  Dynamics of the infectious disease transmission is often best understood
taking into account the structure of population with respect to specific
features, in example age or immunity level. Practical utility of such models
depends on the appropriate calibration with the observed data. Here, we discuss
the Bayesian approach to data assimilation in case of two-state age-structured
model. This kind of models are frequently used to describe the disease dynamics
(i.e. force of infection) basing on prevalence data collected at several time
points. We demonstrate that, in the case when the explicit solution to the
model equation is known, accounting for the data collection process in the
Bayesian framework allows to obtain an unbiased posterior distribution for the
parameters determining the force of infection. We further show analytically and
through numerical tests that the posterior distribution of these parameters is
stable with respect to cohort approximation (Escalator Boxcar Train) to the
solution. Finally, we apply the technique to calibrate the model based on
observed sero-prevalence of varicella in Poland.
