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An Analysis of Pediatric Vaccine Formulary Selection Problems

Department of Operational Sciences, Air Force Institute of Technology, Wright-Patterson AFB, Ohio 45433
Simulation and Optimization Laboratory, Department of Computer Science, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801
Department of Mathematics and Statistics, Southern Illinois University, Edwardsville, Illinois 62026
shane.hall{at}afit.edu
shj{at}illinois.edu
esewell{at}siue.edu

Vaccination against infectious disease is hailed as one of the great achievements in public health. However, the United States Recommended Childhood Immunization Schedule is becoming increasingly complex as it is expanded to cover additional diseases. Moreover, biotechnology advances have allowed vaccine manufacturers to create combination vaccines that immunize against several diseases in a single injection. All these factors are creating a combinatorial explosion of alternatives and choices (each with a different cost) for public health policy makers, pediatricians, and parents/guardians (each with a different perspective). The General Vaccine Formulary Selection Problem (GVFSP) is introduced to model general childhood immunization schedules that can be used to illuminate these alternatives and choices by selecting a vaccine formulary that minimizes the cost of fully immunizing a child and the amount of extraimmunization. Both exact algorithms and heuristics for GVFSP are presented. A computational comparison of these algorithms and heuristics is presented for the 2006 Recommended Childhood Immunization Schedule, as well as several randomly generated childhood immunization schedules that are likely to be representative of future childhood immunization schedules. The results reported here provide both fundamental insights into the structure of the GVFSP models and algorithms and practical value for the public health community.

Subject classifications: health care; pediatric immunization; vaccines; analysis of algorithms; computational complexity; programming; integer algorithms; heuristics; dynamic.
History: Received February 2006; revision received May 2008; accepted June 2008.