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Spurred by reports of doctors in Italy rationing ventilators for coronavirus patients and of overwhelmed hospitals throughout Europe, data scientists have built a mathematical model to help hospitals forecast what they might be facing in the days or weeks to come, based in part on the number of Covid-19 cases in their area.

That model, first offered to administrators at University of Pennsylvania hospitals, shows they could exceed capacity within weeks but, crucially, that social distancing measures now being implemented could avert that, a clear demonstration of the power of countermeasures being adopted by elected officials and others.

“The intention is to see what the capacity requirements for hospitalization, intensive care, and ventilators might be,” said Penn data scientist Corey Chivers. “The more we can get a handle on whether capacity is too low for what an area can expect, the more a hospital system can take steps” to address that shortfall.


The risk that Covid-19 will overwhelm hospitals in the U.S., much as it did first in Wuhan. China, and then in northern Italy, is driving the extraordinary restrictions on public life taken by states and municipalities: canceling sports events and concerts, closing schools, working from home, and other “social distancing” measures all have the goal of “flattening the curve,” or spreading out Covid-19 cases so they do not hit hospitals like a viral tsunami.

“While we don’t think we can completely stop the spread of Covid-19, one of our goals is to lessen the number of individuals exposed,” said Laila Woc-Colburn, an infectious disease specialist at Baylor College of Medicine. “Slowing the spread not only prevents health care workers from being overwhelmed with patients, but also gives those that are most vulnerable to the virus, mainly those over 50 and those who are immunocompromised, a lower chance for illness.”


Any hospital can use the Penn model by entering how many confirmed Covid-19 cases are in the region it draws patients from and how many inpatients it is currently treating, to see what might be in store and compare that to its capacity. Already, hospital systems are postponing elective surgeries, asking cancer patients to reschedule regular checkups (not treatment), and taking other steps to reduce demands on doctors and nurses so they can handle Covid-19 cases.

CHIME (“Covid-19 Hospital Impact Model for Epidemics”), built by Penn’s Chivers and others in “predictive healthcare,” is a basic epidemiological tool of infectious disease spread called a SIR model. It takes what’s known about the number of susceptible (S) people in an area (which for Covid-19 is everyone, since no one has immunity to the new coronavirus that causes it), the number of infected (I) people, and the number of recovered (R) people (who are presumed to be immune from subsequent infection). Because of the disastrous rollout of Covid-19 testing in the U.S., the researchers assume that only 15% of cases have been detected (but say it could be even lower).

The model then uses the best current estimates of how long someone is infectious (14 days); how many new cases each infected person causes (called the effective reproduction number, it’s about 2.5); the percentage of Covid-19 patients who need to be hospitalized (5%, reflecting the fact that most people have only mild or moderate illness); the percentage who need to be in an ICU (2%) or on a ventilator (1%); and the length of stay for each of these three.

If a hospital finds that more or fewer of its Covid-19 patients need to be admitted, or need intensive care or other measures, it can enter different numbers into the dynamic model.

The team built the model to help administrators at Penn’s hospitals determine how many beds and other resources they are likely to need in the coming weeks. Using current data (31 known cases in the region, two patients hospitalized), for instance, CHIME projects that by late April, 40 days from now, there will be 100 Covid-19 patients in the hospital every day, 50 in the ICU, and 30 on ventilators. By early May, 50 days hence, the figures are 300, 150, and 75, reflecting the exponential growth in the epidemic. The model also projects the daily number of new cases in each of these categories: 60, 25, and 12, respectively, 50 days from now.

That would strain and possibly exceed hospital capacity, but it is not inevitable. Although the reproduction number, written R, has acquired a somewhat mythic status since Covid-19 first appeared in Wuhan late last year, it is not set in stone. Measures taken by governments and individuals to reduce exposure to the virus can lower the real-life R (the “effective R,” epidemiologists call it), and did so in China, Singapore, South Korea, and other countries that implemented countermeasures. “You can lower R if there is a decrease in contact rates due to non-pharmacological interventions,” Chivers said.

If the doubling time increases to eight days from the six in the default version of the model, for instance, Penn’s numbers for late April fall dramatically: to five daily admissions, two ICU admissions, and one ventilator patient, with cumulative totals by early May of 60, 30, and 17, respectively.

  • Local governments impose limits on the number of beds, ventilators, and other medical machines. 36 states cause the part of the issue by their laws. The government limits the number of students that can become doctors. They have limits on the size of medical schools. Of the introductory physics classes I taught, I usually had 5 students who were premed. 4 out of the 5 would have made good to great doctors. Only one of the students on average was accepted. That is why many students go overseas for medical training. The bureaucrats at the state and local levels are the cause of medical emergency, and you can’t fire the b*****ds because you do not know they are there and cannot identify them. Wake up voters and get to your politicians to make sure this emergency does happen again.

  • The coronavirus “model” is still educated guess-work due to a huge variable : the willingness of people to participate in minimizing spread. ALL PEOPLE must co-operate in flattening the curve (everyone, voluntarily or mandated, including / particularly still exempted homeless). To avoid overwhelming of health care systems and thus increased death ratios, EVERYONE must hunker down – very well likely for all of 2020. A shocking new world and “lifestyle” , like in war-time but luckily without bullets, just adapt, simplify, expect less luxury, increase hygiene, enjoy simple things, take care of one another. This is Darwin-ian survival of the fittest : just by tempering spread, the survival rate will be better.

    • totally agree, it is a new model of life.
      In Spain, we have changed our habits in 2/3 days and it is very hard.
      But it was too late, the curve is going to be dramatic.
      I hope that next time we will be ready.
      Good luck and especially STAY_AT_HOME.

  • The base model assumes doubling of infected persons every 6 days. But the evidence from Europe is s doubling every 3 days – which would translate into a massively higher burden on healthcare facilities

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