Flu impacts between 5-15% of the world's population annually. The first line of defense against seasonal flu is the annual flu shot, which is comprised of three strains. This proposal focuses on mathematical models for determining the optimal flu shot composition as well as the timing of its production. This decision is greatly complicated by its stochastic and dynamic nature. The flu shot composition must be determined many months before the start of the flu season. The flu shot manufacturing process is inherently uncertain, as it relies on cultivating strains from chicken eggs. Furthermore, the future prevalence of various flu viruses is uncertain, so that the flu shot must be designed without knowing what strains are threats. Currently, three strains are incorporated into the flu shot. By selecting these strains early, society can increase the probability that enough vaccine can be produced. However, this comes at the cost of reduced surveillance, which increases the probability that the wrong strains will be selected. Conversely, delaying the decision will improve surveillance at the expense of decreased manufacturing time. We propose a class of multi-stage stochastic mixed-integer programming (SMIP) models that fully explore these trade-offs and determine the best flu shot composition, along with the timing of its manufacturing. Such models enjoy a well deserved reputation for computational difficulty. We will develop state-of-the-art optimization methods for solving these difficult problems. The potential broader impacts of the proposed research are immense, as seasonal flu has enormous social and economic costs, and an optimized flu shot can mitigate much of these costs. Once successfully calibrated and developed, the proposed mathematical models can inform flu shot policy resulting in better flu shots and more reliable production. The educational impacts of this proposal will be felt by four groups. We will educate medical researchers through short courses and mentoring. Graduate students will benefit, as the results of this research will be taught in PhD courses in Industrial Engineering. Undergraduate students will take part directly in this research through REU programs. Finally, we will continue our outreach to K-12 schools in inner-city Pittsburgh, developing several matching games to illustrate the benefits of mathematical modeling.


Donald Burke

Distinguished University Professor of Health Science and Policy
University of Pittsburgh

Funding Source

Project Period


This site is registered on as a development site.