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Are you sure they have been eaten? as opposed to say rotted away.
I have never known birds go for the florets which after all are flower buds. They do go for the leaves in a big way however!
I have known florets to rot/wither and die back and this is usually a physiological problem rather than a disease.
This can be brought about by watering/feeding wrongly or indeed starvation from both of these, i.e. they have not been watered.
I know in my area May was the driest May since 1990 so this may have played a part.
I'm sorry but I am stumped for ideas not knowing the history of the plant/s