We can consider bee decline as the result of competition between two microbial systems. That is, the microbial system of the honeybee and the microbial system of the Varroa mite.
The assumption is that a change has occurred in the mineral composition of the environment and/or of the pollen/nectar. This has resulted in a shift in the microbial balance in favor of the mite, and possibly also in favor of other diseases and parasites.
By administering extra iron the beekeeper changes the microbial composition in the bees. This then leads to a reduced virulence of Varroa mite.