Well, there are quite a few viruses that can infect multiple different species. Some viruses are very specific to a given species. We have a Pacific salmon parvovirus that we only find in sockeye salmon, for example. Then there are other viruses like the erythorocytic necrosis virus that can be found across salmon, herring and other species and that we know can cause high levels of mortality in herring.
Yes, there is evidence that you can have epidemics occur because of viral infection. The best evidence is in herring, because we can see mass die-offs in herring. But whether viruses themselves alone have caused enough mortality to diminish the biodiversity of salmon, again, I can't answer that question.