Artificial Intelligence Constrained Multi-Objective Optimisation of Community Tuberculosis Contact Tracing Under Variable Sputum Courier Batching: A computed Evaluation of Healthcare Diagnostic Yield Equity

Community tuberculosis contact tracing programmes must allocate scarce sputum courier capacity across households that differ in transmission risk and in the diagnostic yield that timely specimen transport can recover. the present analysis formulates that allocation as a constrained multi-objective optimisation problem in which a planner chooses household visit and batching schedules to maximise expected diagnostic yield while limiting the dispersion of yield across community strata. Because no field data are available, the study characterises the operating characteristics of the proposed estimator under a declared variance structure rather than reporting empirical outcomes. A before-after-control-impact design with between-cluster standard deviation 6.0, residual standard deviation 4.5 and intraclass correlation 0.64 was evaluated across 2000 replications per design cell for cluster counts of 8, 16, 24 and 32 and effect sizes of 3, 5 and 8 percentage points. The analysis identifies the cluster count at which a 5 percentage point yield gain is detectable at 80% power, specifies the minimum detectable effect at 80% power for each cluster count, and derives the conditions under which equity constraints bind without eliminating the yield gain. The contribution is a formal statement of the trade-off between diagnostic yield and yield equity in courier-constrained contact tracing, together with a design-based procedure for sizing evaluations of that trade-off.