Diagnostic Delays Drive Transmission in Dense Cities: An Operational Feasibility Framework for Mitigating the Waiting-Window Effect

In dense urban settings, diagnostic systems reduce transmission only when sampling, result return, and isolation are operationally feasible during the period of peak infectiousness. We define a waiting-window transmission externality that arises when infectious individuals remain mobile between diagnostic sampling and actionable isolation. The term is formalized as E = N × P × TR × D, where N is daily testing volume, P is test positivity, TR is residual transmission during the waiting period, and D is sample-to-action turnaround time. The equation is used as a first-order operational risk-accounting framework rather than as a complete epidemic model. Using Monte Carlo uncertainty propagation, we compare centralized 48 h testing, surge conditions with coupled delay and crowding, near-patient rapid testing, and home sampling with isolation at sampling. Centralized 48 h workflows produce approximately 80 excess waiting-window infections per 1000 tests/day at p = 10% and approximately 401 at p = 50%, increasing to approximately 126 and 628 under surge coupling. Near-patient testing and home sampling reduce these values to approximately 5–26 across the same positivity range. We also distinguish two operationally different but epidemiologically related approaches: home sampling with immediate precautionary isolation reduces TR while laboratory turnaround may remain nonzero, whereas home-based molecular testing reduces D by returning results at the point of collection. Sensitivity checks for surge coupling and household transmission floors show that the qualitative ordering of workflows is preserved, although the magnitude of benefit depends on adherence and local operating conditions. These findings support redesigning diagnostic workflows around sample-to-action time, isolation feasibility, decentralized logistics, and equity rather than assay performance alone.