Editor’s note: This story has been updated to reflect more counties issuing stay-at-home orders.

Many of Texas’ biggest urban cities and counties are ordering residents to stay indoors.

Harris County Judge Lina Hidalgo on Tuesday morning ordered Harris County residents — all 4.5 million of them — to stay in their homes as much as possible as the state grapples with the rapid spread of the novel coronavirus. Further north, Fort Worth Mayor Betsy Price and Tarrant County Judge Glen Whitley issued a similar directive later in the morning. Collin County and El Paso County officials later did the same.

San Antonio Mayor Ron Nirenberg and Bexar County Judge Nelson Wolff on Monday evening issued a “Stay Home, Work Safe” order effective from 11:59 p.m. Tuesday through 11:59 p.m. April 9. The move came one day after Dallas County issued a similar order. And the Austin City Council and Travis County teamed up Tuesday to issue a similar stay-at-home decree.

“All of us should stay home unless our jobs are essential for the health and safety of our community,” Hidalgo said of the county’s “Stay Home, Work Safe” order. “We are taking all of this one step at a time.” Harris and Tarrant counties’ directives are in effect from midnight Tuesday through April 3. San Antonio’s remains in effect until 11:59 p.m. April 9, while Austin’s goes until April 13.

“By staying home, we are saving lives and flattening the curve of the virus,” Hidalgo said.

The orders represent some of the most stringent measures local officials in Texas have taken so far to address the colossal public health crisis. They go a step further than Gov. Greg Abbott, who has ordered bars and restaurants across the state closed for dine-in and told Texans to avoid groups larger than 10 but resisted issuing a complete shelter-in-place order. The governor previously said he supported local jurisdictions issuing such orders if the circumstances warrant them.

“Today’s announcement is not meant to be alarmist or to cause panic,” Price said. “If you’re at your residence, stay home. Go out only for essential items.”

Local officials across the state emphasized that the orders do not completely bar residents from leaving their homes; people are encouraged to go on outdoor walks while keeping a 6-foot distance from others, visit grocery stores and pick up medicine.

Health care workers and other businesses providing “essential services” will still be working in all the counties issuing the mandatory shelter-in-place orders. Gas stations will also remain open.

San Antonio officials said their ordinance will be enforced through civil penalties or fines. The city will also be using law enforcement to ensure people remain in compliance.

The cities of Waco and Lubbock issued similar directives Monday.

In a phone interview Monday morning, Austin Mayor Steve Adler said that many of the major cities had been in contact with one another, with each municipality weighing things like the stress on the economy, health care sector and public in determining whether to issue local mandates.

“Our decisions are being motivated by the analysis being done here and the modeling being done here, but each city and county assess for themselves, while also recognizing there’s benefit in having action that’s unified that covers a lot of the state,” he said.

The orders are not an anomaly globally. Californians are operating under a similar crackdown, as is Italy, which is under lockdown as the death toll Thursday surpassed that of China, where the virus originated.

Still, Abbott has taken a more measured approach statewide. The governor’s order limits social gatherings to 10 people, prohibits eating and drinking at restaurants and bars, closes gyms, and bans people from visiting nursing homes except for critical care, among other things, through midnight April 3.

In a letter to Abbott, some local officials and health care executives requested a statewide directive, which they touted as an aggressive way to mitigate the spread of the contagion while relieving some of the load off of the state’s health care system.

On Monday night, Bexar County Judge Nelson Wolff said the city was taking “the necessary steps to prevent a COVID-19 spike that would overwhelm our hospital system.”

Official numbers from the Texas Department of State Health Services and the Centers for Disease Control and Prevention show that at least 373 people have tested positive for the coronavirus in Texas. The actual number is significantly higher given that the state’s numbers lag behind certain counties’ individual numbers and far fewer than 1% of Texans have been tested.

Disclosure: Steve Adler, a former Texas Tribune board chairman, has been a financial supporter of The Texas Tribune, a nonprofit, nonpartisan news organization that is funded in part by donations from members, foundations and corporate sponsors. Financial supporters play no role in the Tribune's journalism. Find a complete list of them here.