Abstract
This research uses mathematically derived visual logistics to interpret COVID-19 molecular and rapid antigen test (RAgT) performance, determine prevalence boundaries where risk exceeds expectations, and evaluate benefits of recursive testing along home, community, and emergency spatial care paths. Mathematica and open access software helped graph relationships, compare performance patterns, and perform recursive computations. Tiered sensitivity/specificity comprise: (T1) 90%/95%; (T2) 95%/97.5%; and (T3) 100%/≥99%, respectively. In emergency medicine, median RAgT performance peaks at 13.2% prevalence, then falls below T1, generating risky prevalence boundaries. RAgTs in pediatric ERs/EDs parallel this pattern with asymptomatic worse than symptomatic performance. In communities, RAgTs display large uncertainty with median prevalence boundary of 14.8% for 1/20 missed diagnoses, and at prevalence > 33.3−36.9% risk 10% false omissions for symptomatic subjects. Recursive testing improves home RAgT performance. Home molecular tests elevate performance above T1 but lack adequate validation. Widespread RAgT availability encourages self-testing. Asymptomatic RAgT and PCR-based saliva testing present the highest chance of missed diagnoses. Home testing twice, once just before mingling, and molecular-based self-testing, help avoid false omissions. Community and ER/ED RAgTs can identify contagiousness in low prevalence. Real-world trials of performance, cost-effectiveness, and public health impact could identify home molecular diagnostics as an optimal diagnostic portal.