Eucalyptus Lemon (citriodora) is extremely effective against black flies, west nile carrying mosquitos (and all mosquitos), and other summer pests...it was tested by the CDC years ago and was found to be as effective or more effective than DEET...which is man-made and has side effects...I would never put it on myself, much less a child!!
You do not want to get products with Lemon Eucalyptus IN THEM...you just want to get Lemon Eucalyptus in its pure and natural state. Otherwise, you have no idea what else is in the "mix". We carry it (I am an aromatherapist)...you can see my site at www.shiningsunaromatherapy.com
I have also tried using it neat vs mixed in water as a spray. The mix does not work. It is pungent smelling...but that is a small price to pay for a pure medicinal essence which has no side effects other than to boost your immune system and clear your respiratory system...while serving as an amazing insect repellant! So...I drip one or two drops on each arm and rub it in...same on my legs (2-3 there), and maybe one on your neck/upper chest, if it is exposed. On children, a drop rubbed into each of those areas would work wonderfully.
Hope this helps clarify the discussion. I have been doing this for over 10 years, and am very wary of synthetic products...Mother Nature has the answer for virtually anything that ails us! Regards, Audre