If you keep or breed a lot of a similar type of fish in multiple tanks you will eventually come across an illness that is contageous and lethal. Especially if you buy new stock regularly.
I have had the occasional outbreak of things, and now each tank has its own net. In the past I used to sterilise them, but there are problems
hot water - boiling water kills a lot of things - leave them in as long as possible
bleach - killis everything, but rots the net material. Don't use
salty water - a strong (saturated) salt solution soak for a few days will kill most nasties
chemicals like myxazin - may work for specific ailments, but I avoid chemicals whereever possible. You have to throw out the waste water - and we are polluting it enough all ready
drying - as pointed out drying can kill most aquatic pathogens.
Depending on how bad the net is / how contageous the illness I use a mix of the above - or simply chuck out the net and get a new one