Optimal Design of the Seasonal Influenza Vaccine with Manufacturing Autonomy

Influenza (flu) is a serious public health concern. The first line of defense is the flu shot, whose composition is updated annually to adjust for frequent mutations of the circulating viruses. The World Health Organization recommends which strains to include in the flu shot based on global surveillance. Vaccine manufacturers produce trivalent and quadrivalent flu shots. The design of the flu shot, however, affects the manufacturers’ capacity and profit. In return, production decisions of the manufacturers affect the societal vaccination benefit by determining coverage and timely availability. We model this two-level hierarchy using a bilevel multistage stochastic mixed-integer program. Calibrated with publicly available data, our model integrates the flu shot composition and manufacturing in a stochastic and dynamic environment. We derive a branch-and-price algorithm to find the global optimal solution. We also propose an effective heuristic to provide the public health planners with a decision aid tool. Finally, we perform numerical experiments to answer important public health policy questions and to quantify the impact of the proposed modeling extensions. A major conclusion of our work is that the vaccine strain of a category that is not expected to be very prevalent and/or that is unlikely to drift in the upcoming season should be selected as early as possible, especially when the selections for other strain categories have to be postponed to improve the flu shot design.