A wave of preliminary results of antibody tests is adding to our understanding of how the novel coronavirus is moving through the American population. But there are reasons to be cautious about interpreting the findings.

In contrast with tests for active infection, these tests detect antibodies the body creates after someone has been infected with the virus. So they should identify people who got sick and recovered from the disease covid-19, or who carried the virus but had no symptoms.

In recent weeks, in separate studies, researchers have announced that roughly 2.5 to 4 percent of residents in Santa Clara County, Calif.; 3 to 6 percent of people in Los Angeles County; 6 percent in Miami-Dade County; and 14 percent across New York state have been infected at some point by the coronavirus. That last study estimated that as many as 1 in 5 residents of New York City had been infected.

Unfortunately, these new antibody tests can have high error rates, and in the studies involving Los Angeles County, Miami-Dade County and New York, the full scientific reports are not yet available for scientists to review. The Santa Clara County study also came under criticism from other scholars for its methodology and statistical analysis.

What can we learn from these studies? First, they reveal that even in the hardest-hit communities, most people are still at risk of being infected by the virus. We are a long, long way from developing “herd immunity” — meaning that so many are immune that there are not enough susceptible people left for the virus to circulate. This would require at least 60 percent of the population to be infected. With low levels of immunity in the population, if we lift restrictions on movement and “reopen” the economy without proper precautions, the coronavirus outbreak could again take off.

Even more worrisome are some of the other conclusions that people are drawing from the results. Last month, two Stanford Medicine professors who contributed to the Santa Clara and Los Angeles counties studies, Eran Bendavid and Jay Bhattacharya, wrote an opinion article in the Wall Street Journal titled “Is the Coronavirus as Deadly as They Say?” They argued that previous overestimates of the death rate for coronavirus infection — now “corrected” by the antibody studies — meant that massive shutdowns and stay-in place orders were likely excessive.

It was already widely known, however, that we often only identify the most severe covid-19 cases, through testing swab samples. Early (rough) estimates are that a quarter or even as many as half of infections have no symptoms at all; those would be totally missed as well. The current official tally in Santa Clara County is 100 deaths and 2,084 confirmed cases, which would crudely suggest that 4.7 percent of cases are fatal. Naturally, antibody tests can help us pin down the true death rate following infection by allowing us to include everyone, even infections with no symptoms, in the denominator. Based on the Santa Clara and Los Angeles counties studies’ results, only 0.1 to 0.2 percent of infections are fatal.

It’s unclear that this estimate will hold up to further scrutiny. Notably, if the fatality rate were truly only 0.1 percent, that implies that all 8 million people in New York City have already been infected — which seems unlikely. That supposition is also contradicted by the New York antibody test results, which suggest that fatality rates there are closer to 0.5 or 1 percent. But even if the California numbers are accurate, they in no way warrant a conclusion that shutdowns were an overreaction.

If we know anything about this virus, it is that it spreads easily. Unlike influenza, there is virtually no population-level immunity, meaning many more people can be infected, millions in the United States alone. We also know that it overwhelms health-care systems. In New York City, there have been more than 40,000 hospitalizations and nearly 17,000 deaths — and that follows the Italian catastrophe, in which some hospitals, including in the Lombardy region, were reportedly forced to triage care, choosing who would receive scarce ventilators.

With the potential for huge numbers of people to be infected, taking comfort in a lower death rate would be the wrong way to think about the results — and easing up efforts to blunt this deadly public health threat would be a serious mistake. We know firsthand that covid-19 can quickly spiral out of control in cities and entire regions of countries, with devastating consequences. Preventing the disasters we’ve seen in Wuhan, New York City and Lombardy must remain our first priority. Antibody studies alone cannot tell us if we are ready to reopen the economy. That will instead depend on our preparedness to test, trace and isolate infected people so that we don’t end up back where we started.