Purpose: Seasonal influenza is a major public health concern and the first line of defense is the flu shot. Antigenic drifts and high rate of influenza transmission require annual updates in the flu shot composition. We propose a mathematical model to optimize the strain selection decisions for the annual flu shot. We analyze the trade-offs involved with various different policy issues.
Methods: We take the view of the Vaccines and Related Biological Products Advisory Committee of FDA; and optimize strain selections based on a production plan that is designed by the manufacturers exogenously. To select the strains for the flu shot, the committee meets for the first time at the end of February. In this initial meeting, recommendations are made for prevalent strains that have sufficient production yields. On the other hand, if the information is insufficient to select a strain for a category, the final decision of that category is deferred to the next meeting, which is held after four weeks. We propose a multi-stage stochastic mixed-integer program to determine the best flu shot composition, and the optimal time to select it. We consider all three flu strain categories (A/H1N1, A/H3N2, and B). We calibrate the cross-protective immunity among the candidate strains using a shape space model in which only the vaccine strain that has the smallest antigenic distance triggers immune response. The strain selection decisions are made to maximize the expected benefit of immune response minus the expected shortage cost under various different scenarios.
Results: Selecting the strain of each category independent from the others results in a loss of up to 14% of the optimal benefit. The cost of considering only the most prevalent strains might be as high as the 45% of the optimal benefit. Our model allows incorporating more than three strains in the flu shot; hence it can be used to assess the benefits of a tetravalent flu shot. We find that incorporating a fourth strain into the flu shot would potentially prevent over a million flu cases.
Conclusions: Integrating the composition and timing decisions is crucial to design the best flu shot. The uncertainties associated with the flu shot preparation campaign should analytically be incorporated into the strain selection decisions.
Candidate for the Lee B. Lusted Student Prize Competition