NORTH TEXAS (CBSDFW.COM) — Dallas County has hit a grim milestone. More than 4,000 people have now died from COVID infections since the pandemic started. One new death reported on May 19 was in a vaccinated person with high-risk underlying health conditions.

Even the CDC warns that if you have a condition or are taking medications that weaken your immune system, you may not be fully protected even when you’ve been fully vaccinated.

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“Each of these individuals is a family member of someone, is a friend of someone,” said Dr. Julie Trivedi, the Medical Director of Infection Prevention at UT Southwestern Medical Center.

More than 10 million people in the United States have compromised immune systems. That includes organ transplant patients, and those with disorders like Crohn’s disease and Lupus. Dr. Trivedi said even though mask rules are relaxing, these patients and their families still need to take precautions.

“Masking is one of the most effective personal choices that we can make that will protect not only ourselves, but then even those around us,” Dr. Trivedi said. “So if someone is immunocompromised or elderly, they may benefit from wearing a mask so that they are exposed to less virus from those around them, and the individuals who are around these persons might also want to consider masking just to protect their family and loved ones.”

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In Dallas County there’ve been eight vaccine breakthrough deaths. We’re told one was a transplant recipient and the rest were either immunocompromised, on immunosuppressant medication, or had multiple underlying high-risk health conditions.

“It might take a greater number of doses,” said Dr. Robert Gottlieb with Baylor Scott and White Research Institute. “It might take additional factors to optimize that response.”

Dr. Gottlieb is leading several clinical trials at Baylor Scott and White Research Institute. Some of their patients are even taking part in a trial at Johns Hopkins looking into this issue.

In the meantime, he said the best defense is to get as many people vaccinated as possible.

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“It’s both individual protection, but it’s also protecting at the population level,” said Dr. Gottlieb. “To do that we really need to catch up to some of the other states that are ahead of us in that percentage of population that’s been vaccinated.”