The most cited research studied wolves' affect on elk populations in Yellowstone restoring riparian habitats(1).

Wolves' impact on the spread of chronic wasting disease (CWD) in deer has also been studied(2). “CWD prevalence could be halved within a decade and eliminated within the century if a pack of wolves consistently and selectively removed 15% of deer in a closed population” (Waldner, 2016)

I don't know if wolves' impact on tick populations has been explicitly studied, but you can find research on habitat diversity reducing ticks(3); and it follows that the lack of predators contributes to deer population explosion, which in turn provides an unbounded vector for the tick epidemic.

1. https://www.sciencedirect.com/science/article/pii/S235198942...

2. https://wildlifecoexistence.org/blog/wolves-and-chronic-wast...

3. https://pmc.ncbi.nlm.nih.gov/articles/PMC12445845/