Infectious diseases such as avian influenza pose a global threat to human health. Mathematical and statistical models can provide key insights into the mechanisms that underlie the spread and persistence of infectious diseases, though their utility is linked to the ability to adequately calibrate these models to observed data. Performing robust inference for these systems is challenging. The fact that the underlying models exhibit complex non-linear dynamics, coupled with practical constraints to observing key epidemiological events such as transmission, requires the use of inference techniques that are able to numerically integrate over multiple hidden states and/or infer missing information. Simulation-based inference techniques such as Approximate Bayesian Computation (ABC) have shown great promise in this area, since they rely on the development of suitable simulation models, which are often easier to code and generalise than routines that require evaluations of an intractable likelihood function. In this manuscript we make some contributions towards improving the efficiency of ABC-based particle Markov chain Monte Carlo methods, and show the utility of these approaches for performing both model inference and model comparison in a Bayesian framework. We illustrate these approaches on both simulated data, as well as real data from an experimental transmission study of highly pathogenic avian influenza in genetically modified chickens.