Hi Trudy,

The root cause of fungus gnats is overwatering, or maybe a more precise cause is excessive soil moisture at the surface of the soil. Bottom watering only when needed (the tray is dry) is the best prevention. If you have fungus gnats the sticky traps are the best way to reduce the number of breeding adults and as unsightly as they are, I would recommend them to get rid of as many adults as you can. 
For the larva that hatch from the eggs the best method is to mix in and coat the surface of the soil with diatomaceous earth. It won't harm you or any pet. Diatomaceous earth is microscopic silica (probably some calcium carbonate too) exoskeletons of diatoms. Harmless to us with proper handling but like a thousand knives to larva as they crawl through it.
In short, take care of the cause, reduce wet surface soil. Then trap adults to reduce the breeding cycle and add diatomaceous earth to reduce the number of growing larva.
This works with whiteflies too. Whiteflies often come in through screen openings or in bags of soil from garden centers as the bags have small holes to release trapped air so the bags don't burst and to regulate moisture in the potting mix.

I hope this helps.

Here is an article I published on the topic. How to Stop Fungus Gnats From Attacking Your Microgreens.