The best thing I have found for killing anything that feeds on blood, lice, ticks fleas, mosquitos and gnats is Neem oil.
2 Tablespoons Neem
2 " liquid soap or shampoo
2 pints hot water
Mix and sponge all over animal.
You need hot water as Neem solidifies fairly fast and have to sponge it on as it will block the normal fly spray nozzle.
The downside is that Neem stinks like nothing else!
You do get use to the small which does fade after an hour or so.
You can get a human cream which has the smell removed. I fully admit that although I use Neem all the time on the animals (dogs get dunked monthly horses weekly) also in a more dilute version on the garden as it also clears all aphids and plant eating bugs. I would however, not want to swab it all over me (though, with dunking 16 dogs I can be pretty well covered!)