Gene Hackman's wife died of a rare virus that few had heard of before a major update in the case this week ... and TMZ has learned she had about a week after contracting Hantavirus before it quickly became fatal.

Here is the deal ... Santa Fe authorities on Friday shared the shocking revelation that Betsy Arakawa likely died a week before Gene -- and it was the rare virus speared by rats and mice that killed her.

Dr. Jeffrey Klausner, an infectious disease expert and professor at the Keck School of Medicine of USC, tells TMZ ... Hantavirus impacts the body fast – and since symptoms present themselves as a chest cold -- and the virus is so rare -- it is often misdiagnosed.

Hantavirus spreads to humans from rat/mouse poop and urine, which usually is contracted when someone cleans the attic or basement ...  and it kills one in three people, Dr. Klausner tells us.

Like any other severe virus, the percentage of survival is much greater if it's diagnosed immediately and the person is hospitalized ... with Klausner telling TMZ Hantavirus is akin to severe pneumonia.

As for her final days ... Betsy was likely having a harder and harder time breathing, until she finally lost consciousness in the bathroom and died.

As we previously reported ... Authorities believe Gene -- who we now know had Alzheimer's -- died a week later of heart disease and complications caused by the disease.