I would mot say "the rubbish" unless you are referring to rubbish from a very specific location, or unless you had already mentioned rubbish previously (e.g. maybe you had already mentioned rubbish that is currently found in a particular river.) This does NOT seem to be the case in your sentences since you talk very generally about "some rivers".
I would suggest these:
(a) Rubbish pollutes some rivers and causes fish to die.
(b) Rubbish is polluting some rivers, and/so many fish will probably die.
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