# Maximizing the effectiveness of a pediatric vaccine formulary while prohibiting extraimmunization

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## Abstract

The growing complexity of the United States Recommended Childhood Immunization Schedule has resulted in as many as five required injections during a single well-baby office visit. To reduce this number, vaccine manufacturers have developed combination vaccines that immunize against several diseases in a single injection. At the same time, a growing number of parents are challenging the safety and effectiveness of vaccinating children. They are also particularly concerned about the use of combination vaccines, since they believe that injecting a child with multiple antigens simultaneously may overwhelm a child’s immune system. Moreover, combination vaccines make it more likely that extraimmunization (i.e., administering more than the required amount of vaccine antigens) occurs, resulting in greater concerns by parents and vaccine wastage costs borne by an already strained healthcare system. This paper formulates an integer programming model that solves for the maximum number of vaccines that can be administered without any extraimmunization. An exact dynamic programming algorithm and a randomized heuristic for the integer programming model is formulated and the heuristic is shown to be a randomized ξ-approximation algorithm. Computational results are reported on three sets of test problems, based on existing and future childhood immunization schedules, to demonstrate their computational effectiveness and limitations. Given that future childhood immunization schedules may need to be solved for each child, on a case-by-case basis, the results reported here may provide a practical and valuable tool for the public health community.

## Keywords

Pediatric immunization Pediatric vaccines Randomized approximation algorithms Discrete optimization Dynamic programming Heuristics Integer programming## Notes

### Acknowledgements

The authors would like to thank the three anonymous referees for their excellent comments and input, which have resulted in a significantly improved manuscript. The authors would also like to thank Bruce G. Weniger, M.D., M.P.H., Assistant Chief for Vaccine Development, Vaccine Safety and Development Branch, National Immunization Program, Centers for Disease Control and Prevention, for his longstanding encouragement and feedback on this line of research; his input on this work has been invaluable and most appreciated. This research has been supported in part by the National Science Foundation (DMI-0457176, DMI-0456945). The third author has also been supported in part by the Air Force Office of Scientific Research (FA9550-07-1-0232). The views expressed in this paper are those of the authors and do not reflect the official policy or position of the United States Air Force, Department of Defense, National Science Foundation, or the United States Government.

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