SEATTLE — An influential modeling institute is forecasting specific reopening dates for states shut down by the coronavirus. The recommendations are based on projections for when each state’s infections will drop below one per 1 million people. The University of Washington’s Institute for Health Metrics and Evaluation says Hawaii, Montana, Vermont and West Virginia could open by May 4, if they restrict large gatherings, test widely and quarantine the contacts of people who test positive.

According to the model, Arkansas, Florida, Georgia, Iowa, Nebraska, North Dakota, Oklahoma, South Dakota and Utah are among states that would need to wait until late June or early July.

The institute says state decisions on reopening should be made based on the situation closer to the hoped-for date of reopening. Its projections have varied widely over time, drawing criticism from researchers with other types of models. The Seattle model is the one most often mentioned by U.S. health officials at White House briefings.

It uses U.S. hospitalization and death data, along with observed trends in China, Italy and Spain to project what will happen next in the United States. Uncertainty is built into any mathematical model that tries to predict the future.