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Standard epidemic models based on compartmental differential equations areinvestigated under continuous parameter change as external forcing. We showthat seasonal modulation of the contact parameter superimposed a monotonicdecay needs a different description than that of the standard chaotic dynamics.The concept of snapshot attractors and their natural probability distributionhas been adopted from the field of the latest climate-change-research to showthe importance of transient effect and ensemble interpretation of diseasespread. After presenting the extended bifurcation diagram of measles, thetemporal change of the phase space structure is investigated. By definingstatistical measures over the ensemble, we can interpret the internalvariability of the epidemic as the onset of complex dynamics even for thosevalues of contact parameter where regular behavior is expected. We argue thatanomalous outbreaks of infectious class cannot die out until transient chaos ispresented for various parameters. More important, that this fact becomesvisible by using of ensemble approach rather than single trajectoryrepresentation. These findings are applicable generally in nonlinear dynamicalsystems such as standard epidemic models regardless of parameter values.

How can contemporary climate research help to understand epidemic dynamics? -- Ensemble approach and snapshot attractors