  In this project, identifiability, observability and uncertainty properties of
the deterministic and Chain Binomial stochastic SIR, SEIR and SEIAR
epidemiological models are studied. Techniques for modeling overdispersion are
investigated and used to compare simulated trajectories for moderately sized,
homogenous populations. With the chosen model parameters overdispersion was
found to have small impact, but larger impact on smaller populations and
simulations closer to the initial outbreak of an epidemic. Using a software
tool for model identifiability and observability (DAISY[Bellu et al. 2007]),
the deterministic SIR and SEIR models was found to be structurally identifiable
and observable under mild conditions, while SEIAR in general remains
structurally unidentifiable and unobservable. Sequential Monte Carlo and Markov
Chain Monte Carlo methods were implemented in a custom C++ library and applied
to stochastic SIR, SEIR and SEIAR models in order to generate parameter
distributions. With the chosen model parameters overdispersion was found to
have a small impact on parameter distributions for SIR and SEIR models. For
SEIAR, the algorithm did not converge around the true parameters of the
deterministic model. The custom C++ library was found to be computationally
efficient, and is very likely to be used in future projects.
