  Quantifying the attack ratio of disease is key to epidemiological inference
and Public Health planning. For multi-serotype pathogens, however, different
levels of serotype-specific immunity make it difficult to assess the population
at risk. In this paper we propose a Bayesian method for estimation of the
attack ratio of an epidemic and the initial fraction of susceptibles using
aggregated incidence data. We derive the probability distribution of the
effective reproductive number, R t , and use MCMC to obtain posterior
distributions of the parameters of a single-strain SIR transmission model with
time-varying force of infection. Our method is showcased in a data set
consisting of 18 years of dengue incidence in the city of Rio de Janeiro,
Brazil. We demonstrate that it is possible to learn about the initial fraction
of susceptibles and the attack ratio even in the absence of serotype specific
data. On the other hand, the information provided by this approach is limited,
stressing the need for detailed serological surveys to characterise the
distribution of serotype-specific immunity in the population.
