Trends in Biomathematics: Mathematical Modeling for Health, Harvesting, and Population Dynamics pp 299-307 | Cite as

# Optimal Temporary Vaccination Strategies for Epidemic Outbreaks

## Abstract

We propose temporary vaccination strategies in the SIR disease outbreak model, where vaccination starts when the infection level reaches a threshold, and continues until susceptibles drop below a level such that the number of infected hosts is decreasing without further intervention. Costs are assigned to vaccination and disease burden, and we investigate which one of this two parameter family of *VUHIA* (vaccinate until herd immunity achieved) strategies gives the minimal cost. When the cost of vaccination is very small compared to the cost of disease burden, the optimal strategy is to start vaccination as early as possible and as high rate as possible. When vaccination is very expensive, the minimal cost is attained without vaccination. However, when these costs are of similar magnitudes, we uncover some counter-intuitive phenomena, namely the total cost can be a non-monotone function of the vaccination rate and the threshold value. We also show that for different basic reproduction numbers, the corresponding optimal strategies can be very different.

## Notes

### Acknowledgements

AD was supported by the Hungarian National Research, Development and Innovation Office grant NKFIH PD 128363 and the Bolyai Scholarship of HAS. KM was supported by NKFIH FK 124016. GR was supported by EFOP-3.6.1-16-2016-00008 and Marie Skłodowska-Curie Grant No. 748193.

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