Table 1 Summary of model parameter values

R _0max, R _0min

Defining the range of the basic reproductive number

See Ref. [25]

The simulations were performed with the parameters R _0max set ranging from 2.40 to 1.20 and R _0min set ranging from R _0max to 0.80

Temp

Mean temperature

See Additional file 4: Table S3

Taiwan Central Weather Bureau (http://www.cwb.gov.tw/V7/climate/monthlyData/mD.htm)

RH

Mean relative humidity

See Additional file 4: Table S3

Taiwan Central Weather Bureau (http://www.cwb.gov.tw/V7/climate/monthlyData/mD.htm)

AP

Atmospheric pressure

See Additional file 4: Table S3

Taiwan Central Weather Bureau (http://www.cwb.gov.tw/V7/climate/monthlyData/mD.htm)

RF

Relative fitness

Estimated

In terms of transmissibility, representing the strain fitness of a clade as compared with the reference clade

CC

Competition cost

Estimated

In terms of transmissibility, addressing the reduction in strain fitness associated with the interaction between two clades

λ[i]

Force of infection to age group i

Estimated

θ

Transition rate from exposed state to infective state

1/day

Probability of the exposed to become infective per unit of time; assuming latent period around 1 day [26]

α

Recovery rate

0.2/day

Probability of the infectives to become recovered and immune per unit of time; assuming infectious period around 5 days [26]

ν

Proportion of susceptibles becoming immune 15 days after vaccination

See Additional file 5: Table S4, for the progress of annual vaccination program

As the simulated clades were predominantly reported as low reactors to the contemporaneous annual vaccine strains, the model assumed 50% of the vaccinees were protected from infection of the contemporaneous seasonal strains [28, 29]. The assumption was relaxed in the process of assessing the impacts of the annual vaccination program on the 2008–2009 seasonal influenza epidemic (see the “Results” section)