It is also interesting to note that for our set of parameter values used in Figs. 4, 5, the effective reproduction number with vaccine only (see Equations 5-6) has almost the same value as R 0 , to the fourth decimal digit. One explanation for this apparent lack of impact of vaccination during the 2004-2005 flu season, as indicated by the value of R V , is that the vaccination data we used is only for groups 1 (age 0-2) and 7 (age >64). In the formula for R V , or more precisely for R ij V 0 in Equation (7), c ij 2 is the daily contact frequency between groups i and j. The contact frequencies of groups 1 and 7 [Additional file 1: Table A2 ] are substantially smaller than the contact frequencies of the other groups, with the exception of within-group contacts and contact between groups 1 and 2 (age 3-5) in daycare facilities. Therefore, the relative impact of targeting these two groups for vaccination was weakened by their relative inactivity, thus giving further evidence of the lack of impact of vaccinating the very young and the very old on the overall transmissibility of the disease in the community. However, simulation with the same parameter values as in Fig. 3 except assuming no vaccination in the young children and elderly age groups, i.e., υ 1 (t) = υ 7 (t) = 0, and everything else the same produces Fig. 5 , where the result indicates that the impact of no vaccination (red curves) would still be significant, resulting in nearly 4-fold increase in mortality of elderly and 2-fold increase in mortality of adults. Therefore, the impact of vaccination on the disease incidence sometimes might not be fully revealed in the change (or the lack thereof) in the effective reproduction number with intervention but could still be substantial, since it is a simple mathematical property that distinctly different (next generation) matrices may have similar eigenvalues.