  Mechanistic compartmental models are widely used in epidemiology to study the
dynamics of infectious disease transmission. These models have significantly
contributed to designing and evaluating effective control strategies during
pandemics. However, the increasing complexity and the number of parameters
needed to describe rapidly evolving transmission scenarios present significant
challenges for parameter estimation due to intractable likelihoods. To overcome
this issue, likelihood-free methods have proven effective for accurately and
efficiently fitting these models to data. In this study, we focus on
approximate Bayesian computation (ABC) and synthetic likelihood methods for
parameter inference. We develop a method that employs ABC to select the most
informative subset of summary statistics, which are then used to construct a
synthetic likelihood for posterior sampling. Posterior sampling is performed
using Hamiltonian Monte Carlo as implemented in the Stan software. The proposed
algorithm is demonstrated through simulation studies, showing promising results
for inference in a simulated epidemic scenario.
