It is likely that the healthcare system will be the first societal institution to collapse under the strain

Hospital and Healthcare Services
In the event of a major pandemic, healthcare services and especially hospital services will be rapidly overwhelmed. It is likely that the healthcare system will be the first societal institution to collapse under the strain, with recovery not expected until after the return of other essential utilities and services. It is true that the first victims of the flu will get excellent treatment, including hospitalization and even ventilators if required. Before long, though, all the available resources will become exhausted.
In order to reduce healthcare costs, hospitals have significantly reduced the number of available patient beds and nursing staff. In fact it is a common occurrence today for hospitals to be “on bypass” when it comes to accepting critically ill patients in their emergency rooms via ambulance. This happens when every ICU and CCU bed is already occupied in the hospital. During a routine flu season these days, the number of patients hospitalized in critical condition is such that all these critical care beds and available ventilators in many US cities are fully occupied for weeks each year. So you can imagine that if the number of critically ill patients presenting to the hospital emergency department with pulmonary failure from influenza suddenly increased exponentially over those expected with the seasonal flu, the chances of getting an ICU bed or ventilator would not be good. Once the pandemic settles in, the hospitals will be full, including waiting rooms and hallways. The medical staff will be sick themselves; some will be dead. The hospital will quickly run out of supplies such that there will be a shortage of everything from drugs, IV fluids, to body bags. So, in my opinion, it would be unwise to remain in the city so you can take advantage of the healthcare system in case you become ill.