Oooof. Just go to your local auto parts store and look for some heavy duty diesel treatment that inhibits growth. I don't have any recommendations on brand.
After the treatment kills the growth, you are pretty much garaunteed to plug the filters next; if you don't have a primary fuel filter, now is the time to install one. You'll need to be changing it after this.
You may want to consider disposing of that half tank of diesel and scrubbing the tank which is by no means an easy and clean job. You might get away without doing it.
Diesel is an organic fuel and does not keep. You probably want to be burning through all the diesel in the tank every month. Try and get rid of that last half tank either by disposing or running it through and then get a few litres of fresh in there to burn through regularily.
