The largest supplier of eggs in the U.S. has stopped production after chickens at one of its Texas plants tested positive for the highly contagious bird flu, the latest in an spike of the cases across the nation.

The CDC says that "the human health risk to the U.S. public from HPAI (highly pathogenic avian influenza) viruses is considered to be low," according to a news release from the egg supplier, Cal-Maine Foods, which added that "there is no known risk related to HPAI associated with eggs that are currently in the market and no eggs have been recalled."

The U.S. Department of Agriculture (USDA) explains that HPAI "cannot be transmitted through safely handled and properly cooked eggs."

But what does that mean exactly? And are over-easy or sunny side up eggs with runny yolk considered properly cooked? Are the risks associated with eating undercooked eggs more severe now? Social media is buzzing with questions.

Here's everything you need to know, according to experts.

The bird flu and 'properly cooked' eggs

"Safely handled and properly cooked eggs" takes on particular importance as concerns about bird flu grow, said Darin Detwiler, a food safety expert and associate teaching professor of food policy at Northeastern University. "While H5N1 primarily affects birds, the potential for transmission to humans exists, making it crucial to handle and cook eggs with care to minimize any risk of infection."

To safely handle eggs means to store them in a refrigerator at 40°F or colder as soon as you come home from the grocery store to prevent the growth of bacteria, Detwiler said. You also want to avoid using eggs that are cracked or dirty. And remember to wash your hands, utensils and surfaces with soap and water after they come into contact with raw eggs.

Learn more about bird flu:Bird flu outbreak raising concerns about spread. What you need to know.

The FDA also recommends keeping raw poultry and eggs separate from other foods to prevent cross-contamination.

"Properly cooked eggs" refers to eggs that are cooked to an internal temperature of 165˚F, the CDC says, which is likely to kill disease-causing germs. In other words, over-easy and sunny side up eggs with runny yolk are not considered "properly cooked," said Wade Syers, a food safety specialist with Michigan State University Extension.

In typical scenarios without bird flu outbreaks to consider, the USDA says that "everyone is advised against eating raw or undercooked egg yolks, whites or products containing them" — namely to avoid food poisoning caused by the bacteria salmonella, which can linger inside eggs and on outer shells.

The FDA says to cook eggs until both the yolk and the white are firm; and if you're planning on consuming "raw or undercooked" eggs, make sure they have been pasteurized, meaning they have been rapidly heated and held at a minimum required temperature for a specified time to destroy bacteria.

Are runny eggs safe to eat amid the bird flu outbreak in Texas?

Even though Cal-Maine Foods said you shouldn't be concerned about eating contaminated eggs at this time, considering its the largest supplier of eggs in the U.S., experts advise caution.

"On one hand, I would say that everyone should always be cautious about food safety and not eat runny eggs," Detwiler said. But "right now, consumers should definitely be concerned about reputable sources for their food and about proper cooking, handling, refrigeration, etc."

Detwiler concluded: "In the case of avian flu concerns, eggs should be cooked until both the white and yolk are firm," which will "provide an additional layer of safety."

People at higher risk of foodborne illness such as infants, young children, older adults, pregnant women and those with weakened immune systems, should be especially careful with runny eggs at this time, said Syers, who agrees that runny eggs should be avoided.

That said, the FDA says that the "likelihood that eggs from infected poultry are found in the retail market is low" because "of the rapid onset of symptoms in poultry as well as the safeguards in place, which include testing of flocks and federal inspection programs." And when you properly prepare and store your eggs, the risk is even lower, the FDA says.

Natalie Neysa Alund contributed to this report.