Biology – Quantitative Biology – Populations and Evolution
Scientific paper
2009-12-31
Biology
Quantitative Biology
Populations and Evolution
Scientific paper
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.
Dykman Mark I.
Khasin Michael
Meerson Baruch
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