Now in its third week, the coronavirus health emergency has touched every neighborhood in Boston as the number of known “positive” cases within the city grew to 938 — with 3 deaths— amid a worsening statewide and national crisis.

Massachusetts will remain in a state of emergency for the next month, at minimum, as Governor Charlie Baker warned residents to prepare for a surge in COVID-19 patients needing hospitalization projected to hit the state between next Tuesday (April 7) and Fri., April 17.

The overall number of cases statewide crossed the 5,000 mark Monday and reached 6,620 by Tuesday, according to the state’s Department of Public Health. A total of 89 deaths have been attributed to COVID-19 through Tuesday afternoon, an increase of 33 in a single day— the biggest one-day increase in the fatality rate so far.

A week after closing all non-essential businesses to workers and customers, Baker said on Tuesday that he was extending his executive order beyond April 7 to keep most businesses physically closed through at least May 4. (Last Wednesday, he extended his order on the closing of schools until at least that same day.) He also said his order would keep in place the social distancing guidance from the state limiting gatherings to no more than 10 people.

The state was considering taking steps to prevent people from gathering in parks and other public spaces, but stopped short of that while urging everyone to follow the direction on their own. Mayor Walsh gave similar advice and ordered gatherings at basketball and street hockey courts off limits.

“Coronavirus is in each of our neighborhoods,” said Marty Martinez, health and human services chief in Boston, during a Monday press conference at City Hall. Close to half of cases in the city involved infected individuals under the age of 39, he said.

On Tuesday, Baker announced that the state will be turning the DCU Center in Worcester into a 250-bed medical facility to treat patients with lower acuity of symptoms. He noted that it is one of three field medical stations for which the state has requested approval from the federal government through the Massachusetts Emergency Medical Center.

The state has continued to ramp up its testing capacity, with the number of people tested landing at almost 43,000 Monday, an increase of more than 3,700 over Sunday. In a video update posted after three consecutive overnight shifts, emergency physician and Boston state Rep. Jon Santiago said the state’s testing numbers are “fantastic” and said it’s time to focus now on contact tracing.

The governor identified four key areas of focus in the days leading up to the anticipated mid-April peak: protective gear, hospital bed capacity, ventilators, and staffing. One step the administration is taking is setting up dedicated nursing homes to treat older patients with COVID-19, aiming to prevent those individuals from infecting other residents and staff in skilled nursing facilities.

Last Friday, Baker urged people who are thinking about traveling to Massachusetts to reconsider, and said that anyone arriving in the state through an airport or train station will be advised to self-quarantine for 14 days.

“We’re asking that folks considering travel to Massachusetts for whatever reason to not travel to our communities, especially if you have symptoms,” Baker said. The new guidance from Baker follows a recommendation from the White House coronavirus task force on Tuesday that anyone who has left New York or who has passed through New York City —the nation’s hottest coronavirus zones just 200 miles south on Interstate 95 — self-quarantine for two weeks.

On Friday, the House passed a bill (H 4598) that would extend the state income tax filing deadline from April 15 to July 15, something Baker and legislative leaders said they’ve already agreed to; give restaurants the ability to sell beer and wine via take-out or delivery as they try to remain afloat during the pandemic; and give municipalities more flexibility around property tax deadlines.

Also Saturday morning, the White House announced that President Trump had approved the disaster declaration requested Thursday by Baker, opening a spigot for more federal funding to supplement local COVID-19 efforts in the Bay State.

The Baker administration said that the disaster declaration means that “affected local governments, state agencies and certain private non-profit organizations statewide will be reimbursed for 75 percent of their costs associated with response and emergency protective measures.”

It also means that the Mass. Department of Mental Health will receive federal aid to “assist individuals and families in recovering from the psychological effects of the COVID-19 outbreak through electronic phone and chat technology.”

The public health emergency is accompanied by economic gloom. Unemployment claims skyrocketed in Massachusetts last week as the federal Department of Labor reported never-before-seen levels of need nationwide during the coronavirus crisis. The federal agency’s report listed 7,449 non-seasonally adjusted advance claims in Massachusetts during the week ending March 14 and 147,995 during the week ending March 21, a nearly twentyfold increase.

A similar trend carried nationwide: seasonally adjusted initial claims jumped 3 million week over week to about 3.28 million in total, smashing previous records with swaths of the country out of work due to the pandemic.

“This marks the highest level of seasonally adjusted initial claims in the history of the seasonally adjusted series,” the Department of Labor wrote in its report. “The previous high was 695,000 in October of 1982.”

Baker signed a bill last week expediting access to state unemployment benefits for employees who lose access to work because of COVID-19. Those who submit successful applications will no longer face a one-week waiting period and should be able to receive aid within seven to 10 days.

In a report last week, Goldman Sachs estimated the national unemployment rate could rise from 3.5 percent to 9 percent due to the outbreak, with the impact particularly sharp on low-wage jobs vulnerable to economic downturn.

With rents and mortgages due on Wednesday, the first of the month, community groups worry that the Legislature has not yet passed a bill protecting tenants and homeowners from evictions and foreclosures.

Dorchester’s Lew Finfer, co-director of the Massachusetts Communities Action Network, said that the federal relief bill passed last week has holes that leave many tenants exposed if they cannot pay their rents.

And despite Baker’s assurances that nobody can be evicted while the housing courts are closed due to coronavirus, Finfer said many renters don’t understand that and are putting themselves at risk to try to pay rent. (See story, Page 16).

“The courts are closed but that message isn’t generally out there to tenants and if they’re getting eviction notices, they think they’re in trouble. They’re desperate and doing whatever they need to do to be able to pay their rent, or they’re moving,” he said.

A letter signed by 80 community groups and unions urging passage of a tenant-homeowner protection bill was sent to Baker, Speaker Robert DeLeo, Senate President Karen Spilka.

“The House needs to be strong on it, and the governor needs to understand the need for it,” Finfer said.