Estimation of the basic reproduction number for infectious diseases from age-stratified serological survey data

The basic reproduction number of an infection, R-0, is the average number o f secondary infections generated by a single typical infective individual i n a totally susceptible population. It is directly related to the effort re quired to eliminate infection. We consider statistical methods for estimati ng R-0 from age-stratified serological survey data. The main difficulty is indeterminacy, since the contacts between individuals of different ages are not observed. We show that, given an estimate of the average age-specific hazard of infection, a particular leading left eigenfunction is required to specify R-0. We review existing methods of estimation in the light of this indeterminacy. We suggest using data from several infections transmitted v ia the same route, and we propose that the choice of model be guided by a c riterion based on similarity of their contact functions. This approach also allows model uncertainty to be taken into account. It one infection induce s no lasting immunity, we show that the only additional assumption required to estimate R-0 is that the contact function is symmetric. When matched da ta on two or more infections transmitted by the same route are available, t he methods may be extended to incorporate the effect of individual heteroge neity. The approach can also be applied in partially vaccinated populations and to populations comprising loosely linked communities. The methods are illustrated with data on hepatitis A, mumps, rubella, parvovirus, Haemophil us influenzae type b and measles infection.