Fig. 2. Sufficient testing and contact tracing can control the disease spread, while insufficient TTI only slows it.

We consider a test-trace-and-isolate (TTI) strategy with symptom-driven testing (λ_s = 0.1) and two tracing scenarios: For high tracing efficiency (η = 0.66, a–c), the outbreak can be controlled by TTI; for low tracing efficiency (η = 0.33, d, e) the outbreak cannot be controlled because tracing is not efficient enough. a, d The number of infections in the hidden pool grows until the outbreak is noticed on day 0, at which point symptom-driven testing (λ_s = 0.1) and contact tracing (η) starts. b, e The absolute number of daily infections (N) grows until the outbreak is noticed on day 0; the observed number of daily infections (${\widehat{N}}^{\mathrm{obs}}$) shown here is simulated as being inferred from the traced pool and subject to a gamma-distributed reporting delay with a median of 4 days. c, f The observed reproduction number (${\widehat{R}}_t^{\mathrm{obs}}$) is estimated from the observed new infections (${\widehat{N}}^{\mathrm{obs}}$), while the effective reproductive number (${\widehat{R}}_t^{\mathrm{eff}}$) is estimated from the total daily new infections (N). After an initial growth period, it settles to ${\widehat{R}}_t^{\mathrm{obs}}=1$ if the outbreak is controlled (efficient tracing), or to ${\widehat{R}}_t^{\mathrm{obs}}>1$ if the outbreak continues to spread (inefficient tracing). All the curves plotted are obtained from numerical integration of Eqs. (1)–(5).