Does a doctor have more of a responsibility to local public health or global health?

INDIVIDUAL HEALTH. First and foremost, then family, friends, neighborhood, town, community, township, state, country, world.
Posiiton-dependent. A doctor caring for a patient has primary responsibility to that patient. For certain conditions, such as communicable dis, the condition is reportable to local health authorities, who may report it on or need to investigate further. Unusual conditions also need to be reported & may signal an outbreak or new disease. Health authorities have primary responsibility at the level they're employed.
Depends. Most doctors have local concerns and deal with these issues locally. A few are employed or assigned to deal with global health issues. There is little cross over although some pass from one category to another.