OP...what if the mouse your DH fails to catch in a trap is a pregnant female?
Life Cycle info here www.terminix.com/pest-control/mice/life-cycle/
Heading into Winter mice will be looking to get somewhere dry and warm, can't blame them for that, so now is a good time to act.
Personally, I don't agree with so-called humane traps as you are moving the problem elsewhere which is not good from an environmental viewpoint and unless you release the trapped mice etc several times each day, they are likely to starve to death and the 'humane' part of the procedure is a farce.
I'm not a cat lover but don't suggest a cat either...again, what if the mouse has eaten a bait, then the cat will be a victim of secondary poisoning...goodbye kitty cat!
Spring traps and/or wax-based bait blocks work best and what we used 24/7 for many years in the trade.
Hope this helps?
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