How many Mexicans actually cross the border illegally?

• Report based on mathematical calculations indicates the increased border security is work
• Donald Trump's rhetoric has helped fuel most Americans' belief that border traffic is increasing
• Experts believe that other factors, such as increased cost and improved Mexican economy, has reduced crossings

Editor's note: The Arizona Republic originally published this story in October 2016, just before the U.S. presidential election. The data revealed in the Department of Homeland Security report shows increased border security measures over the past decade have resulted in a significant decrease in the number of Mexicans entering the U.S. illegally along the southern border.

NOGALES, Sonora — Pedro Sanchez Valladares climbed over the border fence and trekked through the desert for half an hour. He was almost at a pickup point to meet a smuggling crew to drive him to Phoenix and then to his final destination, Charlotte, N.C.

Then he heard a Border Patrol agent yell, "Stop!"

Sanchez Valladares knew he'd been caught. He didn't run.

"I just sat down," he said.

Crossing the border illegally was far easier 22 years ago, when the migrant, now 37, first came to the U.S. as a 14-year-old.

"I crossed in the middle of the city, in the daytime," recalled Sanchez Valladares, who was deported to Mexico in 2008, leaving behind four children in the U.S., two of them in Charlotte. "It took me about 15 minutes."

Now crossing illegally is "very hard,"  conceded Sanchez Valladares, who is barred from legally returning to the U.S. for 10 years.

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That is confirmed by a new internal Department of Homeland Security report, obtained by The Arizona Republic and azcentral.com, that concludes ramped-up border enforcement is working, helping to reduce successful crossings to one-tenth of what they were a decade earlier across the southern U.S. border with Mexico. The research is based on complicated mathematical calculations using published and internal Border Patrol data.

But the bottom line is this: Far fewer migrants from Mexico are successfully entering the country illegally than a decade ago because stepped-up border enforcement means fewer are trying, more are getting caught and more are giving up.

The report comes as Republican presidential nominee Donald Trump has promised to build a giant wall to keep migrants such as Sanchez Valladares from illegally crossing the border from Mexico into the U.S.

The campaign promise, which Trump repeats to cheers at almost every stump speech, including his Oct. 4 rally in Prescott Valley, has reinforced public perceptions that the border with Mexico remains out of control.

The U.S. has spent $132 billion since fiscal year 2005 on border security, according to the Migration Policy Institute. That spending  includes thousands of additional agents, fencing, ground sensors, surveillance cameras with night vision, radar, helicopters, drones and criminal prosecutions of undocumented migrants caught crossing illegally.

And there is growing evidence, statistical and anecdotal, that the border buildup has significantly deterred illegal border crossings. And that's happening even as the U.S. economy has recovered following the Great Recession, creating job openings in this country that drew waves of undocumented immigrants here in the past.

Border Patrol apprehensions, expected to total about 400,000 in fiscal year 2016, have dropped to the lowest levels since the early 1970s. The size of the nation's undocumented population has leveled off at about 11.1 million after years of rapid growth, according to the Pew Research Center.

And the new report offers even more fresh data. The research mathematically calculates how often undocumented migrants successfully enter the U.S. — not just how many the Border Patrol catches.

There was a time before the Great Recession when the vast majority of migrants who tried to cross the border illegally made it. Those caught by the Border Patrol and returned to Mexico simply turned around and crossed again until they were successful.

That's no longer true, said Bryan Roberts, co-author of the DHS report, done while he was at the Institute for Defense Analysis, which was contracted by DHS. He is now a research economist and previously was DHS assistant director for border and immigration program analysis and evaluation from 2005 to January 2011.

SUMMARY:Internal border report calculates drop in successful illegal entries

According to the DHS report,  the number of successful illegal entries — including people making multiple attempts  — between ports of entry along the entire southern border with Mexico has plummeted from 1.7 million in 2005 to 170,000 in 2015. The calculations are based on a mathematical formula using published Border Patrol apprehension data and internal re-apprehension data and years of data from surveys conducted by researchers in Mexico with deported migrants in Mexico.

In an interview before The Republic obtained a copy of the report, Roberts noted that the calculation is based on migrants from Mexico trying to cross the border without being caught. The number does not include the nearly 80,000 unaccompanied minors and families from Central America who turned themselves in to the Border Patrol in 2015 seeking asylum.

Roberts presented a version of the report with similar findings on Sept. 2 at a forum, broadcast on C-SPAN, at the Cato Institute, a libertarian think tank headquartered in Washington, D.C. There, Roberts noted the Department of Homeland Security had not made public the more detailed version he also worked on while at the Institute for Defense Analysis.

The DHS report calculates that the probability that a migrant will give up trying to cross the border and go home due to stepped-up border enforcement has soared from about 11 percent in 2005 to 58 percent in 2015. Roberts' version presented at the Cato Institute calculated the change from about 12 percent to nearly 70 percent.

DETAILED BORDER REPORT:  Why won't Department of Homeland Security release it?

The findings run counter to public perception, Roberts said. At the Cato presentation, Roberts noted a CNN/ORC 2015 survey that said the majority of Americans, 69 percent, believed illegal immigration had increased in the past few years.

“Think about that. That's amazing. That is a very untold part of what is happened at the border over the last decade,” Roberts said in the interview. The percent change in migrants giving up and going home after being caught "is incredible. That is a sea change in behavior in Mexican nationals who are trying to illegally enter."

What's more, the probability that an an illegal immigrant from Mexico will be caught by the Border Patrol has risen from about 36 percent in 2005 to about 54 percent in 2015, the DHS report estimates.

"All of those factors come together to produce deterrence, to produce the chance that someone even doesn't try to come to the border to cross illegally," Roberts said earlier.

