Speeding up disease extinction with a limited amount of vaccine

TL;DR

This paper develops a model-independent optimal vaccination strategy using short pulses to significantly increase disease extinction probability, especially when vaccination resources are limited, by exploiting resonance effects with disease dynamics.

Contribution

It introduces a theory for fluctuation-induced disease extinction with optimal pulse vaccination, revealing resonance effects and phase synchronization importance.

Findings

Optimal vaccination pulses are short and periodic.

Resonance with disease dynamics enhances extinction probability.

Synchronization with system modulation is crucial for effectiveness.

Abstract

We consider optimal vaccination protocol where the vaccine is in short supply. In this case, disease extinction results from a large and rare fluctuation. We show that the probability of such fluctuation can be exponentially increased by vaccination. For periodic vaccination with fixed average rate, the optimal vaccination protocol is model independent and presents a sequence of short pulses. The effect of vaccination can be resonantly enhanced if the pulse period coincides with the characteristic period of the disease dynamics or its multiples. This resonant effect is illustrated using a simple epidemic model. If the system is periodically modulated, the pulses must be synchronized with the modulation, whereas in the case of a wrong phase the vaccination can lead to a negative result. The analysis is based on the theory of fluctuation-induced population extinction in periodically modulated systems that we develop.