Optimizing Flu Shot Design Under Uncertainity

流感每年影响世界人口的5-15%。预防季节性流感的第一道防线是年度流感？流感疫苗？它由三种菌株组成。该提案侧重于确定最佳流感疫苗成分及其生产时间的数学模型。这种决定是非常复杂的随机和动态的性质。流感疫苗的成分必须在流感季节开始前几个月确定。流感疫苗的生产过程本质上是不确定的，因为它依赖于从鸡蛋中培养菌株。此外，各种流感病毒的未来流行是不确定的，因此必须在不知道哪些菌株是威胁的情况下设计流感疫苗。目前，流感疫苗中含有三种菌株。通过早期选择这些菌株，社会可以增加生产足够疫苗的可能性。然而，这是以减少监测为代价的，这增加了选择错误菌株的可能性。相反，推迟决策将以减少制造时间为代价改善监督。我们提出了一类多阶段随机混合整数规划（SMIP）模型，充分探索这些权衡，并确定最佳流感疫苗组合物，沿着其制造的时间。 这样的模型享有当之无愧的声誉计算困难。 我们将开发最先进的优化方法来解决这些难题。拟议研究的潜在更广泛影响是巨大的，因为季节性流感具有巨大的社会和经济成本，而优化的流感疫苗可以减轻大部分成本。一旦成功校准和开发，所提出的数学模型可以为流感疫苗政策提供信息，从而获得更好的流感疫苗和更可靠的生产。这项建议的教育影响将由四个群体感受到。我们将通过短期课程和指导来教育医学研究人员。研究生将受益，因为这项研究的结果将在工业工程博士课程中教授。本科生将通过REU课程直接参与这项研究。最后，我们将继续推广到匹兹堡市中心的K-12学校，开发几个匹配游戏来说明数学建模的好处。

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.