The long reach of the new coronavirus in the U.S. could be seen Monday in the growing number of people moving into quarantine—from parishioners who shook hands with a priest, to thousands on a cruise ship, to senior aides of a top New York official.

With each new case that is diagnosed—and there are now more than 400, according to the U.S. Centers for Disease Control and Prevention—authorities are recommending everyone who came in close contact with that person while they were infectious isolate themselves to stop the spread of COVID-19.

Despite those precautions, the CDC said Monday that the march of the virus across the country is inevitable—and the outbreak that has already infiltrated 34 states and Washington, D.C., won’t end this year.

“As the trajectory of the outbreak continues, many people in the U.S. at some time either this year or next will be exposed to this virus, and there’s a good chance many will become sick,” Dr. Nancy Messonnier, director of the National Center for Immunization and Respiratory Diseases, said in a teleconference.

The numbers bear that out. As of Monday morning, the CDC had identified 164 cases in the U.S. Shortly after noon, the tally was updated to 423, with 19 deaths. Later in the day, Washington state announced the deaths of three more senior citizens from the Life Care Center nursing home in Kirkland, where dozens of staff members are home sick. California also announced the death of a woman in her 60s.

Washington state and California previously had most of the cases, but New York’s number was up to 142 by Monday, a 35 percent single-day jump and now the second most in the nation—underscoring just how quickly the virus can spread in densely populated areas.

The newly diagnosed New Yorkers include Rick Cotton, the director of the Port Authority, the bi-state agency that controls the airports and other travel hubs. Gov. Andrew Cuomo said Cotton and some members of his senior team will now be under quarantine.

(Cuomo also said the state has created its own brand of hand sanitizer; prison inmates will be making 100,000 gallons per week of the floral-scented product, and it will be provided to schools and public agencies as a hedge against price-gouging.)

In Washington, D.C., anyone who attended Christ Church Georgetown on Feb. 24 or between Feb. 28 and March 3—hundreds of people—has been asked to self-quarantine because a rector there was diagnosed with the coronavirus.

Also in the nation’s capital, several members of Congress announced they were self-quarantining because they came in contact with someone who tested positive while they attended the CPAC confab, although Rep. Louie Gohmert (R-TX) tweeted that he also had contact but was not self-isolating because an unnamed CDC doctor told him it was unnecessary.

Passengers on board the Grand Princess cruise ship, which was held off the coast of California but finally allowed to dock in Oakland on Monday, won’t have a choice. Anyone sick will be sent to urgent care and all other Americans on board will be sent to military bases for 14 days of quarantine.

The quarantines are meant to slow the spread of COVID-19, giving the government and the health-care industry more time to cope. But not everyone is taking them seriously.

A woman’s positive test in Missouri led to an entire school being shuttered after her father and daughter broke voluntary quarantine recommendations and went to a daddy-daughter dance. Officials said they will consider taking legal action if they do it again.

Other schools are taking measures to avoid spreading the virus or just to calm jangled nerves. Columbia University canceled classes for two days because a single person on campus had been exposed; Princeton University said all lectures and seminars will be held via teleconference to reduce crowds; Rice University scrapped all in-person classes for a week, despite no report of exposure.

Globally, more than 110,000 people have been infected with the bug, which originated in Wuhan, China, and the fallout continues to be dramatic.

In Italy, riots broke out in dozens of jails and prisons after visitation rights were curtailed for health reasons. Six inmates were killed and others escaped, guards were taken hostage, and fires were set. Hours later, the country announced a nationwide lockdown, meaning the movements of 60 million people will be restricted.

Saudi Arabia, meanwhile, is barring flights from more countries, adding Germany, France, and Oman to Italy, Lebanon, Egypt, Iraq, United Arab Emirates, Bahrain, and Kuwait. Olympic organizers announced that Thursday’s torch-lighting ceremony will be held without spectators for the first time in decades.