The simultaneous estimation of family and community transmission rates as well as cure rates from panel data in a recurrent Hib (Haemophilus influenzae type b bacteria) infection is considered. An individual-based stationary Markov process model with constant hazards in two age groups is applied to describe recurrent asymptomatic Hib infection in a family with small children. The problem of estimation is solved in terms of the Bayesian posterior of the model parameters. The model is used to predict prevalence and incidence of Hib carriage in families as a function of the family size and age structure.