Journal of Applied Mathematics and Stochastic Analysis
Volume 16 (2003), Issue 4, Pages 361-374

Optimization in HIV screening problems

Lev Abolnikov1 and Alexander Dukhovny2

1Loyola Marymount University, Department of Mathematics, Los Angeles 91316, CA, USA
2San Francisco State University, Department of Mathematics, San Francisco 94132, CA, USA

Received 1 August 2002; Revised 1 March 2003

Copyright © 2003 Lev Abolnikov and Alexander Dukhovny. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.