Using queueing models as a decision support tool in allocating point-of-care HIV viral load testing machines in Kisumu County, Kenya

Point-of-care (POC) technologies-including HIV viral load (VL) monitoring-are expanding globally, including in resource-limited settings. Modelling could allow decision-makers to consider the optimal strategy(ies) to maximize coverage and access, minimize turnaround time (TAT) and minimize cost with limited machines. Informed by formative qualitative focus group discussions with stakeholders focused on model inputs, outputs and format, we created an optimization model incorporating queueing theory and solved it using integer programming methods to reflect HIV VL monitoring in Kisumu County, Kenya. We modelled three scenarios for sample processing: (1) centralized laboratories only, (2) centralized labs with 7 existing POC 'hub' facilities and (3) centralized labs with 7 existing and 1-7 new 'hub' facilities. We calculated total TAT using the existing referral network for scenario 1 and solved for the optimal referral network by minimizing TAT for scenarios 2 and 3. We conducted one-way sensitivity analyses, including distributional fairness in each sub-county. Through two focus groups, stakeholders endorsed the provisionally selected model inputs, outputs and format with modifications incorporated during model-building. In all three scenarios, the largest component of TAT was time spent at a facility awaiting sample batching and transport (scenarios 1-3: 78.7%, 89.9%, 91.8%) and waiting time at the testing site (18.7%, 8.7%, 7.5%); transportation time contributed minimally to overall time (2.6%, 1.3%, 0.7%). In scenario 1, the average TAT was 39.8 h (SD: 2.9), with 1077 h that samples spent cumulatively in the VL processing system. In scenario 2, the average TAT decreased to 33.8 h (SD: 4.8), totalling 430 h. In scenario 3, the average TAT decreased nearly monotonically with each new machine to 31.1 h (SD: 8.4) and 346 total hours. Frequency of sample batching and processing rate most impacted TAT, and inclusion of distributional fairness minimally impacted TAT. In conclusion, a stakeholder-informed resource allocation model identified optimal POC VL hub allocations and referral networks. Using existing-and adding new-POC machines could markedly decrease TAT, as could operational changes.