It is also important to note that while Blue sharks are considered Near Threatened and not Vulnerable or Endangered, they have only been responsible for 13 total attacks world wide.
They are more likely to be responsible for attacks during air or sea disasters, such as the USS Indianapolis incident, than random beach attacks. That being said, species identification is often not recorded unless the shark is easy to identify or is caught during an attack.
On the south coast at Boca Chica there are always dried Nurse sharks for sale along the road to the public beach, so I would assume they are plentiful there. These are easy to identify but still have only been held responsible for 3 attacks worldwide and are fairly docile.
The fatal attack in 2010 at Boca Chica did not identify a species, so who knows? There is a thread about the brothers who hunt sharks and recently brought up a big Tiger at Santo Domingo, so there are large predatory sharks in DR waters.
Given the number of sharks vs the number of people that go into the water each year, they have a lot more reason to be afraid of us than vice versa. As an apex predator their removal from the eco-system would obviously have detrimental effects.