  Standard epidemic models based on compartmental differential equations are
investigated under continuous parameter change as external forcing. We show
that seasonal modulation of the contact parameter superimposed a monotonic
decay needs a different description than that of the standard chaotic dynamics.
The concept of snapshot attractors and their natural probability distribution
has been adopted from the field of the latest climate-change-research to show
the importance of transient effect and ensemble interpretation of disease
spread. After presenting the extended bifurcation diagram of measles, the
temporal change of the phase space structure is investigated. By defining
statistical measures over the ensemble, we can interpret the internal
variability of the epidemic as the onset of complex dynamics even for those
values of contact parameter where regular behavior is expected. We argue that
anomalous outbreaks of infectious class cannot die out until transient chaos is
presented for various parameters. More important, that this fact becomes
visible by using of ensemble approach rather than single trajectory
representation. These findings are applicable generally in nonlinear dynamical
systems such as standard epidemic models regardless of parameter values.
