Here is the May 16 update from ARS Guadeloupe:
There are no new cases on St Barth. Previously reported were a total of 6 cases, all 6 of whom have recovered. There are no longer any confirmed cases on St Barth.
There is 1 new case on St Martin, for a total of 40 cases, including 30 who have recovered , and 4 deceased (including 1 Sint Maarten resident). 1 patient is listed as hospitalized in Martinique, 1 patient is listed as hospitalized in Guadeloupe, 3 are listed as "repatriated", and 1 is listed as confined at home (+1).

The following text, translated by Google, was included with the above update:
[Covid 19] Coronavirus information
Health point of May 16, 2020
A new case in Saint-Martin with 40 cumulative cases of coronavirus confirmed by PCR test and 33 people declared cured by infectiologists.
This new case shows the persistence of sporadic cases on the territory continuing to call for the greatest vigilance even in this period of release from confinement. This patient is currently hospitalized in Guadeloupe. The contact investigation is underway.
In addition, a patient was hospitalized last night at the Saint-Martin hospital. He is a partially Dutch-diagnosed patient who was in segregation at home. He was therefore taken care of for another health problem.
Finally, two other patients have been hospitalized in the Covid unit of Marigot hospital and are awaiting results.
Since Monday, 180 PCR tests have been performed for a total of 501 tests.
No new cases in Saint-Barthélemy, with a total of 6 cumulative cases of coronavirus cases confirmed by PCR and 6 people declared cured by infectious diseases. A total of 97 PCR tests were performed.
Let us continue to be vigilant for the resumption of activities in the presence of the virus: respect the barrier measures so as not to favor new chains of contamination. The strategy to fight the epidemic to avoid a second wave is based on the following 5 actions:
Respect for barrier measures and recommendations for gradually resuming activities
Prescribing PCR tests when in doubt
Investigations of contact persons around a positive case
Isolation of COVID-19 sick people
Epidemiological monitoring of the epidemic
Let us not relax our efforts against Coronavirus but also dengue: containment, barrier measures, destruction of the breeding sites.
Let us continue to be vigilant for the resumption of activities in the presence of the virus: respect the barrier measures so as not to favor new chains of contamination.