Comparison of goodness-of fit indices between a misspecified model and a model with a time-varying parameter.

The reference is a sinusoidal model with 2 periodic components. The parameter values used are in the captions of Fig 3. The indices are computed on Incidence, β and Reff trajectories: RMSE: root mean square error using the median; MAPE: maximum absolute percentage error using the median; MIQR: mean inter-quartile range. For comparison purposes we used a stochastic version of the SIRS models with sinusoidal β and for all figures the observation process is applied to the inferred incidence trajectory.