Widespread testing required for tracking, responding to COVID-19 pandemic

As recently as three months ago, few people in the U.S. were aware of COVID-19, and most of those afflicted were in China. In the intervening weeks, the spread of the coronavirus has strained the American health care system and destabilized the nation’s economy. Public health officials are having great difficulty determining the numbers and concentrations of COVID cases, and the solution to addressing the problem — barring the early find of an effective vaccine — lies in widespread testing, both for the virus and for the antibodies infected people produce in response to the virus.

At least 430,000 people in the U.S. have tested positive for the virus, according to a COVID-19 dashboard created by Johns Hopkins University's Whiting School of Engineering. Some public health officials believe the actual number could be much higher. As the virus has spread around the world, demand for testing has overwhelmed many labs and testing sites, and delays in obtaining results have persisted.

As an applied mathematician, I wondered how I could contribute to the fight against COVID-19, and it occurred to me that it might not be that difficult to make a simple mathematical model. My model assumes exponential growth infections, sickness, recovery and death, as initially societal interactions continue. It assumes that sickness trails infection by generally one to two weeks, and that generally recovery or death occurs one to two weeks after that. These and other parameter values come from the data gathered so far.

My model and other more-sophisticated models provide important information, such as how to keep the total number of those requiring hospitalization down to levels that our health care system can manage — if with great effort. The models make clear that many more people are infected but not yet sick, than the number who are already sick. And it provides the data needed to understand how this pandemic will end.

The data that we already have tell us that left to its own devices — without social distancing—the virus will spread exponentially through a susceptible population, roughly tripling the number who become sick every four or five days. We know that once infected, a person sheds the virus for a period of time before showing symptoms—perhaps a few days, or maybe much longer.

Some people have been infected for at least a few weeks before getting sick; will they eventually become ill, or can they remain infected and shedding virus but appearing well for an indefinite length of time? We also do not know how many people go from being infected to recovering without showing any symptoms. Recent data on newly-confirmed cases from Italy, Germany and New York suggest that the number of newly-confirmed cases may be peaking sooner than was originally projected. These early peaks may indicate that there are more people who have quietly recovered from COVID-19 than we originally expected, but we do not know this for sure.

How do we find these numbers — those infected and quietly carrying the disease, and those who have quietly recovered? The answer is testing. Lots of testing. The tests for the virus itself are needed to find those who carry the virus, and the antibody tests are needed to find those who have recovered without being sick. And we will need an army of medical staff to carry out this testing.

If there are many in the first group and few in the second, then this coronavirus will continue to pose a critical threat to us for some time to come, but, conversely, few in the first group and many in the second indicates that we are far closer to the end of this crisis than we could have previously hoped. Further, some tests will be needed to control viral flare-ups down the road.

It will likely not be possible to test everyone in the U.S. or in the world, so we will need to be very careful how we design our testing. Nonetheless, there would not seem to be any intelligent path out of this crisis that does not involve careful, well-designed, large-scale testing.

Joseph D. Fehribach is an applied mathematician and professor of mathematical sciences at Worcester Polytechnic Institute.