A flu shot that lasts for a decade could be a reality within two years, top hospital executive told CNBC in an interview, along with "real steps" toward a cancer vaccine.

In an interview with CNBC, Mount Sinai Health System CEO and President Kenneth Davis says scientists at Mount Sinai, in collaboration with other researchers, have a "universal flu vaccine" now in development with a company.

According to the Centers for Disease Control and Prevention this year's flu season is "shaping up to be a severe one." The CDC reports 43 states are suffering through "high or widespread" flu activity. Federal health officials are warning this year's flu strain is more virulent than in year's past, and does not match this year's virus.

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For his part, Davis says "some parts of the country are seeing six percent of doctor and ER visits for the flu." He added that the reason this year's flu vaccine is not as effective as in the past is because the virus has mutated.

"What we have a vaccine for is producing antibodies that are somewhat different than what this flu is. That happens." However, the universal flu vaccine in development is aimed at the part of the flu that doesn't actually adapt, he added.

"The ideal vaccine is directed at the stable part of the virus that doesn't change from year-to-year. "That's very hard to do."

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Davis says the progress is promising. "We would hope that in a couple of years we'll have a universal flu vaccine."

Davis also stated that progress was being made in the battle against cancer, where fatalities have fallen sharply as resources and brainpower are channeled at the problem. The American Cancer Society reports cancer deaths are down 22 percent over the past two decades.

Davis says while there's no equivalent of the polio vaccine for cancer, "we've made small steps, but they're all real steps" against the disease over that time.

Davis also told CNBC that promising strides are being made in enhancing the immune system to fight cancer. The trick is that cancer can often deceive an immune system, says Davis, so the body doesn't think the cancer cells are foreign.

"We're asking how our normal defense mechanisms can take out cancer cells," the CEO said. "Why can't they?"

Davis says because of advances in genomics and biology, there are drugs in the pipeline and already approved that can boost your own antibody system. He says the body's own cellular structure can identify cancer agents as foreign, and your immune system attacks them.

"We're getting a hold of the basic biology and pathophysiology of cancer." Davis says, "We understand it in better ways so we can produce drugs that are more focused, have less adverse effects, and are more effective."

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