Optimizing vaccination scheduling during influenza outbreaks: a SEIAR-based model for balancing routine and emergency vaccination demands

Background Efficient scheduling of vaccinations, particularly during influenza outbreaks, poses significant challenges due to limited service capacity and the need to balance routine immunization with emergency vaccination demands. Methods We developed a mathematical optimization model integrating an SEIAR influenza transmission framework to determine optimal service capacity allocation. The model prioritizes routine Category I vaccinations while maximizing emergency influenza vaccination capacity. Model validation employed vaccination data from Nanshan District CDC, Shenzhen ( n = 4,193 children, 11,528 vaccine doses) and an influenza outbreak at a local secondary school. Results The optimized model reduced peak infection counts by 80.6% (from 360 to 70 individuals) and significantly decreased daily vaccination variance (from 38.25 to 3.17, 91.7% reduction), while maintaining 100% coverage for routine vaccinations. The optimal service capacity threshold was determined at 49 individuals per day. Conclusion The proposed balanced vaccination scheduling model offers a practical solution for optimizing vaccination resource allocation during influenza outbreaks. By incorporating vaccination compliance and dynamically adjusting service capacities, the model provides a robust framework for improving vaccine management and epidemic control. This model can be applied in disease prevention and control centers to ensure efficient utilization of vaccination resources, particularly in outbreak scenarios.