The rare respiratory illness that cropped up in multiple states recently has been confirmed in four new states, public health officials said Wednesday.

Cases have been confirmed in Connecticut, Montana, Nebraska and Virginia, according to the Centers for Disease Control and Prevention, which means that 16 states now have confirmed cases of the virus. The others are: Alabama, Colorado, Illinois, Indiana, Iowa, Kansas, Kentucky, Louisiana, Missouri, Oklahoma, Pennsylvania and New York.

The rare virus strain, enterovirus 68, can cause severe breathing problems. There have been 140 cases confirmed by laboratory tests, the CDC said, but it is believed that many more people have the virus and that it will continue to appear in additional states in the near future.

Enteroviruses are very common, causing between 10 million and 15 million infections each year. But this particular strain has not appeared very often since it was first isolated in California in 1962.

Public health officials have said that other states are presumably going to join this list, with cases expected to be confirmed in other places where there have been clusters of children suffering from respiratory illnesses. There are suspected cases in Georgia and Michigan, while health officials in Ohio and Utah have told The Post they suspect that they have cases of the virus.

The CDC expects that the number of infections is going to drop later in the year. Most enterovirus infections in the United States occur in the summer and fall, so these are coming at a typical time, Anne Schuchat, director of the CDC’s National Center for Immunization and Respiratory Diseases, told reporters last week.

Only children have been confirmed to have the virus so far, as they lack the immunity that comes from being exposed to a disease, according to the CDC. The virus spreads when an infected person coughs or sneezes, so health officials are encouraging people to wash their hands and avoid excessive contact with those already sick. (Here’s the advice in infographic form.)