The phrase "a dramatic escalation in" is correct and usable in written English.
It can be used to describe a significant increase or intensification in a particular situation or issue.
Example: "The report highlighted a dramatic escalation in cyberattacks over the past year."
Alternatives: "a significant rise in" or "a sharp increase in".
In recent months, the war between humans and seagulls has seen a dramatic escalation in violence.
"But it would lead to a dramatic escalation in the prevalence of Alzheimer's disease".
Veteran referees say they have seen a dramatic escalation in the last 10 years despite continuing efforts.
If Moscow had a hand in his death it would mark a dramatic escalation in the foreign reach of Russia's war on ter rorism.
Police and crime commissioners across England and Wales are dealing with a dramatic escalation in cases of reported child sexual exploitation.
The activist group Bahrain Watch reports "a dramatic escalation" in the use of birdshot and live ammunition by police against protesters over the past week.
The U.S. carried out a surprise military strike on a Syrian government airfield late Thursday in retaliation for a deadly chemical attack blamed on Syrian regime forces, winning cautious praise from its international allies and raising tensions with Russia in a dramatic escalation of American involvement in the six-year conflict.
"I think we've seen a dramatic escalation of activism in this last year," said Michael Zytkow, a member of Occupy Charlotte.
The military approach to combating drug trafficking, the report said, "has led to a dramatic escalation of homicides in Mexico since 2007, making it the second-most deadly armed conflict in the world in 2015".
The surge in U.S. forces was accompanied by a dramatic escalation of U.S. drone strikes in Pakistan one of which killed Pakistani Taliban leader Baitullah Mehsud.
Britain's top police officer has resigned and turned on the prime minister in a dramatic escalation of the phone-hacking scandal.
