The Western Trust have urged the public not to visit patients in any of their hospitals.
This appeal comes after growing concerns for the potential spread of the Coronavirus.
Yesterday, a spokesperson for the Western Trust stated: "We are taking necessary precautions to protect our patients and staff from COVID-19 (Coronavirus).
"We are asking the public not to visit patients in our hospitals and community facilities unless absolutely essential.
"In relation to outpatient appointments, we would ask where possible, that you attend your appointment on your own.
"Please practice good hand hygiene when attending your appointment and follow guidance on keeping yourself and others safe.
"We thank you for your support."
As of 2pm on Thursday 12 March testing has resulted in two new presumed positive cases bringing the total number of cases in Northern Ireland to 20.
Both cases are adults and both were secondary transmissions.
One case involved recent travel from Italy and the other can be traced to a previously reported case in the UK.
The Public Health Agency is currently undertaking contact tracing for both cases.
In Northern Ireland there have been 279 concluded tests, of which 259 were negative, and 20 were positive.
**Further updated story in Tuesday's Northern Constitution**