Prime Minister Boris Johnson said on Monday that people should avoid gatherings and crowded places, such as pubs, clubs and theatres - to curb the spread of the disease.
But landlords in Scarborough say people are still supporting their locals and some have pledged to stay open until they are ordered to shut.
Tony Snow, licensee at The Courtyard and Chairman of Scarborough Pubwatch, said: “I’m optimistic about it and think a lot of the pubs will be.
“When people were out at the weekend, we did wonder whether people were coming out in case they were going to be stuck at home for the next few weeks.”
He said customers have still been supporting his pub and thinks it may be because there have not been as many confirmed cases of coronavirus in North Yorkshire as other parts of the country.
Mr Snow expects pubs to be forced to close eventually, but said landlords could use this time to carry out updates and refurbishment work.
He cautiously welcomed the Chancellor’s announcement on Tuesday of Government-backed loans, cash grants, and rates-breaks to help see businesses like theirs through the crisis.
But he said more information was needed about the measures, and there should be clarification over when insurance policies would be paid if businesses did shut.
Fellow licensee Danny Smith, who runs Scholars Bar, said the cancellation of so many sports fixtures has hit his trade.
“It’s just uncertainty and people not knowing what’s going to happen and waiting for the inevitable closing,” he said.
“We’re still getting a few people out. I’ve reduced prices to try to keep people in but because we’re a sports bar we’ve been hit quite hard. I’ve cut staff back as well.
“If we have to close, we’ll be OK for a couple of months.
“There’s nothing we can do. It’s nothing we have done wrong.”
The town’s licensees will meet on Monday to discuss the impact of the pandemic on the local pub trade.
Chairman of the Campaign for Real Ale Nik Antona has called for the Government to do more to help pubs, clubs and breweries get through the coming months.
He said: “The Government’s announced measures to mitigate the devasting impact of COVID-19 do not go far enough in ensuring no pub, club or brewery goes out of business as a result of the current crisis.
“While a business rate holiday for all hospitality businesses and rate relief for eligible pubs will help alleviate some costs, this will do little to compensate for the potential collapse of cashflow in businesses which customers have been told to stay away from.”