Fig 3. Reduced contact tracing efficiency with increasing cases leads to accelerating epidemics.

Top panels (A, B, C) show the number of susceptible, infected (latent, pre-symptomatic and symptomatic combined), and recovered individuals. Bottom panels (D, E, F) show the reproductive number, R_t, over time. Left most panels (A, D) show dynamics with no contact tracing but social distancing (κ = 0.58) set to give same initial R₀ (1.35) as with contact tracing. Middle panels (B, E) show dynamics with effectively unlimited contact tracing (1500 contact tracers making 12 calls/day; 10 contacts per case) but no social distancing (κ = 1), with an identical value of R₀ as in panels A, D. Right panels (C, F) show dynamics with the same parameter values as (B, E) except with limited contact tracing (15 contact tracers). R₀ is the same value as in panels D and E (R₀ = 1.35), but R_t increases as cases increase and contact tracing becomes inefficient, which overwhelms the decrease in the fraction of the population that is susceptible. In all panels, the delay from symptom onset to receiving test results, 1/τ_Is, is 5d. All populations start with 100,000 individuals. Note the identical epidemic sizes (final fraction susceptible 0.53) for panels A (social distancing) and B (effectively unlimited contact tracing), but much larger epidemic size for limited contact tracing in panel C (final fraction susceptible 0.14).