  Deterministic compartmental models have been used extensively in modeling
epidemic propagation. These models are required to fit available data and
numerical procedures are often implemented to this end. But not every model
architecture is able to fit the data because the structure of the model imposes
hard constraints on the solutions. We investigate in this work two such
situations: first the distribution of transition times from a compartment to
another may impose a variable number of intermediary states; secondly, a
non-linear relationship between time-dependent measures of compartments sizes
may indicate the need for structurations (i.e., considering several groups of
individuals of heterogeneous characteristics).
