A related issue is that of pre-epidemic immunity. Further sensitivity analysis using pre-immunity in the range of 10%-30% has shown that the results of curve-fittings are not sensitive to small changes in the pre-epidemic immunity. One would expect that pre-epidemic immunity does impact the outbreak, but nonetheless it is not reflected, at least not in the reproduction numbers. Pre-symptomatic infection and asymptomatic infection by asymptomatic infectives were incorporated into the proposed model. To gauge the roles these two features of influenza might play in a seasonal influenza epidemic, we performed the following simulations. Again using Fig. 3 as a benchmark, we first assume no pre-symptomatic infection (τ = 0) with all other parameter values unchanged (Fig. 6 ). Next we assume no asymptomatic infection by asymptomatic infectives (a i = a i V = 0) (Fig. 7) . The results indicate that pre-symptomatic infection seemed to have little effect on the model fits and the fitted parameters; while asymptomatic infection by asymptomatic infectives has a more pronounced impact on the model fit for the elderly, perhaps indicating the comparatively larger role asymptomatic infection plays in disease transmission.