Optimization in HIV screening problems

In this article, the authors use both deterministic and stochastic approaches to the analysis of some optimization problems that arise in the group (“pool”) HIV screening practice. Two kinds of testing policies are considered. For the first kind, group-individual testing, the optimal size of the group that should be selected for testing is found. For more general group–subgroup testing procedure the authors develop a numerical algorithm for finding the sequence of successively selected subgroups that minimizes the total cost of testing. Assuming that both arriving and testing processes have a random nature, the authors suggest a stochastic model in which the optimal size of the group in the group–individual testing procedure is found by using methods of queueing theory.