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

Bayesian inference for age-structured population model of infectious disease with application to varicella in Poland