  The growing literature on the propagation of COVID-19 relies on various
dynamic SIR-type models (Susceptible-Infected-Recovered) which yield
model-dependent results. For transparency and ease of comparing the results, we
introduce a common representation of the SIR-type stochastic epidemiological
models. This representation is a discrete time transition model, which allows
us to classify the epidemiological models with respect to the number of states
(compartments) and their interpretation. Additionally, the transition model
eliminates several limitations of the deterministic continuous time
epidemiological models which are pointed out in the paper. We also show that
all SIR-type models have a nonlinear (pseudo) state space representation and
are easily estimable from an extended Kalman filter.
