In recent weeks, the spread of swine flu in Mexico and the government’s response of shutting down schools and canceling public gatherings brought migration here and elsewhere nearly to a halt. But demographers expect the deep flu-related decline to be temporary.

With so many Mexicans remaining in their home villages, the population of illegal immigrants in the United States stopped growing and might have slightly decreased in the last year, an abrupt shift after a decade of yearly influxes, research by demographers in the United States shows. Mexicans account for 32 percent of immigrants in the United States, and more than half of them lack legal status, the Pew center has reported.

Still, at least 11 million illegal immigrants remain in the United States, the demographers say. Despite collapsing job markets in construction and other low-wage work, there has been no exodus among Mexicans living in the United States, the Mexican census figures show. About the same number of migrants  450,000  returned to Mexico in 2008 as in 2007.

Some researchers argue that the drop in crossings from Mexico proves that tough law enforcement at the border and in American workplaces can reduce illegal immigration in times of rising unemployment in the United States. Immigration and Customs Enforcement officials stepped up factory and community raids last year, and the Border Patrol expanded its force by 17 percent in one year, to nearly 17,500 agents.

“The latest evidence suggests that you can reverse the flow,” said Steven A. Camarota, a demographer at the Center for Immigration Studies, a research group in Washington that calls for reduced immigration. “It is not set in stone, so with some mix of enforcement and the economy, fewer will come and more will go home.”

But Wayne Cornelius, the director of the Center for Comparative Immigration Studies at the University of California, San Diego, predicted that if the United States job market revived, border enforcement would become much less of a deterrent.