Co-director of the intensive care unit at CommonSpirit’s Dignity Health California Hospital Medical Center, Dr. Zafia Anklesaria, 35, who is seven months pregnant, attends to a COVID-19 patient in the hospital where she works, during the coronavirus disease (COVID-19) outbreak, in Los Angeles, California, U.S., May 18, 2020.Lucy Nicholson | ReutersThe average number of new daily cases of the coronavirus in the United States hit another record on Monday as 36 states reported worrying rises in the number of hospitalized patients.The average number of patients hospitalized with Covid-19 over the past seven days rose by at least 5% in 36 states as of Monday, according to a CNBC analysis of data from the Covid Tracking Project. Hospitalizations lag behind cases as it takes time for people to get diagnosed and become sick enough to require medical attention. However, epidemiologists point to hospitalizations as a more telling indicator of the severity of an outbreak than new cases, which can fluctuate based on testing.In Illinois, where Gov. J.B. Pritzker announced new business restrictions last week in four counties and Chicago, 2,638 people were hospitalized with Covid-19 as of Monday, according to data compiled by Covid Tracking Project, which tracks testing, hospitalization and other data on the outbreak. It’s run by journalists at The Atlantic. That pushed their seven-day average up over 2,480, a more than 24% increase compared with a week ago, according to CNBC’s analysis.In Texas, El Paso County Judge Ricardo Samaniego issued a curfew on Sunday to protect “overwhelmed and exhausted” hospitals and workers. More than 5,200 people there were in hospitals with Covid-19 on Monday, Covid Tracking Project’s data shows. The Lone Star state has had an average of about 4,970 Covid-19 patients in hospitals on any given day over the past week, up more than 18% compared with the previous week.”I think that the community and the country needs to realize that this is just the beginning of what could be a dark and tragic time over the next four to six weeks,” Dr. Ogechika Alozie, chief medical officer of Del Sol Medical Center in El Paso, told CNBC’s Shep Smith on Monday.The average number of hospitalized patients over the past seven days declined by 5% or more in just four states: Alaska, Hawaii, Kansas and Maine, according to CNBC’s analysis.”This is a harbinger of a very tough winter that’s coming,” Dr. Bill Schaffner, an epidemiologist at Vanderbilt University, said in a phone interview. “I think hospitals are going to be very, very stressed this fall and winter.”While the number of hospitalized patients steadily marches upward, daily new cases skyrocket. Over the past seven days, the U.S. reported an average of 69,967 new cases every day, the highest seven-day average recorded yet, according to a CNBC analysis of Johns Hopkins University data. The seven-day average is up more than 19% compared with a week ago, according to CNBC’s analysis.At the same time, the U.S. is testing more people than ever, according to the Covid Tracking Project. However, more testing cannot account for the rise in cases, health officials say, because the percent of tests that are positive has increased as well. About 6.3% of tests were positive on Monday based on a seven-day average, according to Johns Hopkins, up from 5.3% a week earlier.Schaffner pointed to progress made by scientists in developing treatments for Covid-19 and doctors’ advances in improving care that both reduce the risk of death. But, he added, “there will be an increase in deaths,” especially as much of the country fails to adhere to public health guidance such as mask wearing and social distancing.He added that flu season typically begins to gain steam in November, and that could add another complication to the U.S. response to the pandemic. The diseases caused by the flu and the coronavirus “look very much alike” and health workers will face new challenges in trying to diagnose Covid-19 and flu patients, he said.Schaffner said the Trump administration is relying largely on research and advances in therapeutics and vaccines for its response to the pandemic. But there’s a misunderstanding among the public that once a vaccine is distributed, people can ignore public health guidance. That won’t be the case, he said, as we don’t know how effective any vaccine in development will prove to be.”We can’t throw our masks in the trash when we’re vaccinated,” he said.The U.S. is not alone in experiencing a worsening outbreak. The virus is surging across much of Europe, as well. The World Health Organization warned Monday that some countries might need to implement severe business restrictions again to take the “heat” out of their outbreaks.”We’re well behind this virus,” Dr. Mike Ryan, executive director of the WHO’s health emergencies program, said during a news conference at the agency’s Geneva headquarters. “We will have to get ahead of this virus, and [that] may require sacrifice for many, many people in terms of their personal lives.”— CNBC’s Nate Rattner and Berkeley Lovelace contributed to this report.