Academic Events

The Sooner, the Better? Optimal Vaccination Policy with Limited Vaccine Supply

Qi (George) Chen

London Business School

We study the optimal single-dose vaccination policy in an infectious disease outbreak, considering both the limited total supply of the vaccine and its imperfect efficacy, which provides partial immunity to each vaccinated individual. The inclusion of imperfect efficacy introduces an additional compartment to the celebrated Susceptible-Infectious-Recovered (SIR) model, giving rise to an infinite horizon nonlinear optimal control problem. To facilitate theoretical analysis, we employ a variable transformation to convert the problem into an equivalent form with linear dynamics. Analyzing the transformed model, we derive a closed-form expression for the optimal vaccination policy under infinite administrative capacity and establish theoretical structures for the optimal policy under finite capacity. Our results suggest that delaying the start of the vaccination process may be optimal, especially when the vaccine is less effective, the vaccine supply is more limited, and the disease is more infectious. We identify terms capturing the individual-level benefit of vaccination with imperfect vaccines, in terms of the reduction of infection risk over the course of a disease outbreak, that reveal the intuition for the delay as an integral part of the transformed analysis: because this benefit is non-monotonic in time, maximizing the overall benefit of vaccination requires a strategic allocation of limited vaccine supply over time. Building on these theoretical findings, our numerical study verifies these insights based on sensitivity results. We demonstrate the significant benefit of delay in reducing the total number of infections compared to policies without delay. Furthermore, we extend the analysis to different model dynamics and objective functions, confirming that our key findings remain robust and methodology valid across different settings. Our study contributes to the methodological framework to analyze optimal vaccination policies for infectious disease control, and uncovers an important policy structure – vaccination delay – that has been overlooked in the literature but has important implications for practice.

Dr. George Chen is an Assistant Professor at London Business School. His research focuses on developing quantitative models and solution methods for operational level decisions involving uncertainty and risks, with applications in public health delivery, revenue management and pricing analytics, and supply chain management. His work has been published in Management Science, Operations Research, Manufacturing & Service Operations Management, and Mathematics of Operations Research. Before joining London Business School, George taught courses at the undergraduate and graduate levels at the University of Michigan and the University of Texas at Dallas. He holds a PhD in Business Administration from the University of Michigan, and a B.Eng. in Automation from Tsinghua University, China.