It would seem not. This is what the Forein & Commonwealth Office say on their web site:
"We strongly recommend that you obtain comprehensive travel and medical insurance before travelling.
There have been occasional outbreaks of malaria mainly in the border areas with Haiti, but recently there have been press reports of isolated cases in the slums around Santo Domingo. The number of cases is very small but visitors are nevertheless advised to seek advice from their GP before departure from the UK.
There is also a year round threat from dengue fever which is contracted from mosquitoes that bite during the daytime, with the highest number of cases usually reported in the hot season from May to November. It is advisable to use anti‑mosquito skin repellents, which are readily available locally.
Rabies exists in the Dominican Republic and so it is always sensible to steer clear of stray dogs and cats.
To reduce the likelihood of contracting gastro‑intestinal viruses, you should not drink tap water nor should you buy food from street vendors.
You should ensure that you have up‑to‑date immunisations and are advised to contact your GP for information prior to departure.
You should be aware of the high prevalence of the HIV/AIDS virus in the Dominican Republic and should take precautions to avoid exposure to it.
For further information on health, check the Dept of Health's website at: www.dh.gov.uk."