The Obama administration says it expects to see more cases of swine flu in more U.S. states, but there are no plans to close the U.S. border with Mexico, the country at the epicenter of the influenza outbreak.  The number of confirmed swine flu cases in the United States has doubled since Monday and now stands at more than four dozen.

One day after President Obama said the spread of swine flu in the United States is cause for concern but not alarm, Homeland Security Secretary Janet Napolitano predicted the number of Americans contracting the virus will continue to grow.

"We anticipate that there will be confirmed cases in more states as we go through the coming days, and I think the feeling ought to be of preparation, not fear," Napolitano said. 

Napolitano was speaking on NBC's Today program.

More than 150 deaths have been blamed on swine flu in Mexico and recent travelers to Mexico account for most infections in other countries.

While the Obama administration is urging Americans to avoid non-essential travel to Mexico, Secretary Napolitano says there are no plans to close the 3,000 kilometer U.S.-Mexico border, which sees hundreds of thousands of crossings each day.

"That is something that always can be considered, but you have to look at the costs," Napolitano said.  "We literally have thousands of trucks and lots of commerce that cross that border."

Instead, the secretary says anyone with flu-like symptoms should stay at home, and that everyone should take simple precautions like washing their hands.

In addition to the United States and Mexico, swine flu cases have been confirmed in New Zealand, Israel, Spain, Scotland, and Canada.  Suspected cases have been reported in several other countries.

No swine flu-related deaths have been reported outside of Mexico.