th group are averaged, i.e., b ij ≡ b i (see next to the last row in bold in Table 2 ).