Influenza Research and Treatment 7 where α i is the age-dependent base instantaneous infection probability of contact i, θ i (t) is her status of vaccination at time t (0 or 1), and δ is the vaccine efficacy, measured as the reduction in the base instantaneous infection probability (achieved after 10 days [61] ). The values of age-dependent base instantaneous infection probabilities were adopted from [46] (see Table 2 ). The disease natural history included a latent period of 29 hours (1.21 days), an incubation period of 46 hours (1.92 days), an infectiousness period from 29 to 127 hours (1.21 to 5.29 days), and a period leading to health outcome from 127 to 240 hours (5.29 to 10 days) [85] .