Theoretical Analysis of Optimal Vaccine Allocation under an Age-Structured Epidemic

This paper develops a theoretical model to analyze the optimal allocation of vaccines in an age-structured population during an infectious disease outbreak. The model explicitly incorporates both deaths caused by infection and mortality risks associated with vaccination, and examines how age-specific vaccination policies affect the total number of deaths over time. Infection dynamics are modeled as depending on the cumulative number of infected individuals and the remaining susceptible population, while vaccination permanently removes individuals from the susceptible pool. The optimal allocation is characterized by a threshold condition determined by age-specific infection fatality rates, population shares and the mortality risk from vaccination. Numerical examples show that, even when the elderly face higher infection fatality rates, prioritizing vaccination for the young can minimize total deaths by dynamically suppressing future infection spread. However, when the vaccination-related mortality risk for the elderly is sufficiently large, refraining from vaccinating the elderly becomes optimal.