(Reuters) – Oil prices fell on Wednesday on fears about fresh outbreaks of COVID-19 but prices drew some support from stimulus measures and positive tests of a drug that could save some critically ill patients.

Brent crude was down 38 cents, or 0.9%, at $40.58 a barrel at 1335 GMT. U.S. West Texas Intermediate (WTI) fell 56 cents, or 1.5%, to $37.82 a barrel.

The World Health Organization said it was moving to update its guidelines after results showed the corticosteroid medication dexamethasone cut death rates by about a third among the most severely ill COVID-19 patients.

Yet concerns persisted about the spread of the virus in some regions and the risk of second waves in places where the spread had started to slow.

“The pandemic is rapidly evolving and the outlook for oil demand will, therefore, remain plagued by a degree of uncertainty,” said Stephen Brennock of broker PVM.

To contain the spread of a new virus outbreak in Beijing, scores of flights were canceled and schools shut.

“We think the oil market is not currently pricing in a significant probability of either second waves of coronavirus cases in key consumers and the associated lockdowns, or anything less than a rapid return to economic business-as-usual,” Standard Chartered analysts said, pointing to a downside risk for prices in the medium term.

Weak economic activity is still weighing on demand for crude. Oil imports in Japan, the world’s fourth-biggest crude buyer, slumped in May to the lowest in almost three decades.

However, the Organization of the Petroleum Exporting Countries forecast a gradual recovery in oil demand and said record supply cuts by the group and other producers were already helping rebalance the market.

Business confidence at Asian companies sank to an 11-year low in the second quarter, a Thomson Reuters/INSEAD survey found, with two-thirds of firms polled seeing a worsening COVID-19 pandemic as the biggest risk over the next six months.

(Reporting by Bozorgmehr Sharafedin in London; Additional reporting Jane Chung in Seoul; Editing by Louise Heavens, Mark Potter and David Clarke)