A Salvadoran father, right, carries his son while running next to another immigrant as they try to board a train heading to the Mexican-U.S. border, in Huehuetoca, near of Mexico City, June 1, 2015. Despite what Donald Trump says, immigrants from Mexico and Central America pose very little risk to Americans in terms of spreading disease. Reuters

Not only are Mexican immigrants wreaking criminal mayhem in America, they’re also unleashing their diseases on the country, according to real estate mogul and White House hopeful Donald Trump, who defended his recent explosive claims about immigrants being rapists and felons with more outrageous allegations, saying they pose a public health threat. In reality, the idea that immigrants pose such a threat is a notion as tenuous as Trump’s political prospects.

Immigrants from Mexico and Central America pose very little risk to U.S. residents in terms of spreading disease. Immunization rates for common infectious illnesses in Mexico and in other countries from which most U.S. immigrants originate are actually relatively high -- in some instances, Mexican and Central American immigrants are even better protected against diseases than Americans. While some immigrants crossing the U.S.-Mexico border are indeed ill, very rarely are there cases of swine flu, dengue fever or tuberculosis, as politicians have previously claimed.

That’s not to say the risk is zero. Some children who end up in U.S. detention centers, for instance, do test positive for tuberculosis, an upper respiratory disease for which treatments are available and effective. And outbreaks of chickenpox have at times plagued immigrant facilities. But it’s hardly the torrent of “tremendous infectious disease” Trump has made it out to be.

U.S. Immigration Statistics - General Overview | InsideGov

Immigrants tend to arrive in the U.S. tired, dehydrated and with injuries like twisted ankles, not dangerous diseases. The chance an unauthorized Mexican immigrant has been vaccinated against common infectious diseases is pretty high, given that Mexico has a relatively robust immunization program and healthy immunization rates. The country has a 99 percent vaccination rate for measles, which is actually higher than the U.S. rate of 92 percent. For other infectious diseases, the U.S. and Mexico have comparable immunization rates, according to the World Bank.

Of course, immigrants aren’t arriving in the U.S. only from Mexico. They’re also coming from Guatemala, Honduras and El Salvador, countries that also have high vaccination rates, around 93 percent -- still higher than in the U.S. (There are 113 countries that have higher immunization rates for some infectious diseases, including measles, than the U.S.)

A child from Guatemala is more likely to have been immunized for most infectious diseases than a young person from Texas, which, along with California, Florida, New York, New Jersey and Illinois, handles the bulk of new immigrants arriving in the U.S., both legally and illegally. Many children and adults coming into the U.S. actually carry their vaccination cards with them, according to NBC News. Anyone arriving in the U.S. legally is given a thorough health screening through a Department of Health and Human Services program and quarantined if there are any red flags.

Not that all immigrants coming into the U.S. are perfectly healthy. Immigrant detention centers have at times had to deal with flare-ups of diseases, including tuberculosis and chickenpox. However, the chickenpox vaccination is part of the U.S. immunization plan anyway, so there’s no risk to anyone who has already been vaccinated or exposed to it. And tuberculosis has long history in the U.S. In 2013, there were 9,500 cases of tuberculosis in the country, according to the Centers for Disease Control and Prevention.

Trump announced his presidential bid June 16. During his announcement speech in New York, Trump said if he were elected, he would “terminate” President Barack Obama’s executive order allowing undocumented immigrants to apply for work visas and claimed Mexico was “sending people [across the border] that have lots of problems, and they're bringing those problems with us. They're bringing drugs. They're bringing crime. They're rapists.”

The billionaire tycoon, who hopes to win the Republican nomination for the 2016 presidential race -- and is actually neck-and-neck with former Florida Gov. Jeb Bush as the party favorite among likely Republican voters -- later doubled down on his remarks about immigrants being rapists and criminals during an interview with CNN in early July. He again defended the comments in a statement Monday, and went one step further by accusing immigrants of being vectors of “tremendous infectious diseases.”

The remarks have been met with criticism from Trump’s opponents, his business partners and even his own party. Trump has lost several business deals because of the claims about Mexicans, including his partnerships with Macy’s department store, NBC, Serta and Nascar. Former Texas Gov. Rick Perry, also a 2016 presidential aspirant, said he was “offended” by Trump’s remarks.

“To paint with that broad a brush that Donald Trump did is -- I mean he's going to have to defend those remarks,” Perry said. “I never will. And I will stand up and say that those are offensive, which they were."

The idea that immigrants are bringing disease into the U.S. isn’t new. Politicians and political pundits, from U.S. Rep. Randy Weber, R-Texas, to conservative television personality Pat Buchanan and author and radio host Lou Dobbs, have often underscored the threat of disease to stigmatize foreigners and immigrants. Such claims have frequently been used to argue immigrant children and mothers should be sent back across the border or to boot out immigrants working legally. Health officials have denounced such claims as rooted in fear-mongering and political gain, not science.

When measles struck California earlier this year, some were quick to blame the outbreak on undocumented immigrants. Rep. Mo Brooks, R-Ala., said a “lot of the diseases” that enter the U.S. are “borne by [an] illegal alien,” and pinned the outbreak that sickened dozens across several states on immigrants.

The measles probably did start because of a virus brought to the U.S. from overseas, but not from Mexico. Health officials said it likely came from a foreign tourist visiting Southern California or from an American who returned with the virus after traveling abroad.

For the most part, there’s nothing coming across the border that U.S. health officials wouldn’t expect to encounter or with which they've never dealt. The most common diseases immigration health officials have encountered are the everyday cold and other respiratory infections, as well as certain stomach bugs and diarrheal conditions. Most health problems in immigration detention facilities have sprung from a lack of hand-washing, according to the Texas Department of State Health, not diseases immigrants brought with them.