Still, while an improvement, the 54 percent apprehension rate is far below the 80 percent interdiction rate put forth by the Border Patrol.

Pipeline of children: A border crisis

One evening in late September, migrants trickled in to the San Juan Bosco shelter in a quiet neighborhood about a mile south of the border in Nogales, Sonora. Some arrived on foot; others came in orange vans driven by Grupo Beta, Mexico's border force providing humanitarian assistance to migrants.

They filed in through a large open door into a chapel and took seats to wait for a tuna and macaroni dinner to be served and then for a chance to sleep in one of the rows of bunk beds lining a dormitory in back.

On that night, 61 men and four women registered at the shelter. Most had already been caught by the Border Patrol and sent back across the border to Mexico and were pondering whether to try again.

Five years ago, the shelter would have been packed with 150 to 200 migrants, said Francisco Loureiro, a 72-year-old businessman who has operated the shelter on the side with help from his family since 1982.

"Many people have stopped coming because it's a lot harder to cross, and they look for other areas," Loureiro said.

He estimated 80 percent of the migrants who came to the shelter used to eventually make it across the border, whether it took them one try or several. Now about 75 percent of them give up and go home, or stay in Nogales on the Mexico side and work, he said.

One of the reasons many migrants now give up is the cost.

In the past, smugglers charged about $1,500 to get a migrant across the border and to his or her final destination.

But because it's so much harder to get across without getting caught, smugglers now charge $6,000 or more, said Joanna Williams, director of education and advocacy at the Kino Border Initiative. The Catholic-sponsored organization operates a soup kitchen for deported migrants in Nogales, Sonora.

"I would say the biggest factor is less the enforcement and more the cost to cross," she said.

Another reason migrants give up is the rise in prosecutions.

A decade ago, migrants caught were rarely prosecuted with criminal offenses for crossing illegally. But since 2007, prosecutions of border crossers have soared under the Border Patrol's Streamline program, and now repeat border crossers often spend months in jail after being prosecuted for misdemeanor and felony charges of illegal entry and re-entry.

At the San Juan Bosco shelter, 38-year-old Sergio Castro Tomas said he was caught by the Border Patrol twice after attempting to enter illegally near Tijuana, south of San Diego. The first time, the Border Patrol sent him back to Tijuana. But the second time he was taken to Tucson and then spent two months in a jail in Florence.

Earlier that day, the Border Patrol had dropped him off at the border in Nogales and sent him back across to Mexico. He did not plan to try and cross a third time.

Instead, he planned to ask Mexican government officials for help buying a bus ticket for 3,000 pesos, or $155 dollars, so he could return to his family in San Pedro Jicayán, Jamiltepec, a town in the southern state of Oaxaca.

But Sanchez Valladares said he is willing to risk it again. He already had hired a new smuggler. He hasn't seen his four children since he was deported in 2008.

"I'm going to give it another try for my kids," he said.

If caught again, he knows what will happen: "I'll probably go to jail."

Experts agree that other factors besides the border buildup have played a role in the decrease in undocumented migrants from Mexico seeking jobs in the U.S.

Notable among those are fewer Mexican women having children, meaning fewer people are entering the workforce, and a stronger economy in Mexico, creating less incentive for workers to leave, Doris Meissner said.

Meissner was commissioner of the former Immigration and Naturalization Service under President Bill Clinton's administration and is now U.S. immigration policy program director at the Migration Policy Institute, a nonpartisan think tank in Washington, D.C.

But she acknowledged that "the investments the U.S has made in border enforcement" along with the strategies the Border Patrol has put into place to use those resources have had "very significant" results.

There is no question the border buildup has deterred illegal crossings on the southern border, confirmed by the report, said Jessica Vaughan, director of policy research at the Center for Immigration Studies, a think tank that pushes for less immigration and more enforcement.

But that doesn't mean there is no longer a problem with illegal immigration, or that some areas of the border are still easier to cross than others, Vaughan said.

She also cited the rise in recent years of migrants from Central America who cross illegally in the Rio Grande Valley of south Texas, now the busiest for illegal crossings on the southern border, and ongoing challenges with undocumented immigrants who overstayed visas.

"I agree that these are very positive trends," Vaughan said of the Cato version of the report.

"But that doesn’t mean we are actually controlling illegal immigration. The focus should be more on policy questions such as how to handle asylum seekers, and (I think) the best bang for the buck we could get on illegal immigration would be to shift the focus more on interior enforcement."

As U.S. Border Patrol agent John Lawson drove along the rust-colored border fence west of Nogales on the morning of Sept. 30, he saw another Border Patrol vehicle whiz by on a dirt road in the other direction.

Lawson did a U-turn and went to investigate. It turned out a ground sensor a couple miles to the west had detected a pair of border crossers who had jumped over the fence and were now headed into the United States on foot.

One of the Border Patrol agents climbed out of his truck and hiked into a ravine to search on foot. Soon several more agents arrived on horseback and began crisscrossing the rocky desert terrain looking for the two migrants.

Border Patrol agents in this area were once the busiest in the nation. But finding migrants has slowed dramatically, Lawson said. In fiscal year 2015, agents in the Tucson Sector, which includes Nogales, recorded 63,397 apprehensions. In 2005, agents in the sector recorded that many apprehensions in a single month, 64,096 that March, and 439,079 for the year.

"They are catching 30 or 40 people a day in Nogales," Lawson said. "It used to be they'd catch 30 or 40 people in half an hour."

Six hours later, around 4:30 that afternoon, Border Patrol agents from the Nogales station caught two migrants from Mexico hiking in the desert about 3¾ miles from the area they searched in the morning. Most likely they were the same ones since there was little traffic in the area that day, Lawson said.