Oregon's cases of novel coronavirus have more than tripled in a week, state health officials announced Saturday. But they said the hospitalization rate remains far below the state's capacity, and urged people to remain at home to keep infections down.

Oregon now has 479 COVID-19 cases. That's more than three times the 137 positive diagnoses the state had last Saturday, an increase that reflects both increased testing capacity and the spread of the virus before social distancing measures were put in place. Thirteen people statewide have died of the virus.

Eighty-one of those cases are in Multnomah County. Washington County remains the state's center of the disease, with 140 cases as of March 28.

The Oregon Health Authority began issuing more detailed updates this week in response to pressure from media outlets including WW. The daily reports now contain updates on the number of intensive care beds available and in use, and the remaining stock of ventilators.

Both those numbers show some reason for hope in Oregon. Thirty-one patients are on ventilators statewide, but 746 ventilators remain available. The supply increased today after the arrival of 140 ventilators shipped to Oregon by the federal government, in response to repeated demands from Gov. Kate Brown.

As quickly as COVID-19 has spread in Oregon, health officials have expressed cautious optimism that the virus won't overwhelm hospital capacity—if people follow Brown's executive order and stay away from each other.

It's still unclear whether that order came fast enough to prevent widespread transmission of COVID-19. But so far, Oregon's rapid increase in COVID-19 cases pales in comparison to the outbreaks in places like New York City and New Orleans.

A per-capita analysis by The New York Times on Friday showed Portland had 0.091 cases of the virus per 1,000 people, meaning less than 1 in 10,000 people have tested positive. In New York City, by comparison, 2.1 people per 1,000 have tested positive, as the world's densest metropolis sees a staggering spread. More than 1 in 1,000 people in New Orleans have the disease—meaning it was 10 times more widespread in that city than in Portland, at least as of Friday, March 27.

The only way to keep those numbers from rising faster? Stay home.