Fig. 8: Adapting testing strategies allows the relaxation of contact constraints to some degree.

The relaxation of contact constraints increases the reproduction number of the hidden pool \({R}_{t}^{H}\), and thus needs to be compensated by adjusting model parameters to keep the system stable. a–c Value of a single parameter required to keep the system stable despite a change in the hidden reproduction number, while keeping all other parameters at default values. a Increasing the rate of symptom-driven testing (λ_s, blue) can in principle compensate for hidden reproduction numbers close to R₀. However, this is optimistic as it requires that anyone with symptoms compatible with COVID-19 gets tested and isolated on average within 2.5 days—requiring extensive resources and efficient organization. Increasing the random-testing rate (λ_r, red) to the capacity limit (for the example Germany, gray line \({\lambda }_{r,\max }\)) would have almost no effect, pooling tests to achieve \(10{\lambda }_{r,\max }\) can compensate partly for larger increases in \({R}_{t}^{H}\). b Increasing the tracing efficiency (η) can compensate only small increases in \({R}_{t}^{H}\). c Decreasing the fraction of symptomatic individuals who avoid testing (φ), the leak from the traced pool (ϵ) or the escape rate from isolation (ν) can in principle compensate for small increases in \({R}_{t}^{H}\). d–i To compensate a 10% or 20% increase of \({R}_{t}^{H}\), while still keeping the system stable, symptom-driven testing (λ_s) could be increased (d), or ϵ or φ could be decreased (h,i). In contrast, only changing λ_r, η, or ν would not be sufficient to compensate a 10 % or 20 % increase in \({R}_{t}^{H}\), because the respective limits are reached (e, f, g). All parameter changes are computed through stability analysis (Supplementary Eq. (1)).