(CNN)- If the United States had begun enforcing social distancing measures just a week earlier in March, an estimated 36,000 lives would have been saved, according to new research from Columbia University.

And if the country had locked down two weeks earlier than it did, the vast majority of deaths — about 84% — would have been avoided, the research team estimated.

While the study has not yet been peer-reviewed, it is a sign of just how steep the cost of inaction was as Covid-19 raced across America. Even small shifts in timing — a matter of days — would have made a difference, preventing much of the virus’ exponential growth in cities like New York, Los Angeles and New Orleans, the university found.

As all 50 states lift lockdowns to varying degrees, the researchers had these words of caution: “Now that Covid-19 is established as a global pandemic, rapid response remains essential to avoid large-scale resurgences of infections and deaths in locations with reopening plans.”

And the pandemic shows no signs of abating. Infection rates are on the rise across Latin America, as restrictions ease elsewhere. The World Health Organization warned yesterday that “we still have a long way to go,” after it recorded the highest total number of infections in a 24-hour period — more than 106,000. Today marks a new milestone: Global coronavirus cases have passed 5 million.