Diagnostic Delays Drive Transmission in Dense Cities: Modeling the Waiting-Window Effect and Its Mitigation

In dense urban settings, delays between diagnostic sampling and effective isolation can sustain transmission during peak infectiousness. We define a waiting-window transmission externality arising when infectious individuals remain mobile while awaiting results, formalized as E = N{middle dot}P{middle dot}TR{middle dot}D, where N is daily testing volume, P test positivity, TR transmission during the waiting period, and D turnaround time. Using Monte Carlo simulation and a susceptible-infectious-recovered (SIR) framework, we quantify excess infections per 1,000 tests/day under multiple diagnostic workflows. A surge scenario incorporates positive coupling between TR and D ({rho} = 0.45), reflecting co-occurrence of laboratory saturation and elevated contacts during system stress. Under centralized 48-hour workflows, excess infections reach [~]80 at P = 10% and [~]401 at P = 50%, increasing to [~]628 under surge conditions. In contrast, near-patient rapid testing and home sampling reduce this to [~]5 and [~]25-26, respectively. Workflows that eliminate the waiting window--either through immediate isolation at sampling or through home-based PCR that returns results at the point of collection--effectively collapse the transmission term. These findings identify diagnostic delay as a modifiable driver of epidemic dynamics. Operational redesign of testing workflows, including decentralized sampling and home-based molecular diagnostics, offers a scalable pathway to improve epidemic controllability and reduce inequities in dense urban environments.