German researchers report that Lithium salts are an effective systemic agent against varroa and are tolerated by bees.  Their research was published Jan 12, 2018 in the journal Nature. 

Viz: https://www.nature.com/articles/s41598-017-19137-5.pdf

Lithium chloride effectively kills the honey bee parasite Varroa destructor by a systemic mode of action
Bettina Ziegelmann, Elisabeth Abele, Stefan Hannus, Michaela Beitzinger, Stefan Berg &
Peter Rosenkranz

Here, we show that the lithium chloride that
was used to precipitate RNA and other lithium compounds is highly effective at killing Varroa mites
when fed to host bees at low millimolar concentrations. Experiments with caged bees and brood-free
artificial swarms consisting of a queen and several thousand bees clearly demonstrate the potential
of lithium as miticidal agent with good tolerability in worker bees providing a promising basis for the
development of an effective and easy-to-apply control method for mite treatment.

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