(4) A fraction of the infectives has no symptoms or only subclinical symptoms, and is classified as asymptomatic infectives with reduced infectivity [14] . migration rate of symptomatic infectives 0 θ immigration rate of the population 0 θ 1 immigration rate of symptomatic infectives 0 q quarantine rate of unvaccinated exposed individuals 0 q V quarantine rate of vaccinated exposed individuals 0 1-home withdrawal rate of untreated symptomatic infectives 0 1-1 home withdrawal rate of all "well" individuals 0 τ reduction in infectivity of unvaccinated pre-symptomatic infectives 0.4 τ 1 reduction in infectivity of asymptomatic infectives 0.5 [15] τ 2 reduction factor in contact due to hospital isolation 0 reduction in infectivity of vaccinated infectives 0.5 [15] Table 2 Age-specific model parameters with the following sources: the age-specific values of vaccine efficacy and effectiveness [8, 9] , fraction of the symptomatic infectives [15] and [28] , and all other values from 2003-2006 Taiwan flu monitor surveillance data. 