Transmission Waiting Time: A Unifying Metric for Outbreak Controllability

The feasibility of containing infectious disease outbreaks depends on whether interventions can act faster than pathogen transmission. Classical controllability theory links outbreak control to the timing of symptom onset relative to infectiousness, reflecting an era in which isolation and contact tracing were necessarily triggered by clinical symptoms. This framework therefore implies intrinsic limits for pathogens with substantial pre-symptomatic or asymptomatic transmission. However, the widespread availability of molecular diagnostics now enables infection detection and isolation independent of symptoms, fundamentally altering the operational basis of outbreak control. Here we introduce the transmission waiting time--the interval between infection and the first onward transmission event--as a symptom-agnostic timescale that defines the intrinsic speed limit for effective intervention. We derive this quantity analytically from two fundamental epidemiological parameters, the basic reproduction number and the generation-interval distribution, yielding closed-form benchmarks for the minimum isolation speed and coverage required for control. Applying this framework across diverse pathogens reveals substantial differences in intrinsic controllability driven by variation in both overall transmissibility and the timing of infectiousness. We show that transmission heterogeneity reshapes controllability primarily through changes in the temporal distribution of infectiousness, and that homogeneous predictions often provide conservative bounds. By mapping complex test-trace-isolate operations onto a low-dimensional delay-coverage intervention landscape, this framework clarifies the conditions under which such containment efforts are feasible.