Fig. 5: Testing and tracing give rise to two TTI-stabilized regimes of spreading dynamics.

In addition to the intrinsically stable regime of the simple SIR model (blue region), our model exhibits two TTI-stabilized regimes that arise from the isolation of formerly “hidden” infected individuals uncovered through symptom-based testing alone (green region) or additional contact tracing (amber region). Due to the external influx, the number of observed new cases reaches a nonzero equilibrium \({\hat{N}}_{\infty }^{\,\text{obs}\,}\) that depends on the hidden reproductive number (colored lines). These equilibrium numbers of new cases diverge when approaching the respective critical hidden reproductive numbers (\({R}_{\,\text{crit}\,}^{H}\)) calculated from linear stability analysis (dotted horizontal lines). Taking into account a finite tracing capacity \({N}_{\max }\) shrinks the testing-and-tracing stabilized regime and makes it metastable (dotted amber line). Note that, for our standard parameter set, the natural base reproduction number R₀ lies in the unstable regime. Please see Supplementary Fig. 5 for a full phase diagram and Supplementary Note 1 for the linear stability analysis.