https://www.ncbi.nlm.nih.gov/books/NBK545493/table/rc1121.ap...
But since you're being needlessly snarky about it (it's not productive to suggest killing "the rabbits and chipmunks and mice and squirrels"), here:
https://pubmed.ncbi.nlm.nih.gov/25118409/
>After hunts were initiated, number and frequency of deer observations in the community were greatly reduced as were resident-reported cases of Lyme disease. Number of resident-reported cases of Lyme disease per 100 households was strongly correlated to deer density in the community. Reducing deer density to 5.1 deer per square kilometer resulted in a 76% reduction in tick abundance, 70% reduction in the entomological risk index, and 80% reduction in resident-reported cases of Lyme disease in the community from before to after a hunt was initiated.
I’m not optimistic this will be all that helpful. Just because the tick you found is negative, that tells you nothing about those you did not find. Just because a tick is positive, that does not mean that it has infected whoever it was attached to.
My understanding is that the ticks only transmit disease after they have been attached long enough to become engorged. None of the ticks shown were engorged.
I’ve hear stats as long as 24 hours and as short as 30 seconds. One nurse told me that removing ticks by grasping and pulling means they transmit immediately, because you squeeze their contents through their mouths. I no longer believe any of the stats; seems like it could be at any time.
Whenever someone recommends removal using tweezers, I wonder if the person offering this advice has ever removed a well attached tick. I’ve found tools like a Tick Tornado work better, but are still problematic with smaller ticks.
https://www.zenpetusa.com/tick-tornado
Just breaking out the tweezers and yanking away was most emphatically not recommended. It can leave the mouth parts behind, if nothing else.
Another is Alpha Gal. It is a molecule carried in tick saliva that can cause serious allergies to red meat and even dairy. Because the molecule is in the saliva, it can be delivered immediately.
If someone doesn’t notice a tick then they aren’t going to be considering prophylactic treatment anyway. It’s for the cases where ticks are discovered.
Next to that, in The Netherlands we have a site to report tick bites and if they had lyme disease or not. It’s good to know if you should be extra vigilant after a bite from a certain area. I think the self-test could be very useful for such sites.