Directly measuring evidence of influenza infections is difficult, especially in low surveillance settings such as sub-Saharan Africa. Using a Bayesian model, we estimated unobserved infection times and underlying antibody responses to influenza A/H3N2 using cross-sectional serum antibody responses to four strains in children aged 24-60 months. Among the 242 individuals, we estimated a variable seasonal attack rate and found that most children had at least one infection before two years of age. Our results are consistent with previously published high attack rates in children. The modelling approach highlights how cross-sectional serological data can be used to estimate epidemiological dynamics.